return [ rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 87)( 34, 60)
        ( 35, 91)( 38, 43)( 39, 72)( 41, 47)( 42, 73)( 45, 76)( 46, 99)( 49, 55)( 50, 62)( 51, 77)( 53, 59)( 54, 96)
        ( 57, 80)( 58,103)( 61, 67)( 63, 95)( 65, 71)( 66, 78)( 69, 75)( 70,101)( 74,102)( 79,100)( 81, 86)( 82,107)
        ( 84, 90)( 85,112)( 88, 94)( 89,114)( 92, 98)( 93,118)( 97,106)(104,110)(105,119)(108,111)(109,122)(113,117)
        (115,121)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 27)(  7, 16)(  9, 20)( 10, 31)( 13, 19)( 14, 43)( 15, 21)
        ( 17, 24)( 18, 47)( 22, 39)( 23, 35)( 25, 30)( 26, 48)( 28, 34)( 29, 56)( 32, 38)( 33, 59)( 36, 51)( 37, 63)
        ( 40, 46)( 41, 75)( 42, 52)( 44, 50)( 45, 79)( 49, 55)( 53, 71)( 54, 67)( 57, 62)( 58, 80)( 60, 66)( 61, 88)
        ( 64, 70)( 65, 91)( 68, 83)( 69, 95)( 72, 78)( 73,106)( 74, 84)( 76, 82)( 77,110)( 81, 87)( 85,102)( 86, 99)
        ( 89, 94)( 90,111)( 92, 98)( 93,119)( 96,101)( 97,117)(100,114)(103,109)(104,122)(105,115)(107,113)(108,123)
        (112,118)(116,120)(121,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 80)
        ( 38, 43)( 39, 61)( 41, 64)( 42, 89)( 45, 51)( 46, 94)( 47, 65)( 49, 55)( 50, 98)( 53, 68)( 54,102)( 57, 63)
        ( 58, 92)( 59, 84)( 62, 88)( 66, 85)( 67, 91)( 69, 75)( 70,114)( 71,106)( 73, 79)( 74,115)( 77, 83)( 78,112)
        ( 81, 87)( 82,117)( 86, 97)( 90, 93)( 95,101)( 96,118)( 99,105)(100,121)(103,109)(104,122)(107,110)(108,123)
        (111,116)(113,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 74)( 27, 55)( 29, 35)( 30, 78)( 33, 59)( 34, 82)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 91)( 44, 67)( 45, 92)( 48, 54)( 49, 97)( 50, 68)( 52, 58)( 53,101)( 56, 71)
        ( 57,105)( 60, 66)( 61, 95)( 62, 86)( 65, 90)( 69, 87)( 70, 94)( 72, 77)( 73,109)( 75, 81)( 76,114)( 79, 85)
        ( 80,115)( 83, 89)( 84,117)( 88,100)( 93, 96)( 98,104)( 99,118)(102,108)(103,121)(106,112)(107,122)(110,113)
        (111,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 43)( 26, 32)( 27, 80)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 86)( 38, 42)( 39, 71)( 41, 46)( 44, 75)( 45, 72)( 48, 54)( 49,101)( 50, 76)( 52, 58)( 53,105)( 56, 79)
        ( 57,109)( 60, 66)( 61, 99)( 62, 90)( 64, 70)( 65,117)( 68, 74)( 69,118)( 73, 96)( 77, 97)( 78, 94)( 81, 85)
        ( 82,113)( 84, 89)( 87, 93)( 88,114)( 91,103)( 92,121)( 95,119)( 98,104)(100,120)(102,108)(106,112)(107,122)
        (110,116)(111,123)(115,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 77)( 28, 53)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 68)( 42, 72)( 43, 92)( 46, 52)( 47,101)( 48, 73)( 50, 56)( 51,105)( 54, 76)( 55,109)
        ( 58, 64)( 59, 99)( 60, 87)( 62, 67)( 63,117)( 66, 71)( 69, 91)( 70,118)( 74, 97)( 75, 94)( 78, 82)( 79,113)
        ( 81, 86)( 84, 90)( 85,114)( 88,103)( 89,121)( 93, 96)( 95,119)( 98,104)(100,120)(102,108)(106,112)(107,122)
        (110,116)(111,123)(115,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 47)( 24, 43)( 26, 31)( 27, 34)( 28, 55)( 30, 35)( 33, 59)( 37, 42)
        ( 38, 71)( 40, 46)( 41, 79)( 44, 74)( 45, 82)( 48, 54)( 49, 93)( 50, 75)( 52, 58)( 53, 97)( 56, 62)( 57,101)
        ( 60, 66)( 61,105)( 64, 70)( 65,109)( 68, 73)( 69,113)( 72, 78)( 76, 90)( 77, 86)( 80, 85)( 81,114)( 83, 89)
        ( 84,115)( 87,117)( 88,111)( 91, 96)( 92,118)( 94,100)( 95,122)( 98,104)( 99,123)(102,108)(103,124)(106,112)
        (107,120)(110,116)(119,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 47)( 24, 43)( 26, 31)( 27, 34)( 28, 55)( 30, 35)( 33, 59)( 37, 42)
        ( 38, 71)( 40, 46)( 41, 80)( 44, 75)( 45, 82)( 48, 54)( 49, 94)( 50, 76)( 52, 58)( 53, 97)( 56, 62)( 57,101)
        ( 60, 66)( 61,105)( 64, 70)( 65,109)( 68, 74)( 69,113)( 72, 79)( 73,114)( 77, 90)( 78, 86)( 81, 85)( 83, 89)
        ( 84,115)( 87,117)( 88,111)( 91, 96)( 92,122)( 93,118)( 95,100)( 98,104)( 99,123)(102,108)(103,124)(106,112)
        (107,120)(110,116)(119,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 34)( 28, 56)( 30, 35)( 33, 60)( 37, 43)
        ( 38, 80)( 39, 69)( 41, 47)( 42, 83)( 45, 72)( 46, 86)( 49, 55)( 50, 98)( 51, 73)( 53, 59)( 54,102)( 57, 63)
        ( 58,105)( 61, 67)( 62,109)( 65, 71)( 66,113)( 70, 76)( 74, 94)( 75, 90)( 77, 82)( 78, 88)( 79,114)( 81, 85)
        ( 84, 89)( 87, 93)( 91,117)( 92,115)( 95,101)( 96,122)( 97,118)( 99,104)(100,123)(103,108)(106,112)(107,124)
        (110,116)(111,120)(119,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 39)( 23, 35)( 26, 51)( 27, 47)( 29, 34)( 30, 63)( 32, 38)( 33, 75)( 36, 66)
        ( 37, 78)( 40, 46)( 41, 90)( 42, 67)( 44, 50)( 45, 94)( 48, 70)( 49, 97)( 52, 58)( 53,109)( 54, 71)( 56, 62)
        ( 57,113)( 60, 65)( 61,114)( 64, 74)( 68, 86)( 69, 82)( 72,105)( 73,101)( 76, 81)( 77,115)( 79, 85)( 80,111)
        ( 83,117)( 84,107)( 87, 93)( 88,122)( 89,118)( 91, 96)( 92,123)( 95,100)( 98,104)( 99,124)(102,108)(103,120)
        (106,112)(110,116)(119,121),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 73)( 33, 56)( 34, 76)
        ( 38, 43)( 39, 64)( 41, 68)( 42, 85)( 45, 51)( 46, 95)( 47, 69)( 49, 55)( 50, 99)( 53, 72)( 54,100)( 57, 63)
        ( 58,111)( 59, 80)( 62, 67)( 65, 84)( 66,112)( 70, 91)( 71, 87)( 74, 79)( 75,103)( 77, 83)( 78,116)( 81,107)
        ( 82,118)( 86, 90)( 88,109)( 89,113)( 92, 98)( 93,119)( 94,110)( 96,102)( 97,122)(101,106)(104,115)(105,123)
        (108,114)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 61)( 23, 44)( 24, 41)( 26, 32)( 27, 76)( 28, 52)( 31, 56)( 34, 40)( 35, 84)
        ( 36, 64)( 38, 43)( 39, 88)( 42, 68)( 45, 51)( 46, 95)( 47, 69)( 49, 55)( 50, 99)( 53, 72)( 54,100)( 57, 63)
        ( 58,107)( 59, 77)( 62, 67)( 65, 80)( 66,108)( 70, 91)( 71, 89)( 73, 79)( 74,114)( 75,101)( 78,103)( 81, 87)
        ( 82,121)( 83,111)( 85, 90)( 86, 94)( 92, 98)( 93,122)( 96,102)( 97,117)(104,110)(105,120)(106,115)(109,113)
        (112,118)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 29)( 18, 32)( 19, 60)( 23, 40)( 25, 31)( 26, 68)( 27, 48)( 30, 52)( 33, 39)( 34, 76)( 35, 61)
        ( 37, 43)( 38, 80)( 41, 47)( 42, 83)( 45, 51)( 46, 87)( 49, 64)( 50, 91)( 53, 59)( 54, 99)( 55, 69)( 57, 63)
        ( 58,102)( 62, 72)( 65, 71)( 66,110)( 67, 92)( 70, 95)( 73, 79)( 74,117)( 75,103)( 77, 82)( 78,121)( 81, 86)
        ( 84, 90)( 85,122)( 88, 94)( 89,109)( 93,106)( 96,101)( 97,116)( 98,111)(100,105)(104,114)(107,113)(108,123)
        (112,119)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 30)( 18, 33)( 19, 60)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 50)( 31, 53)( 34, 40)( 35, 83)
        ( 36, 64)( 38, 44)( 39, 87)( 42, 68)( 43, 90)( 46, 52)( 47, 98)( 48, 69)( 51, 72)( 54, 59)( 55,105)( 56, 77)
        ( 58, 63)( 61, 67)( 62,106)( 65, 80)( 66,109)( 70, 94)( 71, 91)( 73, 79)( 74,121)( 75, 99)( 78,101)( 81, 86)
        ( 82,113)( 84, 89)( 85,120)( 88, 93)( 92,117)( 95,100)( 96,124)( 97,118)(102,108)(103,111)(104,122)(107,112)
        (110,116)(114,119)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 29)( 17, 32)( 18, 56)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 45)( 30, 48)( 33, 39)( 34, 77)( 35, 60)
        ( 37, 43)( 38, 80)( 41, 64)( 42, 83)( 46, 68)( 47, 65)( 49, 55)( 50, 99)( 51, 73)( 53, 59)( 54,102)( 57, 63)
        ( 58,105)( 61, 76)( 62,109)( 66, 91)( 67, 87)( 69, 75)( 70,121)( 71, 92)( 74, 95)( 78, 82)( 79,113)( 81, 86)
        ( 84, 90)( 85,114)( 88, 94)( 89,120)( 93,117)( 96,101)( 97,107)( 98,122)(100,104)(103,108)(106,112)(110,116)
        (111,123)(115,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 25)(  7, 16)(  9, 20)( 10, 28)( 13, 19)( 14, 40)( 15, 21)
        ( 17, 24)( 18, 44)( 22, 36)( 23, 32)( 26, 31)( 27, 48)( 29, 35)( 30, 57)( 33, 52)( 34, 60)( 37, 43)( 38, 72)
        ( 39, 53)( 41, 47)( 42, 76)( 45, 51)( 46, 77)( 49, 56)( 50, 80)( 54, 68)( 55, 64)( 58, 63)( 59, 84)( 61, 67)
        ( 62, 93)( 65, 88)( 66, 96)( 69, 75)( 70,106)( 71, 89)( 73, 79)( 74,110)( 78, 83)( 81, 87)( 82,111)( 85, 92)
        ( 86,114)( 90,103)( 91,100)( 94, 99)( 95,117)( 97,102)( 98,124)(101,121)(104,109)(105,122)(107,113)(108,119)
        (112,116)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 25)(  7, 16)(  9, 20)( 10, 28)( 13, 19)( 14, 40)( 15, 21)
        ( 17, 24)( 18, 44)( 22, 36)( 23, 32)( 26, 31)( 27, 48)( 29, 35)( 30, 57)( 33, 52)( 34, 60)( 37, 43)( 38, 72)
        ( 39, 53)( 41, 47)( 42, 76)( 45, 51)( 46, 80)( 49, 56)( 50, 81)( 54, 68)( 55, 64)( 58, 63)( 59, 84)( 61, 67)
        ( 62, 93)( 65, 88)( 66, 96)( 69, 75)( 70,106)( 71, 89)( 73, 79)( 74,110)( 77, 83)( 78,113)( 82, 87)( 85, 92)
        ( 86,114)( 90,103)( 91,100)( 94, 99)( 95,117)( 97,102)( 98,124)(101,121)(104,109)(105,122)(107,112)(108,119)
        (111,116)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 36)(  8, 17)( 10, 21)( 11, 40)( 14, 20)( 15, 52)
        ( 16, 29)( 18, 32)( 19, 56)( 22, 28)( 23, 68)( 24, 44)( 26, 31)( 27, 72)( 30, 48)( 33, 39)( 34, 80)( 35, 60)
        ( 37, 43)( 38, 84)( 41, 47)( 42, 88)( 45, 64)( 46, 92)( 49, 55)( 50, 99)( 51, 73)( 53, 59)( 54,103)( 57, 63)
        ( 58,107)( 61, 76)( 62,110)( 65, 71)( 66,117)( 67, 93)( 69, 75)( 70,121)( 74, 95)( 77, 83)( 78, 97)( 79,114)
        ( 81, 87)( 82,123)( 85, 91)( 86,119)( 89, 94)( 90,120)( 96,102)( 98,122)(100,106)(101,115)(104,109)(105,112)
        (108,113)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 66)( 23, 48)( 24, 44)( 26, 31)( 27, 82)( 28, 55)( 30, 35)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 70)( 41, 47)( 42, 98)( 45, 74)( 46,102)( 49, 54)( 50, 57)( 51, 75)( 53, 58)( 56, 78)
        ( 60, 65)( 61,110)( 62, 86)( 64, 69)( 67, 73)( 68,111)( 71, 90)( 72,114)( 76, 81)( 77,103)( 79, 85)( 80,118)
        ( 84, 89)( 87,106)( 88,119)( 91, 97)( 92,108)( 93,115)( 95,101)( 96,122)( 99,105)(100,123)(104,117)(107,113)
        (109,121)(112,116)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 66)( 23, 48)( 24, 44)( 26, 32)( 27, 82)( 28, 55)( 30, 35)( 31, 86)( 34, 59)
        ( 37, 43)( 38, 94)( 39, 70)( 41, 47)( 42, 98)( 45, 74)( 46,102)( 49, 54)( 50, 57)( 51, 75)( 53, 58)( 56, 78)
        ( 60, 65)( 61,110)( 62, 87)( 64, 69)( 67, 73)( 68,111)( 71, 90)( 72,114)( 76, 81)( 77,103)( 79, 85)( 80,118)
        ( 83, 89)( 84,121)( 88,106)( 91, 97)( 92,108)( 93,115)( 95,101)( 96,123)( 99,105)(100,120)(104,117)(107,113)
        (109,122)(112,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 79)( 28, 52)( 30, 35)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 68)( 41, 47)( 42, 95)( 45, 71)( 46, 99)( 50, 55)( 51, 72)( 53, 75)( 54, 73)( 57, 63)
        ( 58,110)( 59, 83)( 61, 67)( 62,111)( 65, 70)( 66,114)( 69, 87)( 74,103)( 76, 82)( 77,117)( 78,104)( 81, 86)
        ( 84,106)( 85,118)( 88, 94)( 89,108)( 90,115)( 92, 98)( 93,122)( 96,102)( 97,123)(100,105)(101,120)(107,113)
        (109,121)(112,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 52)( 30, 35)( 31, 83)( 34, 56)
        ( 37, 43)( 38, 91)( 39, 68)( 41, 47)( 42, 95)( 45, 71)( 46, 99)( 50, 55)( 51, 72)( 53, 75)( 54, 73)( 57, 63)
        ( 58,110)( 59, 84)( 61, 67)( 62,111)( 65, 70)( 66,114)( 69, 87)( 74,103)( 76, 82)( 77,117)( 78,104)( 80, 86)
        ( 81,121)( 85,106)( 88, 94)( 89,108)( 90,115)( 92, 98)( 93,123)( 96,102)( 97,119)(100,105)(101,120)(107,113)
        (109,122)(112,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 78)( 28, 55)( 30, 35)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 70)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 54)( 50,102)( 53, 58)( 56, 74)( 57,103)
        ( 60, 66)( 61,110)( 62, 82)( 64, 69)( 65,113)( 68, 73)( 71, 86)( 72,114)( 75, 81)( 76,117)( 77,104)( 80, 85)
        ( 83,106)( 84,118)( 87, 93)( 88,108)( 89,115)( 91, 97)( 92,122)( 95,101)( 96,123)( 99,105)(100,120)(107,112)
        (109,121)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 55)( 30, 35)( 31, 82)( 34, 59)
        ( 37, 43)( 38, 90)( 39, 70)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 54)( 50,102)( 53, 58)( 56, 74)( 57,103)
        ( 60, 66)( 61,110)( 62, 83)( 64, 69)( 65,113)( 68, 73)( 71, 86)( 72,114)( 75, 81)( 76,117)( 77,104)( 79, 85)
        ( 80,121)( 84,106)( 87, 93)( 88,108)( 89,115)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,105)(100,120)(107,112)
        (109,122)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 78)( 28, 52)( 30, 35)( 33, 56)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 68)( 41, 47)( 42, 94)( 45, 71)( 46, 98)( 50, 55)( 51, 72)( 53, 74)( 54,103)( 57, 63)
        ( 58,110)( 59, 82)( 61, 67)( 62,113)( 65, 70)( 66,114)( 69, 86)( 73,102)( 75, 81)( 76,117)( 77,104)( 80, 85)
        ( 83,106)( 84,118)( 87, 93)( 88,108)( 89,115)( 91, 97)( 92,122)( 95,101)( 96,123)( 99,105)(100,120)(107,112)
        (109,121)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 52)( 30, 35)( 31, 82)( 34, 56)
        ( 37, 43)( 38, 90)( 39, 68)( 41, 47)( 42, 94)( 45, 71)( 46, 98)( 50, 55)( 51, 72)( 53, 74)( 54,103)( 57, 63)
        ( 58,110)( 59, 83)( 61, 67)( 62,113)( 65, 70)( 66,114)( 69, 86)( 73,102)( 75, 81)( 76,117)( 77,104)( 79, 85)
        ( 80,121)( 84,106)( 87, 93)( 88,108)( 89,115)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,105)(100,120)(107,112)
        (109,122)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 78)( 28, 56)( 30, 35)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 70)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 55)( 50,102)( 53, 58)( 54,103)( 57, 74)
        ( 60, 66)( 61,110)( 62, 82)( 64, 69)( 65,114)( 68, 73)( 71, 86)( 72,115)( 75, 81)( 76,117)( 77,104)( 80, 85)
        ( 83,106)( 84,118)( 87, 93)( 88,108)( 89,112)( 91, 97)( 92,122)( 95,101)( 96,123)( 99,105)(100,120)(107,113)
        (109,121)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 56)( 30, 35)( 31, 82)( 34, 59)
        ( 37, 43)( 38, 90)( 39, 70)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 55)( 50,102)( 53, 58)( 54,103)( 57, 74)
        ( 60, 66)( 61,110)( 62, 83)( 64, 69)( 65,114)( 68, 73)( 71, 86)( 72,115)( 75, 81)( 76,117)( 77,104)( 79, 85)
        ( 80,121)( 84,106)( 87, 93)( 88,108)( 89,112)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,105)(100,120)(107,113)
        (109,122)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 79)( 28, 53)( 30, 35)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 90)( 39, 68)( 41, 47)( 42, 94)( 45, 72)( 46, 98)( 49, 55)( 50,103)( 51, 73)( 54, 75)( 57, 63)
        ( 58,110)( 59, 83)( 61, 67)( 62,114)( 65, 71)( 66,115)( 69, 87)( 70,112)( 74,102)( 76, 82)( 77,117)( 78,104)
        ( 81, 86)( 84,106)( 85,118)( 88, 93)( 89,108)( 91, 97)( 92,122)( 95,101)( 96,123)( 99,105)(100,120)(107,113)
        (109,121)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 53)( 30, 35)( 31, 83)( 34, 56)
        ( 37, 43)( 38, 90)( 39, 68)( 41, 47)( 42, 94)( 45, 72)( 46, 98)( 49, 55)( 50,103)( 51, 73)( 54, 75)( 57, 63)
        ( 58,110)( 59, 84)( 61, 67)( 62,114)( 65, 71)( 66,115)( 69, 87)( 70,112)( 74,102)( 76, 82)( 77,117)( 78,104)
        ( 80, 86)( 81,121)( 85,106)( 88, 93)( 89,108)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,105)(100,120)(107,113)
        (109,122)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 43)( 24, 40)( 26, 31)( 27, 79)( 28, 51)( 30, 35)( 33, 55)( 34, 80)
        ( 38, 42)( 39, 67)( 41, 71)( 44, 50)( 45, 91)( 46, 72)( 48, 54)( 49, 95)( 52, 75)( 53, 96)( 56, 62)( 57,103)
        ( 58, 83)( 60, 66)( 61,106)( 64, 70)( 65,109)( 68, 74)( 69,113)( 73, 87)( 76, 82)( 77,117)( 78, 97)( 81, 86)
        ( 84, 99)( 85,118)( 88, 94)( 89,123)( 90,114)( 92, 98)( 93,120)(100,105)(101,111)(102,121)(104,108)(107,112)
        (110,116)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 31)( 18, 35)( 19, 62)( 23, 43)( 25, 30)( 26, 74)( 27, 51)( 29, 34)( 32, 55)( 33, 75)( 36, 42)
        ( 37, 86)( 38, 66)( 40, 46)( 41, 87)( 44, 50)( 45, 90)( 48, 54)( 49, 94)( 52, 70)( 53, 98)( 56, 61)( 57,106)
        ( 58, 78)( 60, 65)( 63, 69)( 64,107)( 67, 82)( 68,104)( 71, 77)( 72,117)( 73, 99)( 76, 81)( 79,102)( 80,118)
        ( 83, 89)( 84,122)( 85,109)( 88, 93)( 91, 97)( 92,123)( 95,101)( 96,116)(100,113)(103,108)(105,112)(110,121)
        (111,119)(114,120)(115,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 12)(  7, 35)(  8, 17)( 10, 20)( 11, 39)( 14, 19)( 15, 34)
        ( 16, 28)( 18, 31)( 21, 27)( 22, 55)( 23, 43)( 25, 30)( 26, 59)( 29, 47)( 32, 38)( 33, 48)( 36, 42)( 37, 63)
        ( 40, 46)( 41, 67)( 44, 51)( 45, 71)( 49, 66)( 50, 60)( 52, 58)( 53, 87)( 54, 75)( 56, 62)( 57, 91)( 61, 79)
        ( 64, 70)( 65, 80)( 68, 74)( 69, 95)( 72, 78)( 73, 99)( 76, 83)( 77,103)( 81, 98)( 82, 92)( 84, 90)( 85,118)
        ( 86,107)( 88, 94)( 89,119)( 93,110)( 96,102)( 97,111)(100,106)(101,122)(104,109)(105,117)(108,114)(112,124)
        (113,120)(115,121)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 41)( 16, 32)( 18, 36)( 22, 43)( 23, 39)( 25, 31)( 26, 62)( 27, 51)( 29, 35)( 30, 66)( 33, 55)( 34, 70)
        ( 38, 42)( 40, 56)( 44, 50)( 45, 71)( 46, 57)( 48, 54)( 49, 74)( 52, 58)( 53, 78)( 59, 65)( 60, 90)( 61, 82)
        ( 63, 69)( 64, 94)( 67, 73)( 68, 98)( 72, 77)( 75, 81)( 76, 99)( 79, 85)( 80,102)( 83, 86)( 84,106)( 87, 93)
        ( 88,115)( 89,110)( 91, 97)( 92,117)( 95,101)( 96,121)(100,105)(103,109)(104,122)(107,113)(108,123)(111,114)
        (112,119)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 46)( 12, 21)( 14, 19)
        ( 15, 41)( 16, 32)( 18, 36)( 22, 43)( 23, 39)( 25, 31)( 26, 62)( 27, 50)( 29, 35)( 30, 66)( 33, 54)( 34, 70)
        ( 38, 42)( 40, 55)( 44, 49)( 45, 56)( 47, 53)( 48, 75)( 51, 58)( 52, 78)( 57, 74)( 59, 65)( 60, 90)( 61, 82)
        ( 63, 69)( 64, 94)( 67, 73)( 68, 98)( 71, 77)( 72,102)( 76, 81)( 79, 85)( 80,103)( 83, 86)( 84,106)( 87, 93)
        ( 88,115)( 89,110)( 91, 97)( 92,117)( 95,101)( 96,121)( 99,105)(100,122)(104,109)(107,113)(108,123)(111,114)
        (112,119)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 37)(  8, 17)( 10, 21)( 11, 41)( 14, 20)( 15, 53)
        ( 16, 29)( 18, 33)( 19, 57)( 22, 28)( 23, 69)( 24, 45)( 26, 32)( 27, 72)( 30, 49)( 31, 76)( 34, 40)( 35, 87)
        ( 36, 61)( 38, 44)( 39, 91)( 42, 48)( 43, 95)( 46, 65)( 47, 99)( 50, 56)( 51,106)( 52, 80)( 54, 60)( 55,110)
        ( 58, 64)( 59,111)( 62, 83)( 63,114)( 66, 71)( 67,117)( 68,100)( 70, 75)( 73, 79)( 74,118)( 77, 82)( 78,121)
        ( 81,102)( 84, 90)( 85,108)( 86,115)( 88, 94)( 89,104)( 92, 98)( 93,123)( 96,101)( 97,120)(103,109)(105,122)
        (107,113)(112,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 73)( 28, 54)( 30, 36)( 31, 76)( 34, 57)
        ( 35, 80)( 38, 44)( 39, 91)( 40, 66)( 42, 48)( 43, 95)( 46, 52)( 47, 99)( 50, 56)( 51,103)( 55, 69)( 58, 64)
        ( 59,110)( 60, 84)( 62, 68)( 63,114)( 67, 87)( 70, 75)( 71,117)( 72,104)( 74, 79)( 77, 83)( 78,118)( 81, 86)
        ( 82,121)( 85,106)( 88, 94)( 89,112)( 90,115)( 92, 98)( 93,108)( 96,102)( 97,123)(100,105)(101,120)(107,113)
        (109,122)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 56)( 30, 36)( 31, 79)( 34, 60)
        ( 35, 83)( 38, 44)( 39, 93)( 40, 69)( 42, 48)( 43, 97)( 46, 52)( 47,101)( 50, 55)( 51,105)( 54, 59)( 57, 72)
        ( 58,106)( 61, 67)( 62,113)( 63, 87)( 65, 71)( 66,114)( 70, 90)( 73, 78)( 74,117)( 75,107)( 77, 82)( 80, 86)
        ( 81,118)( 84, 89)( 85,121)( 88,109)( 91, 96)( 92,115)( 94,100)( 95,111)( 98,104)( 99,123)(102,108)(103,120)
        (110,116)(112,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 56)( 30, 36)( 31, 79)( 34, 60)
        ( 35, 83)( 38, 44)( 39, 94)( 40, 69)( 42, 48)( 43, 98)( 46, 52)( 47,102)( 50, 55)( 51,106)( 54, 59)( 57, 72)
        ( 58,107)( 61, 67)( 62,114)( 63, 87)( 65, 71)( 66, 93)( 70, 90)( 73, 78)( 74,117)( 75,108)( 77, 82)( 80, 86)
        ( 81,118)( 84, 89)( 85,121)( 88,110)( 91, 97)( 92,115)( 95,101)( 96,112)( 99,105)(100,123)(103,109)(104,120)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 57)( 30, 36)( 31, 79)( 34, 60)
        ( 35, 83)( 38, 44)( 39, 94)( 40, 69)( 42, 48)( 43, 98)( 46, 52)( 47,102)( 50, 56)( 51,106)( 54, 59)( 55,107)
        ( 58, 72)( 61, 67)( 62,114)( 63, 87)( 65, 71)( 66, 93)( 70, 90)( 73, 78)( 74,117)( 75,108)( 77, 82)( 80, 86)
        ( 81,118)( 84, 89)( 85,121)( 88,110)( 91, 97)( 92,115)( 95,101)( 96,112)( 99,105)(100,123)(103,109)(104,120)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 42)( 26, 32)( 27, 76)( 28, 52)( 30, 36)( 31, 80)( 34, 56)
        ( 35, 84)( 38, 43)( 39, 47)( 40, 68)( 45, 51)( 46, 93)( 49, 55)( 50, 96)( 53, 72)( 54,100)( 57, 63)( 58,107)
        ( 59, 88)( 61, 67)( 62,111)( 65, 71)( 66,112)( 69, 92)( 70,109)( 73, 79)( 74,114)( 75,101)( 77, 83)( 78,118)
        ( 81, 87)( 82,122)( 85, 91)( 86,123)( 89,103)( 90,120)( 94, 99)( 95,105)( 97,102)( 98,117)(104,110)(106,116)
        (108,113)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 45)( 24, 42)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 38, 44)( 39, 95)( 40, 65)( 43, 68)( 46, 52)( 47, 99)( 48, 69)( 50, 56)( 51,103)( 54, 71)( 55,107)
        ( 58, 64)( 59, 94)( 60, 87)( 63, 67)( 66, 91)( 70, 96)( 72, 78)( 73,114)( 74,108)( 76, 82)( 77,118)( 80, 86)
        ( 81,122)( 84, 90)( 85,123)( 88,110)( 89,120)( 92, 98)( 93,111)( 97,102)(100,106)(101,112)(104,109)(105,117)
        (113,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 84)( 28, 56)( 30, 36)( 31, 88)( 34, 60)
        ( 35, 92)( 38, 44)( 39,104)( 40, 72)( 42, 48)( 43,108)( 46, 76)( 47, 83)( 50, 55)( 51, 77)( 53, 59)( 54, 78)
        ( 57, 80)( 58, 79)( 61, 67)( 62,102)( 63, 96)( 65, 71)( 66,112)( 69, 75)( 70,115)( 73,100)( 74,116)( 81, 87)
        ( 82,109)( 85, 91)( 86,118)( 89, 95)( 90,122)( 93, 99)( 94,123)( 97,106)( 98,120)(101,107)(103,114)(105,111)
        (110,121)(113,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 55)( 29, 35)( 30, 79)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 64)( 41, 47)( 42, 98)( 45, 67)( 46,102)( 49, 54)( 50, 57)( 51, 68)( 53, 58)( 56, 71)
        ( 60, 66)( 61,110)( 62, 87)( 65, 91)( 69, 74)( 70,103)( 72, 78)( 73,115)( 76, 82)( 77,118)( 80, 86)( 81,122)
        ( 84, 90)( 85,123)( 88,106)( 89,120)( 92, 97)( 93,111)( 95,101)( 96,112)( 99,105)(100,108)(104,114)(107,113)
        (109,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 53)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 84)( 38, 44)( 39, 96)( 40, 65)( 42, 48)( 43, 99)( 46, 68)( 47,103)( 51, 56)( 52, 69)( 54, 72)( 55, 70)
        ( 58, 64)( 59, 95)( 60, 88)( 63, 67)( 66, 92)( 71,107)( 73, 79)( 74,114)( 75,108)( 77, 83)( 78,118)( 81, 87)
        ( 82,122)( 85, 91)( 86,123)( 89,110)( 90,120)( 93, 98)( 94,111)( 97,102)(100,106)(101,112)(104,109)(105,117)
        (113,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 66)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 55)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 70)( 41, 47)( 42, 95)( 45, 51)( 46, 98)( 49, 54)( 50,102)( 53, 58)( 56, 74)( 57,103)
        ( 60, 65)( 61,110)( 62, 90)( 64, 69)( 67, 73)( 68,111)( 71, 94)( 72,112)( 75, 81)( 76,114)( 77,104)( 79, 85)
        ( 80,118)( 83, 89)( 84,122)( 87, 93)( 88,123)( 91,106)( 92,120)( 96,101)( 97,108)( 99,105)(100,117)(107,113)
        (109,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 38, 44)( 39, 95)( 40, 65)( 42, 48)( 43, 98)( 46, 68)( 47,102)( 51, 56)( 52, 69)( 54, 71)( 55,107)
        ( 58, 63)( 59, 94)( 60, 87)( 62, 67)( 66, 91)( 70,106)( 72, 78)( 73,114)( 74,108)( 76, 82)( 77,118)( 80, 86)
        ( 81,122)( 84, 90)( 85,123)( 88,110)( 89,120)( 92, 97)( 93,111)( 96,101)( 99,105)(100,112)(103,109)(104,117)
        (113,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 56)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 70)( 41, 47)( 42, 95)( 45, 51)( 46, 98)( 49, 55)( 50,102)( 53, 58)( 54,103)( 57, 74)
        ( 60, 66)( 61,110)( 62, 90)( 64, 69)( 65,111)( 68, 73)( 71, 94)( 72,112)( 75, 81)( 76,114)( 77,104)( 79, 85)
        ( 80,118)( 83, 89)( 84,122)( 87, 93)( 88,123)( 91,106)( 92,120)( 96,101)( 97,108)( 99,105)(100,117)(107,113)
        (109,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 75)( 28, 54)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 38, 44)( 39, 91)( 40, 66)( 42, 48)( 43, 95)( 46, 68)( 47, 99)( 50, 56)( 51,104)( 52, 69)( 55, 71)
        ( 58, 64)( 59,111)( 60, 87)( 62, 67)( 63, 94)( 70,103)( 72, 78)( 73,114)( 74,105)( 76, 82)( 77,118)( 80, 86)
        ( 81,122)( 84, 90)( 85,123)( 88,107)( 89,120)( 92, 98)( 93,112)( 96,102)( 97,109)(100,106)(101,117)(108,113)
        (110,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 23)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 43)( 24, 30)( 25, 66)( 26, 51)( 28, 34)( 29, 70)( 32, 55)( 33, 74)( 36, 42)
        ( 37, 82)( 38, 60)( 40, 46)( 41, 86)( 44, 50)( 45, 90)( 48, 54)( 49, 94)( 52, 62)( 53, 98)( 56, 61)( 57, 85)
        ( 58, 78)( 63, 69)( 64,110)( 65, 99)( 67, 73)( 68,114)( 71, 77)( 72,118)( 75, 81)( 76,119)( 79,102)( 80,116)
        ( 83, 89)( 84,103)( 87, 93)( 88,121)( 91, 97)( 92,122)( 95,101)( 96,109)(100,106)(104,124)(105,112)(107,113)
        (108,123)(111,117)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 61)( 23, 48)( 24, 44)( 26, 32)( 27, 76)( 28, 53)( 30, 36)( 31, 80)( 34, 56)
        ( 35, 84)( 38, 43)( 39, 96)( 40, 64)( 42, 47)( 45, 68)( 46, 97)( 49, 55)( 50,104)( 51, 69)( 54, 72)( 57, 63)
        ( 58,111)( 59, 88)( 62, 67)( 65, 92)( 66,112)( 70,100)( 71, 98)( 73, 79)( 74,114)( 75,105)( 77, 83)( 78,118)
        ( 81, 87)( 82,122)( 85, 91)( 86,123)( 89,107)( 90,120)( 93, 99)( 94,103)( 95,109)(101,106)(102,117)(108,113)
        (110,116)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 34)(  8, 17)( 10, 21)( 11, 37)( 14, 20)( 15, 49)
        ( 16, 29)( 18, 33)( 19, 52)( 22, 28)( 23, 64)( 24, 41)( 26, 32)( 27, 68)( 30, 45)( 31, 72)( 35, 40)( 36, 56)
        ( 38, 44)( 39, 81)( 42, 60)( 43, 84)( 46, 51)( 47, 95)( 48, 76)( 50, 55)( 53, 59)( 54, 96)( 57, 80)( 58, 93)
        ( 61, 67)( 62,106)( 63, 88)( 65, 71)( 66,110)( 69, 75)( 70,114)( 73, 79)( 74,117)( 77, 91)( 78,121)( 82, 87)
        ( 83, 98)( 85, 90)( 86,105)( 89,102)( 92, 97)( 94,101)( 99,104)(100,122)(103,109)(107,113)(108,123)(111,116)
        (112,119)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 20)(  4,  9)(  6, 12)(  7, 28)(  8, 14)( 10, 16)( 11, 32)( 15, 24)( 17, 23)
        ( 18, 44)( 19, 36)( 21, 27)( 22, 48)( 25, 31)( 26, 52)( 29, 35)( 30, 56)( 33, 39)( 34, 60)( 37, 40)( 38, 64)
        ( 41, 47)( 42, 75)( 43, 68)( 45, 51)( 46, 79)( 49, 55)( 50, 83)( 53, 59)( 54, 87)( 57, 63)( 58, 91)( 61, 67)
        ( 62, 95)( 65, 71)( 66, 99)( 69, 72)( 70,103)( 73, 78)( 74,107)( 76, 82)( 77,111)( 80, 86)( 81,114)( 84, 90)
        ( 85,118)( 88, 94)( 89,122)( 92, 98)( 93,123)( 96,102)( 97,120)(100,106)(101,116)(104,109)(105,113)(108,110)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 35)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 55)( 16, 28)( 18, 32)( 19, 59)( 23, 43)( 24, 39)( 27, 31)( 29, 51)( 30, 48)( 33, 38)( 34, 63)( 36, 42)
        ( 37, 76)( 40, 67)( 41, 79)( 44, 50)( 45, 90)( 46, 68)( 49, 74)( 52, 58)( 53, 98)( 54, 71)( 56, 62)( 57,102)
        ( 60, 66)( 61,103)( 64, 75)( 65,106)( 69, 86)( 70, 82)( 72, 94)( 73, 91)( 77, 81)( 78,110)( 80, 85)( 83,114)
        ( 84,111)( 87, 93)( 88,119)( 89,115)( 92,120)( 95,101)( 96,116)( 97,118)( 99,105)(100,122)(104,109)(107,113)
        (108,123)(112,124)(117,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 64)( 41, 47)( 42, 94)( 45, 67)( 46, 98)( 49, 54)( 50,106)( 51, 68)( 53, 58)( 56, 71)
        ( 57,107)( 60, 66)( 61, 90)( 62, 83)( 65, 87)( 69,102)( 70, 99)( 72, 78)( 73,118)( 74,108)( 77, 82)( 80, 86)
        ( 81,119)( 84,110)( 85,122)( 88, 93)( 89,111)( 92, 97)( 95,101)( 96,112)(100,114)(103,109)(104,121)(105,115)
        (113,117)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 56)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 88)( 39, 64)( 41, 47)( 42, 91)( 45, 67)( 46, 95)( 49, 55)( 50,103)( 51, 68)( 53, 58)( 54,104)
        ( 57, 71)( 60, 66)( 61,111)( 62, 83)( 65, 87)( 69, 99)( 70, 96)( 72, 78)( 73,118)( 74,105)( 77, 82)( 80, 86)
        ( 81,119)( 84,107)( 85,122)( 89, 94)( 90,112)( 92, 98)( 93,109)( 97,114)(100,106)(101,121)(102,115)(108,113)
        (110,117)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 81)( 34, 60)
        ( 35, 84)( 38, 44)( 39, 96)( 40, 69)( 42, 48)( 43,100)( 46, 72)( 47,104)( 50, 55)( 51, 73)( 53, 59)( 54,113)
        ( 57, 76)( 58,115)( 61, 67)( 62, 94)( 63, 88)( 65, 71)( 66, 95)( 70, 92)( 74,112)( 75,108)( 77, 83)( 78,118)
        ( 79,110)( 82, 87)( 85, 91)( 86,119)( 89, 98)( 90,122)( 93, 99)( 97,103)(101,107)(102,123)(105,111)(106,121)
        (109,116)(114,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 84)( 34, 60)
        ( 35, 85)( 38, 44)( 39, 96)( 40, 69)( 42, 48)( 43,100)( 46, 72)( 47,104)( 50, 55)( 51, 73)( 53, 59)( 54,113)
        ( 57, 76)( 58,115)( 61, 67)( 62, 94)( 63, 88)( 65, 71)( 66, 95)( 70, 92)( 74,112)( 75,108)( 77, 83)( 78,118)
        ( 79,110)( 81, 87)( 82,121)( 86, 91)( 89, 98)( 90,122)( 93, 99)( 97,103)(101,107)(102,123)(105,111)(106,120)
        (109,116)(114,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 80)( 34, 60)
        ( 35, 83)( 38, 43)( 39, 95)( 40, 71)( 42, 47)( 45, 51)( 46, 96)( 49, 55)( 50, 99)( 53, 59)( 54,103)( 57, 75)
        ( 58,107)( 61, 66)( 62, 69)( 63, 87)( 65, 70)( 68, 74)( 72, 91)( 73, 88)( 76, 82)( 77,121)( 78,110)( 81, 86)
        ( 84, 90)( 85,122)( 89,116)( 92, 98)( 93,119)( 94,114)( 97,102)(100,106)(101,120)(104,109)(105,112)(108,113)
        (111,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 49)( 24, 45)( 26, 32)( 27, 72)( 28, 53)( 30, 36)( 31, 73)( 34, 57)
        ( 35, 76)( 38, 44)( 39, 84)( 40, 59)( 42, 48)( 43, 88)( 46, 64)( 47, 91)( 51, 56)( 52, 65)( 54, 68)( 55,100)
        ( 58, 63)( 60, 80)( 66, 99)( 67, 95)( 69, 75)( 70,114)( 71,103)( 74, 79)( 77, 83)( 78,115)( 81, 87)( 82,118)
        ( 85, 90)( 86,121)( 89, 94)( 92, 98)( 93,122)( 96,107)( 97,113)(101,106)(102,108)(104,110)(105,109)(111,117)
        (112,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 42)( 26, 32)( 27, 80)( 28, 53)( 30, 36)( 31, 84)( 34, 57)
        ( 35, 87)( 38, 44)( 39, 98)( 40, 68)( 43, 72)( 46, 52)( 47,106)( 48, 73)( 50, 56)( 51,110)( 54, 76)( 55,114)
        ( 58, 64)( 59, 97)( 60, 91)( 62, 67)( 63, 70)( 66, 71)( 69, 95)( 74,102)( 75, 99)( 77, 83)( 78,117)( 79,115)
        ( 81, 86)( 82,121)( 85, 90)( 88, 94)( 89,122)( 92,100)( 93,105)( 96,101)(103,109)(104,123)(107,113)(108,119)
        (111,116)(112,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 44)( 39, 95)( 40, 67)( 42, 47)( 43, 98)( 46, 71)( 49, 55)( 50,106)( 51, 72)( 53, 58)( 54,110)
        ( 57, 75)( 60, 66)( 61, 69)( 62, 90)( 65, 70)( 68, 94)( 73,102)( 74, 99)( 76, 81)( 77,117)( 78,111)( 80, 85)
        ( 83, 89)( 84,118)( 87, 93)( 88,121)( 91, 97)( 92,116)( 96,101)(100,113)(103,109)(104,123)(105,114)(107,112)
        (108,120)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 87)( 34, 60)
        ( 35, 91)( 38, 43)( 39, 72)( 41, 47)( 42, 73)( 45, 75)( 46, 70)( 49, 55)( 50, 96)( 51, 76)( 53, 59)( 54, 99)
        ( 57, 79)( 58,103)( 61, 67)( 62, 77)( 63, 95)( 65, 71)( 66, 78)( 69, 74)( 80, 86)( 81,112)( 82,107)( 84, 90)
        ( 85,114)( 88, 94)( 89,118)( 92, 98)( 93,122)( 97,102)(100,106)(101,123)(104,110)(105,120)(108,111)(109,116)
        (113,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 73)( 27, 55)( 29, 35)( 30, 77)( 33, 59)( 34, 81)
        ( 37, 42)( 38, 90)( 39, 64)( 41, 46)( 44, 67)( 45, 91)( 48, 54)( 49, 97)( 50, 68)( 52, 58)( 53,101)( 56, 70)
        ( 57,105)( 60, 66)( 61, 95)( 62, 85)( 65, 89)( 69, 93)( 71, 76)( 72,109)( 74, 80)( 75,114)( 78, 84)( 79,115)
        ( 82, 88)( 83,117)( 86, 99)( 87,121)( 92, 96)( 94,100)( 98,104)(102,108)(103,122)(106,112)(107,123)(110,113)
        (111,119)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 47)( 24, 43)( 26, 32)( 27, 78)( 28, 55)( 30, 36)( 31, 81)( 34, 59)
        ( 35, 85)( 38, 42)( 39, 67)( 41, 46)( 44, 71)( 45, 68)( 48, 54)( 49, 97)( 50, 72)( 52, 58)( 53,101)( 56, 74)
        ( 57,105)( 60, 66)( 61, 95)( 62, 89)( 65, 70)( 69, 96)( 73, 93)( 75, 80)( 76,114)( 77,109)( 79, 84)( 82, 88)
        ( 83,115)( 86, 92)( 87,117)( 90, 99)( 91,121)( 94,100)( 98,104)(102,108)(103,122)(106,112)(107,123)(110,113)
        (111,119)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 59)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 72)( 32, 51)( 33, 75)( 36, 42)
        ( 37, 86)( 38, 63)( 40, 46)( 41, 89)( 44, 67)( 45, 93)( 49, 71)( 50, 68)( 52, 58)( 53,109)( 54, 79)( 56, 62)
        ( 57,110)( 60, 66)( 61,111)( 64, 83)( 65,107)( 69,101)( 70, 97)( 73, 78)( 74,102)( 76, 82)( 77,118)( 80,105)
        ( 81,121)( 84, 88)( 85,113)( 87, 92)( 90, 96)( 91,114)( 94,100)( 95,123)( 98,104)( 99,120)(103,117)(106,112)
        (108,116)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 46)( 23, 42)( 25, 31)( 26, 70)( 27, 54)( 29, 35)( 30, 74)( 33, 58)( 34, 78)
        ( 37, 41)( 38, 63)( 40, 45)( 43, 60)( 44, 64)( 47, 53)( 48, 79)( 49, 61)( 51, 57)( 52, 82)( 55, 66)( 56, 86)
        ( 59, 65)( 67, 73)( 68, 98)( 69, 90)( 71, 77)( 72,102)( 75, 81)( 76,106)( 80, 85)( 83, 89)( 84,107)( 87, 93)
        ( 88,110)( 91, 94)( 92,114)( 95,101)( 96,119)( 97,115)( 99,105)(100,120)(103,109)(104,122)(108,113)(111,117)
        (112,123)(116,118)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 85)( 28, 57)( 30, 36)( 31, 89)( 34, 61)
        ( 35, 92)( 38, 44)( 39,103)( 40, 73)( 42, 48)( 43,106)( 46, 77)( 47,110)( 50, 56)( 51, 67)( 52, 78)( 54, 60)
        ( 55, 63)( 58, 81)( 59, 97)( 62, 68)( 64, 96)( 66, 72)( 70, 76)( 71, 79)( 74,100)( 75,112)( 80,111)( 82, 88)
        ( 83,119)( 84,114)( 86, 91)( 87,121)( 90, 95)( 93, 99)( 94,122)( 98,117)(101,105)(102,108)(104,109)(107,113)
        (115,118)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 83)( 28, 57)( 30, 36)( 31, 86)( 34, 61)
        ( 35, 90)( 38, 44)( 39, 98)( 40, 73)( 42, 48)( 43, 99)( 46, 76)( 47,101)( 50, 56)( 51,113)( 52, 77)( 54, 60)
        ( 55,117)( 58, 80)( 59,121)( 62, 68)( 63,111)( 64, 94)( 66, 72)( 67,107)( 70, 75)( 71,103)( 74, 97)( 78,109)
        ( 79,105)( 81, 85)( 82,122)( 84, 89)( 87, 93)( 88,123)( 91, 96)( 92,119)( 95,115)(100,104)(102,108)(106,112)
        (110,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 59)( 33, 63)( 34, 72)( 37, 43)
        ( 38, 79)( 39, 64)( 41, 47)( 42, 83)( 45, 67)( 46, 87)( 49, 54)( 50, 68)( 52, 58)( 53, 92)( 56, 62)( 57, 95)
        ( 60, 71)( 61, 99)( 65, 75)( 66, 73)( 69, 91)( 70, 88)( 74,103)( 76, 82)( 77,110)( 78,104)( 80, 86)( 81,114)
        ( 84, 90)( 85,118)( 89,106)( 93, 98)( 94,107)( 96,102)( 97,122)(100,105)(101,113)(108,121)(109,119)(111,117)
        (112,123)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 47)( 24, 44)( 26, 32)( 27, 75)( 28, 55)( 30, 36)( 31, 79)( 34, 59)
        ( 35, 83)( 38, 43)( 39, 70)( 40, 65)( 42, 46)( 45, 67)( 48, 54)( 49, 88)( 50, 68)( 52, 58)( 53, 91)( 56, 71)
        ( 57, 95)( 60, 66)( 61, 69)( 62, 87)( 72, 78)( 73,107)( 74, 99)( 76, 82)( 77,110)( 80, 86)( 81,113)( 84, 90)
        ( 85,117)( 89, 94)( 92, 98)( 93,118)( 96,102)( 97,121)(100,103)(101,122)(104,109)(105,115)(106,123)(108,112)
        (111,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 61)( 23, 44)( 24, 41)( 26, 32)( 27, 75)( 28, 52)( 30, 36)( 31, 79)( 34, 56)
        ( 35, 83)( 39, 43)( 40, 64)( 42, 67)( 45, 51)( 46, 88)( 47, 68)( 49, 55)( 50, 91)( 53, 71)( 54, 95)( 57, 63)
        ( 58, 69)( 59, 87)( 62, 66)( 65, 70)( 72, 78)( 73,107)( 74, 99)( 76, 82)( 77,110)( 80, 86)( 81,113)( 84, 90)
        ( 85,117)( 89, 94)( 92, 98)( 93,118)( 96,102)( 97,121)(100,103)(101,122)(104,109)(105,115)(106,123)(108,112)
        (111,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 34)(  8, 17)( 10, 21)( 11, 37)( 14, 20)( 15, 48)
        ( 16, 29)( 18, 33)( 19, 52)( 22, 28)( 23, 64)( 24, 41)( 26, 32)( 27, 68)( 30, 45)( 31, 72)( 35, 40)( 36, 56)
        ( 38, 44)( 39, 81)( 42, 60)( 43, 84)( 46, 51)( 47, 76)( 49, 55)( 50, 88)( 53, 59)( 54, 90)( 57, 80)( 58, 94)
        ( 61, 67)( 62, 99)( 63, 85)( 65, 71)( 66,102)( 69, 75)( 70,106)( 73, 79)( 74,110)( 77, 87)( 78,114)( 82, 86)
        ( 83, 98)( 89, 93)( 91, 97)( 92,115)( 95,101)( 96,118)(100,105)(103,109)(104,119)(107,113)(108,122)(111,117)
        (112,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 99)( 40, 71)( 42, 48)( 43,103)( 46, 52)( 47,107)( 50, 55)( 51,110)( 54, 59)( 57, 75)
        ( 58,111)( 61, 66)( 62, 91)( 64, 70)( 65,115)( 68, 74)( 69,116)( 72, 95)( 73,118)( 76, 82)( 77,105)( 78,112)
        ( 80, 86)( 81,101)( 84, 90)( 85, 97)( 88, 94)( 89,122)( 92,114)( 93,123)( 96,102)( 98,121)(100,106)(104,109)
        (108,113)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 42)( 26, 32)( 27, 71)( 28, 52)( 30, 36)( 31, 75)( 34, 56)
        ( 35, 79)( 38, 43)( 39, 47)( 40, 65)( 45, 51)( 46, 62)( 49, 55)( 50, 58)( 53, 67)( 54, 84)( 57, 63)( 59, 83)
        ( 61, 66)( 68, 74)( 69, 95)( 70, 87)( 72, 78)( 73, 99)( 76, 82)( 77,103)( 80, 86)( 81,107)( 85, 90)( 88, 91)
        ( 89,108)( 92, 98)( 93,119)( 94,111)( 96,102)( 97,120)(100,106)(101,117)(104,110)(105,122)(109,114)(112,115)
        (113,123)(116,121)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 41)( 24, 39)( 26, 32)( 27, 71)( 28, 49)( 30, 36)( 31, 75)( 34, 53)
        ( 35, 79)( 40, 64)( 42, 48)( 43, 59)( 44, 65)( 46, 52)( 47, 55)( 50, 67)( 51, 84)( 54, 60)( 56, 83)( 58, 63)
        ( 62, 66)( 68, 74)( 69, 95)( 70, 87)( 72, 78)( 73, 99)( 76, 82)( 77,103)( 80, 86)( 81,107)( 85, 90)( 88, 91)
        ( 89,108)( 92, 98)( 93,119)( 94,111)( 96,102)( 97,120)(100,106)(101,117)(104,110)(105,122)(109,114)(112,115)
        (113,123)(116,121)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 32)( 18, 36)( 19, 60)( 23, 44)( 25, 31)( 26, 71)( 27, 49)( 29, 35)( 30, 75)( 33, 52)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 63)( 41, 47)( 42, 95)( 45, 51)( 46, 70)( 50, 67)( 53, 59)( 54, 90)( 55, 83)( 57, 62)
        ( 58, 65)( 61, 66)( 64, 87)( 68, 74)( 69, 96)( 72, 78)( 73,103)( 76, 82)( 77,107)( 80, 86)( 81,111)( 84, 99)
        ( 85,114)( 88, 94)( 89,100)( 92, 98)( 93,118)( 97,106)(101,121)(102,115)(104,110)(105,119)(108,113)(109,124)
        (112,117)(116,122)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 49)( 29, 35)( 30, 75)( 33, 52)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 63)( 41, 47)( 42, 95)( 45, 51)( 46, 70)( 50, 67)( 53, 59)( 54, 90)( 55, 83)( 57, 62)
        ( 58, 65)( 61, 66)( 64, 87)( 68, 74)( 69, 96)( 72, 78)( 73,103)( 76, 82)( 77,107)( 80, 86)( 81,111)( 84, 99)
        ( 85,112)( 88, 94)( 89,100)( 92, 98)( 93,118)( 97,106)(101,121)(102,115)(104,110)(105,119)(108,114)(109,124)
        (113,117)(116,122)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 49)( 29, 35)( 30, 75)( 33, 52)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 63)( 41, 47)( 42, 95)( 45, 51)( 46, 70)( 50, 67)( 53, 59)( 54, 90)( 55, 83)( 57, 62)
        ( 58, 65)( 61, 66)( 64, 87)( 68, 74)( 69, 96)( 72, 78)( 73,103)( 76, 82)( 77,107)( 80, 86)( 81,111)( 84, 99)
        ( 85,114)( 88, 94)( 89,100)( 92, 98)( 93,121)( 97,106)(101,124)(102,117)(104,110)(105,122)(108,113)(109,119)
        (112,116)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 49)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 67)( 27, 52)( 29, 35)( 30, 71)( 33, 55)( 34, 75)
        ( 37, 43)( 38, 87)( 39, 60)( 41, 47)( 42, 91)( 45, 51)( 46, 66)( 50, 54)( 53, 63)( 56, 62)( 57, 86)( 58, 79)
        ( 61, 83)( 64, 70)( 65, 92)( 68, 74)( 69, 99)( 72, 78)( 73,103)( 76, 82)( 77,107)( 80, 95)( 81,111)( 84, 90)
        ( 85, 96)( 88, 94)( 89,117)( 93,102)( 97,120)( 98,114)(100,106)(101,118)(104,110)(105,123)(108,113)(109,124)
        (112,116)(115,121)(119,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 67)( 27, 52)( 29, 35)( 30, 71)( 33, 55)( 34, 75)
        ( 37, 43)( 38, 87)( 39, 60)( 41, 47)( 42, 91)( 45, 50)( 46, 66)( 49, 54)( 53, 63)( 56, 62)( 57, 86)( 58, 79)
        ( 61, 83)( 64, 70)( 65, 92)( 68, 74)( 69, 99)( 72, 78)( 73,103)( 76, 82)( 77,107)( 80, 95)( 81,110)( 84, 90)
        ( 85, 96)( 88, 94)( 89,117)( 93,102)( 97,120)( 98,114)(100,106)(101,118)(104,109)(105,123)(108,113)(111,116)
        (112,124)(115,121)(119,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 21)(  4,  9)(  6, 12)(  7, 33)(  8, 14)( 10, 17)( 11, 37)( 15, 29)( 16, 25)
        ( 18, 24)( 19, 53)( 20, 41)( 22, 28)( 23, 57)( 26, 45)( 27, 61)( 30, 36)( 31, 72)( 32, 46)( 34, 40)( 35, 76)
        ( 38, 44)( 39, 80)( 42, 49)( 43, 84)( 47, 69)( 48, 65)( 50, 56)( 51, 90)( 52, 85)( 54, 60)( 55, 94)( 58, 64)
        ( 59, 98)( 62, 68)( 63,102)( 66, 87)( 67,106)( 70, 75)( 71, 88)( 73, 79)( 74,111)( 77, 83)( 78,114)( 81, 86)
        ( 82, 93)( 89,110)( 91, 97)( 92,115)( 95,101)( 96,118)( 99,105)(100,122)(103,109)(104,123)(107,113)(108,120)
        (112,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 32)( 19, 64)( 23, 44)( 24, 40)( 27, 31)( 28, 52)( 30, 56)( 33, 39)( 34, 77)( 35, 68)
        ( 37, 43)( 38, 78)( 41, 72)( 42, 80)( 45, 51)( 46, 92)( 47, 73)( 49, 55)( 50, 95)( 53, 59)( 54, 99)( 57, 63)
        ( 58,103)( 61, 67)( 62,107)( 65, 71)( 66,111)( 69, 76)( 70,112)( 74, 88)( 75, 84)( 79, 83)( 81, 87)( 82,113)
        ( 85,115)( 86,109)( 89, 94)( 90,122)( 91,116)( 93, 98)( 96,102)( 97,123)(100,106)(101,121)(104,110)(105,118)
        (108,114)(117,119)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 59)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 68)( 32, 51)( 33, 71)( 36, 42)
        ( 37, 77)( 38, 63)( 40, 46)( 41, 73)( 44, 50)( 45, 70)( 49, 67)( 52, 58)( 53, 83)( 54, 75)( 56, 62)( 57, 87)
        ( 60, 66)( 61, 91)( 64, 79)( 65, 95)( 69, 74)( 72, 78)( 76, 80)( 81, 86)( 82, 99)( 84, 90)( 85,104)( 88, 94)
        ( 89,107)( 92, 98)( 93,111)( 96,102)( 97,115)(100,103)(101,118)(105,110)(106,121)(108,114)(109,122)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 75)( 28, 54)( 30, 36)( 31, 78)( 34, 57)
        ( 35, 82)( 38, 44)( 39, 94)( 40, 67)( 42, 48)( 43, 97)( 46, 71)( 47,101)( 50, 56)( 51,109)( 52, 72)( 55, 74)
        ( 58, 63)( 59, 69)( 60, 86)( 62, 66)( 65, 70)( 68, 90)( 73,105)( 76, 81)( 77,110)( 79, 85)( 80,114)( 83, 89)
        ( 84,117)( 87, 93)( 88,121)( 91, 96)( 92,122)( 95,100)( 98,104)( 99,123)(102,108)(103,119)(106,112)(107,116)
        (111,113)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)( 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 45)( 26, 32)( 27, 76)( 28, 56)( 30, 36)( 31, 79)( 34, 60)
        ( 35, 83)( 38, 44)( 39, 92)( 40, 68)( 42, 47)( 43, 95)( 46, 71)( 49, 55)( 50,103)( 51, 72)( 53, 59)( 54,107)
        ( 57, 75)( 58,111)( 61, 66)( 62, 94)( 63, 87)( 65, 70)( 69, 91)( 73, 99)( 74, 96)( 77, 82)( 78,114)( 80, 86)
        ( 81,118)( 84, 90)( 85,121)( 88, 97)( 89,102)( 93, 98)(100,106)(101,122)(104,110)(105,123)(108,113)(109,120)
        (112,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 60)( 23, 43)( 25, 31)( 26, 67)( 27, 51)( 29, 35)( 30, 71)( 33, 55)( 34, 75)
        ( 37, 42)( 38, 61)( 40, 46)( 41, 57)( 44, 50)( 45, 80)( 48, 54)( 49, 83)( 52, 63)( 53, 87)( 56, 62)( 58, 79)
        ( 64, 70)( 65, 99)( 66, 91)( 68, 74)( 69,100)( 72, 78)( 73,103)( 76, 82)( 77,107)( 81, 86)( 84, 90)( 85,108)
        ( 88, 94)( 89,111)( 92, 95)( 93,115)( 96,102)( 97,122)( 98,118)(101,106)(104,110)(105,123)(109,114)(112,117)
        (113,124)(116,120)(119,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 61)( 23, 44)( 24, 41)( 26, 32)( 27, 68)( 28, 52)( 30, 36)( 31, 72)( 34, 56)
        ( 35, 76)( 38, 43)( 39, 62)( 42, 58)( 45, 51)( 46, 77)( 47, 59)( 49, 55)( 50, 80)( 53, 64)( 54, 84)( 57, 63)
        ( 65, 71)( 66, 95)( 67, 88)( 69, 75)( 70, 99)( 73, 79)( 74,103)( 78, 83)( 81, 87)( 82,104)( 85, 91)( 86,107)
        ( 89, 92)( 90,111)( 93, 98)( 94,115)( 96,102)( 97,119)(100,106)(101,122)(105,110)(108,114)(109,123)(112,117)
        (113,121)(116,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 22)(  4,  9)(  6, 12)(  7, 33)(  8, 17)( 10, 21)( 11, 37)( 14, 20)( 15, 44)
        ( 16, 25)( 18, 29)( 19, 48)( 23, 28)( 24, 38)( 26, 40)( 27, 35)( 30, 36)( 31, 43)( 32, 52)( 34, 39)( 41, 47)
        ( 42, 57)( 45, 51)( 46, 60)( 49, 55)( 50, 64)( 53, 56)( 54, 68)( 58, 63)( 59, 72)( 61, 67)( 62, 77)( 65, 71)
        ( 66, 80)( 69, 75)( 70, 84)( 73, 76)( 74, 88)( 78, 83)( 79, 92)( 81, 87)( 82, 97)( 85, 91)( 86,100)( 89, 95)
        ( 90,104)( 93, 96)( 94,108)( 98,103)( 99,112)(101,107)(102,117)(105,111)(106,119)(109,115)(110,122)(113,116)
        (114,123)(118,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114,115)(116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 35)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 29)( 18, 32)( 19, 63)( 23, 43)( 24, 39)( 27, 31)( 28, 51)( 30, 55)( 33, 38)( 34, 67)( 36, 42)
        ( 37, 68)( 40, 71)( 41, 75)( 44, 50)( 45, 87)( 46, 72)( 48, 54)( 49, 91)( 52, 58)( 53, 95)( 56, 62)( 57, 99)
        ( 60, 66)( 61,103)( 64, 70)( 65,107)( 69, 78)( 73, 83)( 74, 79)( 76, 82)( 77,108)( 80, 86)( 81,111)( 84, 90)
        ( 85,114)( 88, 94)( 89,118)( 92, 98)( 93,122)( 96,102)( 97,123)(100,106)(101,120)(104,110)(105,116)(109,113)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 35)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 29)( 18, 32)( 19, 63)( 23, 43)( 24, 39)( 26, 31)( 27, 51)( 30, 55)( 33, 38)( 34, 67)( 36, 42)
        ( 37, 68)( 40, 71)( 41, 75)( 44, 50)( 45, 87)( 46, 72)( 48, 54)( 49, 91)( 52, 58)( 53, 95)( 56, 62)( 57, 99)
        ( 60, 66)( 61,103)( 64, 70)( 65,107)( 69, 78)( 73, 83)( 74, 79)( 76, 82)( 77,108)( 80, 86)( 81,111)( 84, 90)
        ( 85,114)( 88, 94)( 89,118)( 92, 98)( 93,122)( 96,102)( 97,123)(100,106)(101,120)(104,110)(105,116)(109,113)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 27)( 18, 55)( 22, 39)( 23, 35)( 26, 47)( 28, 34)( 29, 68)( 30, 59)( 32, 38)( 33, 70)( 36, 63)
        ( 37, 74)( 40, 46)( 41, 86)( 42, 64)( 44, 50)( 45, 90)( 48, 54)( 49, 94)( 52, 58)( 53, 98)( 56, 62)( 57,102)
        ( 60, 67)( 61,106)( 65, 82)( 66, 78)( 69, 73)( 71, 77)( 72,107)( 75, 81)( 76,110)( 79, 85)( 80,111)( 83, 89)
        ( 84,114)( 87, 93)( 88,118)( 91, 97)( 92,122)( 95,101)( 96,123)( 99,105)(100,120)(103,109)(104,116)(108,113)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 43)( 23, 39)( 25, 30)( 26, 51)( 28, 34)( 29, 68)( 32, 55)( 33, 71)( 37, 42)
        ( 38, 60)( 40, 63)( 41, 80)( 44, 50)( 45, 91)( 46, 64)( 48, 54)( 49, 95)( 52, 67)( 53, 96)( 56, 62)( 57,106)
        ( 58, 75)( 61, 79)( 65, 87)( 66, 83)( 69, 74)( 70, 99)( 72, 78)( 73,115)( 76,103)( 77,117)( 81, 86)( 82,107)
        ( 84,110)( 85,108)( 88, 94)( 89,121)( 90,111)( 92, 98)( 93,122)( 97,102)(100,114)(101,123)(104,109)(105,113)
        (112,118)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 88)( 45, 51)( 46, 98)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,103)( 57, 63)
        ( 58,114)( 59, 83)( 61, 66)( 62,117)( 65, 70)( 68, 87)( 69,118)( 73, 94)( 74, 90)( 77, 82)( 78,106)( 80, 86)
        ( 81,107)( 84,110)( 85,121)( 89, 93)( 91,112)( 92,119)( 95,101)( 96,122)( 97,113)( 99,105)(100,123)(104,109)
        (108,124)(111,116)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 58)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 70)( 32, 51)( 33, 73)( 36, 42)
        ( 37, 85)( 38, 62)( 40, 46)( 41, 89)( 44, 65)( 45, 93)( 49, 69)( 50, 66)( 52, 57)( 53,109)( 54, 77)( 56, 61)
        ( 59, 64)( 60,110)( 63, 81)( 67,101)( 68, 97)( 71, 76)( 72,102)( 74, 80)( 75,114)( 78,105)( 79,117)( 82, 88)
        ( 83,107)( 84,111)( 86, 92)( 87,122)( 90, 96)( 91,123)( 94,100)( 95,119)( 98,104)( 99,116)(103,113)(106,112)
        (108,121)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64)( 65, 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 58)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 71)( 32, 51)( 33, 74)( 36, 42)
        ( 37, 85)( 38, 62)( 40, 46)( 41, 89)( 44, 66)( 45, 93)( 49, 70)( 50, 67)( 52, 57)( 53,109)( 54, 78)( 56, 61)
        ( 59, 65)( 60,110)( 63, 82)( 64,111)( 68,101)( 69, 97)( 72, 77)( 73,102)( 75, 81)( 76,114)( 79,105)( 80,117)
        ( 83, 88)( 84,107)( 86, 92)( 87,122)( 90, 96)( 91,123)( 94,100)( 95,119)( 98,104)( 99,116)(103,113)(106,112)
        (108,121)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 61)( 23, 44)( 24, 40)( 26, 32)( 27, 68)( 28, 52)( 30, 36)( 31, 72)( 34, 56)
        ( 35, 76)( 39, 43)( 41, 58)( 42, 62)( 45, 51)( 46, 77)( 47, 59)( 49, 55)( 50, 80)( 53, 64)( 54, 84)( 57, 63)
        ( 65, 71)( 66, 95)( 67, 88)( 69, 75)( 70, 99)( 73, 79)( 74,103)( 78, 83)( 81, 87)( 82,104)( 85, 91)( 86,107)
        ( 89, 92)( 90,111)( 93, 98)( 94,114)( 96,102)( 97,119)(100,106)(101,121)(105,110)(108,113)(109,122)(112,117)
        (115,118)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 41)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 67)( 42, 71)( 45, 51)( 46, 99)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,106)( 57, 63)
        ( 58, 90)( 59, 83)( 61, 66)( 62, 69)( 65, 70)( 68, 87)( 73, 95)( 74, 92)( 77, 82)( 78,110)( 80, 86)( 81,118)
        ( 84,113)( 85,121)( 88, 94)( 89,114)( 93,115)( 96,101)( 97,122)( 98,116)(100,105)(103,109)(104,123)(107,112)
        (108,120)(111,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 53)( 30, 36)( 31, 84)( 34, 57)
        ( 35, 88)( 39, 44)( 40, 69)( 42, 73)( 43, 70)( 46, 52)( 47, 99)( 48, 74)( 50, 56)( 51,103)( 54, 77)( 55,107)
        ( 58, 64)( 59,105)( 60, 92)( 62, 68)( 63,101)( 66, 72)( 67, 98)( 71, 76)( 75, 96)( 78, 83)( 79,111)( 81, 87)
        ( 82,116)( 85, 91)( 86,118)( 89, 95)( 90,121)( 93,109)( 94,122)( 97,102)(100,106)(104,110)(108,114)(112,115)
        (113,123)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 53)( 29, 35)( 30, 76)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 61)( 41, 47)( 42, 94)( 45, 64)( 46, 98)( 49, 55)( 50,106)( 51, 65)( 54, 68)( 57, 63)
        ( 58, 90)( 59, 83)( 62, 87)( 66,102)( 67, 99)( 69, 75)( 70,117)( 71,107)( 73, 79)( 74,118)( 77, 82)( 78,121)
        ( 81, 86)( 84,109)( 85,122)( 88, 93)( 89,110)( 92, 97)( 95,101)( 96,111)(100,113)(103,108)(104,120)(105,114)
        (112,116)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 49)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 75)( 33, 56)( 34, 79)
        ( 37, 43)( 38, 86)( 39, 61)( 41, 47)( 42, 90)( 45, 63)( 46, 94)( 50, 55)( 51, 64)( 53, 67)( 54,102)( 57, 62)
        ( 58, 89)( 59, 82)( 65,101)( 66, 98)( 68, 74)( 69,113)( 70,103)( 72, 78)( 73,114)( 76, 81)( 77,117)( 80, 85)
        ( 83,105)( 84,118)( 87, 93)( 88,106)( 91, 97)( 92,107)( 95,100)( 96,122)( 99,109)(104,110)(108,121)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 66)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 57)( 30, 36)( 31, 82)( 34, 61)
        ( 35, 86)( 38, 44)( 39, 97)( 40, 69)( 42, 48)( 43,101)( 46, 72)( 47,105)( 50, 56)( 51,113)( 52, 73)( 54, 60)
        ( 55,114)( 58, 75)( 59,115)( 62, 68)( 63, 96)( 64, 90)( 67, 71)( 70, 94)( 74,109)( 76, 81)( 77,117)( 78,111)
        ( 80, 85)( 83, 89)( 84,118)( 87, 93)( 88,121)( 91, 99)( 92,122)( 95,100)( 98,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 66)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 57)( 30, 36)( 31, 83)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 97)( 40, 69)( 42, 48)( 43,101)( 46, 72)( 47,105)( 50, 56)( 51,113)( 52, 73)( 54, 60)
        ( 55,114)( 58, 75)( 59,115)( 62, 68)( 63, 96)( 64, 90)( 67, 71)( 70, 94)( 74,109)( 76, 82)( 77,117)( 78,111)
        ( 80, 86)( 81,118)( 84, 89)( 85,121)( 88, 93)( 91, 99)( 92,122)( 95,100)( 98,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 82)( 34, 60)
        ( 35, 86)( 38, 44)( 39, 97)( 40, 68)( 42, 48)( 43,101)( 46, 71)( 47,105)( 50, 55)( 51, 72)( 53, 59)( 54,114)
        ( 57, 75)( 58,115)( 61, 66)( 62, 96)( 63, 90)( 65, 70)( 69, 94)( 73,113)( 74,109)( 76, 81)( 77,117)( 78,111)
        ( 80, 85)( 83, 89)( 84,118)( 87, 93)( 88,121)( 91, 99)( 92,122)( 95,100)( 98,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 97)( 40, 68)( 42, 48)( 43,101)( 46, 71)( 47,105)( 50, 55)( 51, 72)( 53, 59)( 54,114)
        ( 57, 75)( 58,115)( 61, 66)( 62, 96)( 63, 90)( 65, 70)( 69, 94)( 73,113)( 74,109)( 76, 82)( 77,117)( 78,111)
        ( 80, 86)( 81,118)( 84, 89)( 85,121)( 88, 93)( 91, 99)( 92,122)( 95,100)( 98,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 85)( 34, 60)
        ( 35, 89)( 38, 44)( 39, 98)( 40, 70)( 42, 48)( 43,101)( 46, 74)( 47,105)( 50, 55)( 51,114)( 52, 75)( 54, 59)
        ( 57, 78)( 58,115)( 61, 66)( 62, 72)( 63, 93)( 65, 69)( 68, 73)( 71, 97)( 76,113)( 77,109)( 79, 84)( 80,117)
        ( 81,111)( 83, 88)( 86, 92)( 87,118)( 90, 96)( 91,121)( 94,100)( 95,122)( 99,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 86)( 34, 60)
        ( 35, 90)( 38, 44)( 39, 98)( 40, 70)( 42, 48)( 43,101)( 46, 74)( 47,105)( 50, 55)( 51,114)( 52, 75)( 54, 59)
        ( 57, 78)( 58,115)( 61, 66)( 62, 72)( 63, 93)( 65, 69)( 68, 73)( 71, 97)( 76,113)( 77,109)( 79, 85)( 80,117)
        ( 81,111)( 83, 89)( 84,118)( 87, 92)( 88,121)( 91, 96)( 94,100)( 95,122)( 99,104)(102,108)(103,123)(106,112)
        (107,120)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 36)(  8, 17)( 10, 21)( 11, 40)( 14, 20)( 15, 52)
        ( 16, 29)( 18, 33)( 19, 56)( 22, 28)( 23, 68)( 24, 44)( 26, 32)( 27, 72)( 30, 48)( 31, 76)( 34, 39)( 35, 60)
        ( 37, 43)( 38, 85)( 41, 47)( 42, 88)( 45, 64)( 46, 92)( 49, 55)( 50, 99)( 51, 80)( 53, 59)( 54,100)( 57, 63)
        ( 58, 97)( 61, 84)( 62,102)( 65, 71)( 66,110)( 67, 93)( 69, 75)( 70,114)( 73, 79)( 74,115)( 77, 83)( 78,118)
        ( 81, 95)( 82,122)( 86, 91)( 87,106)( 89, 94)( 90,113)( 96,101)( 98,105)(103,109)(104,123)(107,112)(108,120)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 36)(  8, 17)( 10, 21)( 11, 40)( 14, 20)( 15, 52)
        ( 16, 29)( 18, 33)( 19, 56)( 22, 28)( 23, 68)( 24, 44)( 26, 32)( 27, 72)( 30, 48)( 31, 76)( 34, 39)( 35, 60)
        ( 37, 43)( 38, 85)( 41, 47)( 42, 88)( 45, 64)( 46, 92)( 49, 55)( 50, 99)( 51, 80)( 53, 59)( 54,100)( 57, 63)
        ( 58, 97)( 61, 84)( 62,102)( 65, 71)( 66,110)( 67, 93)( 69, 75)( 70,114)( 73, 79)( 74,117)( 77, 83)( 78,121)
        ( 81, 95)( 82,122)( 86, 91)( 87,106)( 89, 94)( 90,113)( 96,101)( 98,105)(103,109)(104,123)(107,112)(108,119)
        (111,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 43)( 24, 39)( 26, 31)( 27, 51)( 29, 35)( 30, 72)( 33, 55)( 34, 75)
        ( 38, 42)( 40, 67)( 41, 64)( 44, 50)( 45, 91)( 46, 68)( 48, 54)( 49, 92)( 52, 71)( 53, 95)( 56, 62)( 57,107)
        ( 58, 79)( 60, 66)( 61,108)( 65, 86)( 69, 87)( 70, 83)( 73, 78)( 74, 99)( 76, 82)( 77,115)( 80,103)( 81,117)
        ( 84,111)( 85,109)( 88, 94)( 89,122)( 90,112)( 93, 98)( 96,102)( 97,123)(100,114)(101,119)(104,110)(105,113)
        (106,121)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 25, 31)( 26, 75)( 27, 52)( 29, 35)( 30, 79)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 67)( 41, 47)( 42, 95)( 45, 51)( 46, 99)( 49, 55)( 50,103)( 53, 71)( 54,107)( 57, 63)
        ( 58, 89)( 59, 83)( 61, 66)( 62,111)( 65, 70)( 68, 87)( 69,112)( 72, 78)( 73,117)( 74,108)( 76, 82)( 77,121)
        ( 81, 86)( 84, 93)( 85,122)( 88, 94)( 90,113)( 92, 98)( 96,102)( 97,123)(100,106)(101,119)(104,110)(105,116)
        (109,114)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 82)( 34, 60)
        ( 35, 86)( 38, 44)( 39, 98)( 40, 71)( 42, 48)( 43,102)( 46, 74)( 47,106)( 50, 55)( 51,114)( 52, 75)( 54, 59)
        ( 57, 78)( 58,115)( 61, 67)( 62, 96)( 63, 90)( 65, 70)( 66, 97)( 69, 73)( 72, 94)( 76,110)( 77,107)( 80, 85)
        ( 81,116)( 83, 89)( 84,112)( 87, 93)( 88,120)( 91,100)( 92,122)( 95,101)( 99,105)(103,109)(104,123)(108,118)
        (111,117)(113,119)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)( 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96, 97)
        ( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 57)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 98)( 40, 71)( 42, 48)( 43,102)( 46, 75)( 47,106)( 50, 56)( 51,114)( 52, 76)( 54, 59)
        ( 55,115)( 58, 79)( 61, 67)( 62, 97)( 63, 91)( 65, 70)( 66, 73)( 69, 74)( 72, 95)( 77,110)( 78,107)( 81, 86)
        ( 82,116)( 84, 90)( 85,112)( 88, 94)( 89,120)( 92,100)( 93,122)( 96,101)( 99,105)(103,109)(104,123)(108,118)
        (111,117)(113,119)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 73)( 28, 57)( 30, 36)( 31, 76)( 34, 61)
        ( 35, 80)( 38, 44)( 39, 91)( 40, 69)( 42, 48)( 43, 95)( 46, 52)( 47, 99)( 50, 56)( 51,103)( 54, 60)( 55,107)
        ( 58, 72)( 59,108)( 62, 67)( 63, 90)( 64, 84)( 66, 71)( 70, 88)( 74, 79)( 75,111)( 77, 83)( 78,115)( 81, 87)
        ( 82,118)( 85, 93)( 86,122)( 89, 94)( 92, 98)( 96,102)( 97,123)(100,106)(101,120)(104,110)(105,117)(109,113)
        (112,114)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 57)( 30, 36)( 31, 79)( 34, 61)
        ( 35, 83)( 38, 44)( 39, 92)( 40, 71)( 42, 48)( 43, 95)( 46, 52)( 47, 99)( 50, 56)( 51,103)( 54, 60)( 55,107)
        ( 58, 75)( 59,110)( 62, 67)( 63, 73)( 64, 87)( 66, 70)( 69, 74)( 72, 91)( 77, 82)( 78,111)( 80, 86)( 81,115)
        ( 84, 90)( 85,118)( 88, 94)( 89,122)( 93, 98)( 96,102)( 97,123)(100,106)(101,120)(104,109)(105,117)(108,113)
        (112,114)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 87)( 34, 60)
        ( 35, 88)( 38, 43)( 39, 71)( 41, 47)( 42, 96)( 45, 75)( 46, 99)( 49, 55)( 50,110)( 51, 76)( 53, 59)( 54,111)
        ( 57, 79)( 58,112)( 61, 66)( 62, 69)( 63, 91)( 65, 70)( 68, 74)( 72, 95)( 73, 92)( 77,106)( 78,103)( 80, 86)
        ( 81,121)( 82,108)( 84, 90)( 85,116)( 89, 94)( 93,117)( 97,102)( 98,114)(100,105)(101,123)(104,118)(107,113)
        (109,119)(115,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 48)( 24, 45)( 26, 32)( 27, 76)( 28, 56)( 30, 36)( 31, 80)( 34, 60)
        ( 35, 84)( 38, 44)( 39, 92)( 40, 66)( 42, 47)( 43, 93)( 46, 68)( 49, 55)( 50, 96)( 51, 69)( 53, 59)( 54,100)
        ( 57, 72)( 58,104)( 61, 67)( 62, 95)( 63, 88)( 70, 89)( 71, 94)( 73, 79)( 74,114)( 75,107)( 77, 83)( 78,117)
        ( 81, 87)( 82,118)( 85, 91)( 86,121)( 90, 99)( 97,103)( 98,122)(101,106)(102,113)(105,109)(108,110)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109)(110,111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 32)( 18, 36)( 19, 59)( 23, 40)( 25, 31)( 26, 70)( 27, 48)( 29, 35)( 30, 74)( 33, 52)( 34, 78)
        ( 38, 43)( 39, 62)( 41, 47)( 42, 87)( 45, 51)( 46, 90)( 49, 66)( 50, 94)( 53, 58)( 54, 64)( 55, 82)( 57, 61)
        ( 60, 65)( 63, 86)( 67, 73)( 68,106)( 69, 98)( 71, 77)( 72,109)( 75, 81)( 76,110)( 79, 85)( 80,113)( 83, 89)
        ( 84,117)( 88, 93)( 91, 97)( 92,118)( 95,101)( 96,121)( 99,102)(100,122)(103,108)(104,115)(105,123)(107,112)
        (111,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 39)( 16, 32)( 18, 36)( 22, 44)( 23, 41)( 25, 31)( 26, 67)( 27, 52)( 29, 35)( 30, 71)( 33, 56)( 34, 75)
        ( 37, 43)( 38, 57)( 42, 60)( 45, 51)( 46, 80)( 47, 61)( 49, 55)( 50, 83)( 53, 63)( 54, 87)( 58, 62)( 59, 79)
        ( 64, 70)( 65, 99)( 66, 91)( 68, 74)( 69,102)( 72, 78)( 73,106)( 76, 82)( 77,110)( 81, 86)( 84, 90)( 85,111)
        ( 88, 94)( 89,114)( 92, 95)( 93,118)( 96,101)( 97,121)( 98,119)(100,105)(103,109)(104,122)(107,113)(108,123)
        (112,117)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 72)( 27, 55)( 29, 35)( 30, 75)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 88)( 44, 67)( 45, 89)( 48, 54)( 49, 99)( 50, 68)( 52, 58)( 53,103)( 56, 71)
        ( 57,107)( 60, 66)( 61, 93)( 62, 83)( 65, 87)( 69, 95)( 70, 91)( 73, 78)( 74,108)( 76, 82)( 77,115)( 80, 86)
        ( 81,117)( 84,111)( 85,121)( 90, 94)( 92,112)( 96,102)( 97,122)( 98,113)(100,106)(101,123)(104,110)(105,119)
        (109,114)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 72)( 27, 55)( 29, 35)( 30, 75)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 88)( 44, 67)( 45, 89)( 48, 54)( 49, 98)( 50, 68)( 52, 58)( 53,102)( 56, 71)
        ( 57,106)( 60, 66)( 61, 93)( 62, 83)( 65, 87)( 69, 95)( 70, 91)( 73, 78)( 74,107)( 76, 82)( 77,115)( 80, 86)
        ( 81,117)( 84,110)( 85,121)( 90, 94)( 92,111)( 96,101)( 97,112)( 99,105)(100,123)(103,109)(104,119)(108,114)
        (113,122)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 42)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 38, 44)( 39, 59)( 40, 65)( 43, 67)( 46, 52)( 47, 87)( 48, 68)( 50, 56)( 51, 91)( 54, 71)( 55, 95)
        ( 58, 63)( 60, 70)( 62, 66)( 69, 84)( 72, 78)( 73,104)( 74, 99)( 76, 82)( 77,107)( 80, 86)( 81,111)( 85, 90)
        ( 88, 94)( 89,112)( 92, 98)( 93,115)( 96,102)( 97,118)(100,103)(101,122)(105,110)(106,123)(108,114)(109,120)
        (113,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 43)( 12, 21)( 14, 19)
        ( 15, 55)( 16, 32)( 18, 36)( 22, 40)( 23, 38)( 25, 31)( 26, 63)( 27, 47)( 29, 35)( 30, 67)( 33, 51)( 34, 71)
        ( 39, 56)( 41, 46)( 42, 57)( 44, 50)( 45, 53)( 48, 59)( 49, 76)( 52, 58)( 54, 75)( 60, 66)( 61, 87)( 62, 79)
        ( 64, 70)( 65, 91)( 68, 74)( 69, 95)( 72, 78)( 73, 99)( 77, 82)( 80, 83)( 81,100)( 84, 90)( 85,110)( 86,103)
        ( 88, 94)( 89,111)( 92, 98)( 93,114)( 96,102)( 97,118)(101,106)(104,107)(105,119)(108,113)(109,122)(112,117)
        (115,121)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 58)( 16, 32)( 18, 36)( 19, 59)( 23, 44)( 25, 31)( 26, 69)( 27, 51)( 29, 35)( 30, 73)( 33, 54)( 34, 77)
        ( 37, 43)( 38, 89)( 39, 62)( 41, 47)( 42, 93)( 45, 50)( 46, 68)( 49, 53)( 52, 65)( 55, 61)( 56, 88)( 57, 81)
        ( 60, 64)( 63, 85)( 66, 72)( 67, 94)( 70, 76)( 71,101)( 74, 80)( 75,105)( 78, 84)( 79,109)( 82, 97)( 83,113)
        ( 86, 92)( 87, 98)( 90, 96)( 91,117)( 95,104)( 99,120)(100,114)(102,108)(103,118)(106,112)(107,123)(110,116)
        (111,124)(115,121)(119,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 37)(  8, 17)( 10, 21)( 11, 41)( 14, 20)( 15, 53)
        ( 16, 29)( 18, 33)( 19, 54)( 22, 28)( 23, 61)( 24, 45)( 26, 32)( 27, 65)( 30, 49)( 31, 69)( 34, 40)( 35, 77)
        ( 36, 55)( 38, 44)( 39, 81)( 42, 48)( 43, 85)( 46, 57)( 47, 89)( 50, 56)( 51, 80)( 52, 73)( 58, 64)( 59, 96)
        ( 60, 90)( 62, 68)( 63,100)( 66, 72)( 67,104)( 70, 76)( 71,108)( 74, 92)( 75,111)( 78, 84)( 79, 93)( 82, 88)
        ( 83,118)( 86, 91)( 87, 99)( 94,121)( 95,114)( 97,103)( 98,119)(101,107)(102,124)(105,110)(106,116)(109,113)
        (112,117)(115,122)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 72)( 31, 61)( 33, 39)( 34, 76)
        ( 37, 64)( 38, 77)( 41, 47)( 42, 87)( 43, 65)( 45, 51)( 46, 91)( 49, 55)( 50, 94)( 53, 59)( 54, 98)( 57, 63)
        ( 58,102)( 62, 68)( 66, 84)( 67, 80)( 69, 75)( 70,114)( 71,103)( 73, 79)( 74,115)( 78, 83)( 81,106)( 82,116)
        ( 85, 90)( 86,107)( 88, 93)( 89,119)( 92, 97)( 95,101)( 96,120)( 99,105)(100,122)(104,110)(108,118)(109,112)
        (111,117)(113,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 84)( 28, 56)( 30, 36)( 31, 88)( 34, 60)
        ( 35, 92)( 38, 43)( 39, 72)( 41, 47)( 42,101)( 45, 76)( 46,103)( 49, 55)( 50, 66)( 51, 77)( 53, 59)( 54, 62)
        ( 57, 80)( 58, 97)( 61, 67)( 63, 96)( 65, 71)( 69, 75)( 70, 78)( 73,100)( 74,105)( 79,104)( 81, 87)( 82,112)
        ( 83,107)( 85, 91)( 86,114)( 89, 95)( 90,118)( 93, 99)( 94,121)( 98,110)(102,106)(108,111)(109,122)(113,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 57)
        ( 35, 87)( 39, 44)( 40, 68)( 42, 72)( 43, 69)( 46, 52)( 47, 92)( 48, 73)( 50, 56)( 51, 98)( 54, 76)( 55,102)
        ( 58, 64)( 59, 74)( 60, 91)( 62, 67)( 63, 96)( 66, 71)( 70, 97)( 75, 95)( 77, 82)( 78,106)( 80, 86)( 81,111)
        ( 84, 90)( 85,113)( 88, 94)( 89,117)( 93,101)( 99,105)(100,118)(103,109)(104,121)(107,110)(108,122)(112,116)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 39)( 23, 35)( 26, 51)( 27, 47)( 29, 34)( 30, 63)( 32, 38)( 33, 72)( 36, 67)
        ( 37, 73)( 40, 46)( 41, 83)( 42, 68)( 44, 50)( 45, 86)( 48, 54)( 49, 90)( 52, 58)( 53, 94)( 56, 62)( 57, 98)
        ( 60, 66)( 61,102)( 64, 71)( 65,105)( 69, 79)( 70, 75)( 74, 78)( 76,109)( 77,106)( 80, 85)( 81,121)( 82,110)
        ( 84, 89)( 87, 93)( 88,122)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,104)(100,115)(103,108)(107,116)(111,117)
        (112,113)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 28)(  7, 16)(  9, 15)( 10, 40)( 11, 21)( 13, 19)( 14, 44)
        ( 17, 24)( 18, 48)( 22, 36)( 23, 32)( 25, 31)( 26, 63)( 27, 52)( 29, 35)( 30, 67)( 33, 56)( 34, 71)( 37, 43)
        ( 38, 83)( 39, 57)( 41, 47)( 42, 87)( 45, 51)( 46, 91)( 49, 55)( 50, 95)( 53, 60)( 54, 99)( 58, 79)( 59, 75)
        ( 61, 66)( 62,103)( 64, 70)( 65,112)( 68, 74)( 69,113)( 72, 78)( 73,105)( 76,107)( 77,101)( 80, 86)( 81,118)
        ( 82,108)( 84, 90)( 85,119)( 88, 94)( 89,122)( 92, 98)( 93,117)( 96,102)( 97,110)(100,106)(104,111)(109,114)
        (115,121)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 28)(  7, 16)(  9, 15)( 10, 40)( 11, 21)( 13, 19)( 14, 44)
        ( 17, 24)( 18, 48)( 22, 36)( 23, 32)( 25, 31)( 26, 64)( 27, 52)( 29, 35)( 30, 67)( 33, 56)( 34, 71)( 37, 43)
        ( 38, 83)( 39, 57)( 41, 47)( 42, 87)( 45, 51)( 46, 91)( 49, 55)( 50, 95)( 53, 60)( 54, 99)( 58, 79)( 59, 75)
        ( 61, 66)( 62,112)( 63,103)( 65, 70)( 68, 74)( 69,113)( 72, 78)( 73,105)( 76,107)( 77,101)( 80, 86)( 81,118)
        ( 82,108)( 84, 90)( 85,121)( 88, 94)( 89,122)( 92, 98)( 93,117)( 96,102)( 97,110)(100,106)(104,111)(109,114)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 22)(  4,  9)(  6, 12)(  7, 32)(  8, 17)( 10, 21)( 11, 36)( 14, 20)( 15, 48)
        ( 16, 25)( 18, 29)( 19, 52)( 23, 28)( 24, 40)( 26, 44)( 27, 60)( 30, 35)( 31, 56)( 33, 39)( 34, 68)( 37, 43)
        ( 38, 71)( 41, 59)( 42, 75)( 45, 51)( 46, 87)( 47, 63)( 49, 55)( 50, 91)( 53, 58)( 54, 95)( 57, 67)( 61, 66)
        ( 62, 79)( 64, 83)( 65,100)( 69, 74)( 70, 96)( 72, 78)( 73,108)( 76, 82)( 77,111)( 80, 99)( 81,115)( 84, 90)
        ( 85,122)( 86,103)( 88, 94)( 89,123)( 92, 98)( 93,120)( 97,107)(101,106)(102,116)(104,118)(105,113)(109,114)
        (110,121)(112,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 42)( 12, 21)( 14, 19)
        ( 15, 40)( 16, 32)( 18, 36)( 22, 33)( 23, 39)( 25, 31)( 26, 54)( 27, 46)( 29, 35)( 30, 58)( 34, 45)( 38, 41)
        ( 43, 49)( 44, 59)( 47, 50)( 48, 62)( 51, 57)( 52, 74)( 53, 66)( 55, 61)( 56, 78)( 60, 65)( 63, 69)( 64, 79)
        ( 67, 70)( 68, 82)( 71, 77)( 72, 94)( 73, 86)( 75, 81)( 76, 98)( 80, 85)( 83, 89)( 84, 99)( 87, 90)( 88,102)
        ( 91, 97)( 92,113)( 93,106)( 95,101)( 96,117)(100,105)(103,109)(104,118)(107,110)(108,121)(111,116)(112,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 37)(  8, 17)( 10, 21)( 11, 41)( 14, 20)( 15, 53)
        ( 16, 29)( 18, 33)( 19, 57)( 22, 28)( 23, 69)( 24, 45)( 26, 32)( 27, 70)( 30, 49)( 31, 73)( 34, 40)( 35, 85)
        ( 36, 61)( 38, 44)( 39, 89)( 42, 48)( 43, 93)( 46, 65)( 47, 97)( 50, 56)( 51,104)( 52, 77)( 54, 60)( 55,107)
        ( 58, 64)( 59,111)( 62, 81)( 63,112)( 66, 72)( 67,114)( 68, 98)( 71, 76)( 74, 80)( 75,115)( 78,100)( 79,118)
        ( 82, 88)( 83,102)( 84,109)( 86, 92)( 87,123)( 90, 96)( 91,120)( 94, 99)( 95,117)(101,106)(103,122)(105,110)
        (108,113)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)(118,119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 25, 31)( 26, 72)( 27, 52)( 29, 35)( 30, 73)( 33, 56)( 34, 76)
        ( 37, 43)( 38, 88)( 39, 65)( 41, 47)( 42, 92)( 45, 51)( 46, 96)( 49, 55)( 50,100)( 53, 68)( 54,101)( 57, 63)
        ( 58,108)( 59, 80)( 61, 67)( 62,111)( 66, 84)( 69, 75)( 70,114)( 71,102)( 74, 79)( 77, 83)( 78,115)( 81,104)
        ( 82,118)( 85, 91)( 86,106)( 87,112)( 89, 95)( 90,123)( 93, 99)( 94,120)( 97,103)( 98,117)(105,110)(107,122)
        (109,113)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 49)( 24, 45)( 26, 32)( 27, 78)( 28, 53)( 30, 36)( 31, 82)( 34, 56)
        ( 35, 86)( 38, 44)( 39, 94)( 40, 67)( 42, 48)( 43, 98)( 46, 70)( 47,102)( 51, 55)( 52, 71)( 54, 74)( 57, 62)
        ( 58,110)( 59, 87)( 61, 66)( 64, 69)( 65,111)( 68, 90)( 72, 77)( 73,103)( 75, 81)( 76,115)( 79, 85)( 80,117)
        ( 83, 89)( 84,121)( 88,106)( 91, 97)( 92,108)( 93,112)( 95,101)( 96,123)( 99,105)(100,119)(104,114)(107,113)
        (109,122)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96, 97)
        ( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 38, 44)( 39, 94)( 40, 67)( 42, 48)( 43, 98)( 46, 71)( 47,102)( 50, 55)( 51, 72)( 54, 75)( 57, 62)
        ( 58,110)( 59, 88)( 61, 66)( 64, 70)( 65,111)( 68, 91)( 69,112)( 73, 78)( 74,103)( 76, 82)( 77,115)( 80, 86)
        ( 81,117)( 84, 90)( 85,121)( 89,106)( 92, 97)( 93,108)( 95,101)( 96,123)( 99,105)(100,119)(104,114)(107,113)
        (109,122)(116,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 54)( 30, 36)( 31, 77)( 34, 57)
        ( 35, 80)( 38, 44)( 39, 91)( 40, 68)( 42, 48)( 43, 95)( 46, 52)( 47, 99)( 50, 56)( 51,103)( 55, 72)( 58, 64)
        ( 59,110)( 60, 84)( 62, 67)( 63,111)( 66, 71)( 69, 88)( 70,112)( 73, 79)( 74,114)( 75,104)( 78, 83)( 81, 87)
        ( 82,115)( 85,106)( 86,118)( 89, 94)( 90,108)( 92, 98)( 93,123)( 96,102)( 97,120)(100,105)(101,117)(107,113)
        (109,122)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 54)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 84)( 38, 44)( 39, 91)( 40, 68)( 42, 48)( 43, 95)( 46, 52)( 47, 99)( 50, 56)( 51,103)( 55, 72)( 58, 64)
        ( 59,110)( 60, 85)( 62, 67)( 63,111)( 66, 71)( 69, 88)( 70,112)( 73, 79)( 74,114)( 75,104)( 77, 83)( 78,117)
        ( 81, 87)( 82,121)( 86,106)( 89, 94)( 90,108)( 92, 98)( 93,123)( 96,102)( 97,119)(100,105)(101,116)(107,113)
        (109,122)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 48)( 24, 44)( 26, 31)( 27, 76)( 28, 53)( 30, 35)( 33, 56)( 34, 77)
        ( 37, 43)( 38, 87)( 39, 64)( 41, 47)( 42, 91)( 45, 68)( 46, 95)( 49, 55)( 50,103)( 51, 69)( 54, 72)( 57, 63)
        ( 58,110)( 59, 80)( 62, 67)( 65, 84)( 66,111)( 70, 99)( 71, 96)( 73, 79)( 74,117)( 75,104)( 78, 83)( 81,106)
        ( 82,118)( 85, 90)( 86,108)( 88, 94)( 89,122)( 92, 98)( 93,116)( 97,113)(100,105)(101,120)(102,114)(107,112)
        (109,121)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 37)(  8, 17)( 10, 21)( 11, 41)( 14, 20)( 15, 53)
        ( 16, 29)( 18, 33)( 19, 57)( 22, 28)( 23, 65)( 24, 45)( 26, 32)( 27, 69)( 30, 49)( 31, 73)( 34, 40)( 35, 84)
        ( 36, 58)( 38, 44)( 39, 88)( 42, 48)( 43, 92)( 46, 61)( 47, 96)( 50, 56)( 51,103)( 52, 76)( 54, 60)( 55,107)
        ( 59, 80)( 62, 68)( 63,110)( 64, 97)( 66, 72)( 67,114)( 70, 75)( 71,117)( 74, 79)( 77, 99)( 78,118)( 81, 87)
        ( 82,105)( 83,108)( 85, 91)( 86,101)( 89, 95)( 90,122)( 93, 98)( 94,113)(100,106)(102,121)(104,109)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 46)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 45)( 24, 41)( 26, 32)( 27, 77)( 28, 49)( 30, 36)( 31, 81)( 34, 53)
        ( 35, 85)( 39, 44)( 40, 65)( 42, 69)( 43, 93)( 47, 52)( 48, 70)( 50, 73)( 51,101)( 54, 60)( 55,107)( 56, 88)
        ( 58, 64)( 59,108)( 62, 68)( 63,105)( 66, 92)( 67,110)( 71,100)( 72, 96)( 74, 80)( 75,115)( 76, 98)( 78, 84)
        ( 79,118)( 82, 87)( 83,121)( 86, 91)( 89,103)( 90,122)( 94, 99)( 95,114)( 97,102)(104,109)(106,113)(111,117)
        (112,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 86)( 38, 44)( 39, 95)( 40, 68)( 42, 48)( 43, 98)( 46, 72)( 47,102)( 50, 55)( 51,110)( 52, 73)( 54, 59)
        ( 57, 75)( 58,111)( 61, 67)( 62, 70)( 63, 90)( 66, 71)( 69, 94)( 74,106)( 76, 82)( 77,113)( 78,108)( 80, 85)
        ( 81,117)( 84, 89)( 87, 93)( 88,118)( 91, 97)( 92,121)( 96,101)( 99,105)(100,122)(103,109)(104,116)(107,112)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 41)( 16, 32)( 18, 36)( 22, 43)( 23, 39)( 25, 31)( 26, 63)( 27, 51)( 29, 35)( 30, 67)( 33, 55)( 34, 71)
        ( 38, 42)( 40, 56)( 44, 50)( 45, 78)( 46, 57)( 48, 54)( 49, 82)( 52, 59)( 53, 86)( 58, 75)( 60, 66)( 61, 97)
        ( 62, 90)( 64, 70)( 65,101)( 68, 74)( 69,105)( 72, 77)( 73,109)( 76, 81)( 79, 85)( 80,110)( 83, 89)( 84,113)
        ( 87, 93)( 88,117)( 91, 94)( 92,121)( 95,100)( 96,122)( 98,104)( 99,123)(102,108)(103,119)(106,112)(107,115)
        (111,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 39)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 35)( 23, 31)( 26, 47)( 27, 43)( 30, 34)( 32, 59)( 33, 56)( 36, 42)( 37, 72)
        ( 38, 60)( 40, 46)( 41, 75)( 44, 63)( 45, 79)( 48, 54)( 49, 91)( 50, 64)( 52, 58)( 53, 95)( 57, 70)( 61, 71)
        ( 62, 67)( 65, 87)( 66, 83)( 68, 99)( 69, 96)( 73, 78)( 74,100)( 76, 82)( 77,111)( 80, 86)( 81,113)( 84,103)
        ( 85,117)( 88, 94)( 89,121)( 90,104)( 92, 98)( 93,122)( 97,109)(101,110)(102,106)(105,118)(107,115)(108,123)
        (112,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 46)( 23, 42)( 25, 31)( 26, 73)( 27, 54)( 29, 35)( 30, 77)( 33, 58)( 34, 81)
        ( 37, 41)( 38, 63)( 40, 45)( 43, 66)( 44, 64)( 47, 53)( 48, 86)( 49, 67)( 51, 57)( 52, 89)( 55, 69)( 56, 93)
        ( 59, 65)( 60, 68)( 61, 85)( 70, 76)( 71,102)( 72, 97)( 74, 80)( 75,105)( 78, 84)( 79,109)( 82, 88)( 83,113)
        ( 87, 92)( 90, 96)( 91,114)( 94,100)( 95,117)( 98,101)( 99,121)(103,108)(104,122)(106,112)(107,123)(110,116)
        (111,119)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 25, 31)( 26, 70)( 27, 52)( 29, 35)( 30, 74)( 33, 56)( 34, 78)
        ( 37, 43)( 38, 58)( 39, 64)( 41, 47)( 42, 83)( 45, 51)( 46, 86)( 49, 55)( 50, 90)( 53, 66)( 54, 94)( 57, 62)
        ( 59, 82)( 61, 65)( 67, 73)( 68,105)( 69, 98)( 71, 77)( 72,109)( 75, 81)( 76,110)( 79, 85)( 80,113)( 84, 89)
        ( 87, 93)( 88,114)( 91, 97)( 92,117)( 95,101)( 96,121)( 99,102)(100,122)(103,108)(104,123)(106,112)(107,119)
        (111,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 23)( 11, 44)( 12, 21)( 14, 19)
        ( 15, 51)( 16, 31)( 18, 35)( 22, 43)( 24, 30)( 25, 55)( 26, 45)( 28, 34)( 29, 59)( 32, 47)( 33, 63)( 36, 42)
        ( 37, 75)( 38, 52)( 40, 46)( 41, 58)( 48, 54)( 49, 83)( 50, 67)( 53, 71)( 56, 62)( 57, 76)( 60, 66)( 61, 87)
        ( 64, 70)( 65, 91)( 68, 79)( 69, 95)( 72, 78)( 73,107)( 74, 84)( 77, 90)( 80, 86)( 81,106)( 82, 99)( 85,103)
        ( 88, 94)( 89,108)( 92, 98)( 93,115)( 96,102)( 97,119)(100,111)(101,122)(104,110)(105,112)(109,118)(113,117)
        (114,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 40)( 26, 32)( 27, 76)( 28, 52)( 30, 36)( 31, 80)( 34, 56)
        ( 35, 84)( 39, 43)( 41, 68)( 42, 65)( 45, 51)( 46, 89)( 47, 69)( 49, 55)( 50, 95)( 53, 72)( 54, 99)( 57, 63)
        ( 58, 70)( 59, 88)( 61, 67)( 62, 93)( 66, 94)( 71, 92)( 73, 79)( 74,108)( 75,103)( 77, 83)( 78,109)( 81, 87)
        ( 82,111)( 85, 91)( 86,115)( 90, 98)( 96,102)( 97,116)(100,106)(101,119)(104,107)(105,122)(110,114)(112,118)
        (113,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 23)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 43)( 24, 30)( 25, 67)( 26, 51)( 28, 34)( 29, 71)( 32, 55)( 33, 75)( 36, 42)
        ( 37, 86)( 38, 60)( 40, 46)( 41, 90)( 44, 50)( 45, 94)( 48, 54)( 49, 98)( 52, 63)( 53, 99)( 56, 62)( 57,106)
        ( 58, 79)( 61, 83)( 64, 70)( 65,109)( 66,100)( 68, 74)( 69,113)( 72, 78)( 73,114)( 76, 82)( 77,117)( 80,102)
        ( 81,118)( 84, 89)( 85,107)( 87, 93)( 88,104)( 91, 97)( 92,122)( 95,101)( 96,112)(103,108)(105,121)(110,116)
        (111,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 57)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 49)( 29, 35)( 30, 73)( 33, 52)( 34, 76)
        ( 37, 43)( 38, 88)( 39, 60)( 41, 47)( 42, 91)( 45, 64)( 46, 95)( 50, 68)( 51, 65)( 53, 59)( 54, 62)( 55, 80)
        ( 58, 63)( 61, 84)( 66,102)( 67, 99)( 69, 75)( 70,109)( 71,103)( 74, 79)( 77, 83)( 78,110)( 81, 87)( 82,113)
        ( 85, 90)( 86,117)( 89, 94)( 92, 98)( 93,118)( 96,101)( 97,121)(100,105)(104,106)(107,112)(108,122)(111,116)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 28)(  7, 16)(  9, 15)( 10, 39)( 11, 21)( 13, 19)( 14, 43)
        ( 17, 24)( 18, 47)( 22, 35)( 23, 31)( 25, 30)( 26, 63)( 27, 51)( 29, 34)( 32, 55)( 33, 64)( 36, 42)( 37, 75)
        ( 38, 56)( 40, 46)( 41, 79)( 44, 50)( 45, 80)( 48, 54)( 49, 83)( 52, 59)( 53, 87)( 57, 71)( 58, 67)( 60, 66)
        ( 61,100)( 62, 91)( 65, 70)( 68, 95)( 69,101)( 72, 78)( 73,111)( 74, 96)( 76, 82)( 77,114)( 81, 86)( 84, 90)
        ( 85,115)( 88, 94)( 89,118)( 92, 99)( 93,122)( 97,107)( 98,103)(102,106)(104,110)(105,123)(108,113)(109,120)
        (112,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 28)(  7, 16)(  9, 15)( 10, 39)( 11, 21)( 13, 19)( 14, 43)
        ( 17, 24)( 18, 47)( 22, 35)( 23, 31)( 25, 30)( 26, 63)( 27, 51)( 29, 34)( 32, 55)( 33, 64)( 36, 42)( 37, 75)
        ( 38, 56)( 40, 46)( 41, 79)( 44, 50)( 45, 80)( 48, 54)( 49, 83)( 52, 59)( 53, 87)( 57, 71)( 58, 67)( 60, 66)
        ( 61,102)( 62, 91)( 65, 70)( 68, 94)( 69,103)( 72, 78)( 73,111)( 74, 95)( 76, 82)( 77,114)( 81, 86)( 84, 90)
        ( 85,115)( 88, 93)( 89,118)( 92, 98)( 96,110)( 97,106)( 99,105)(100,108)(101,119)(104,109)(107,122)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 43)( 26, 32)( 27, 80)( 28, 55)( 30, 36)( 31, 81)( 34, 59)
        ( 35, 83)( 38, 42)( 39, 71)( 41, 46)( 44, 75)( 45, 72)( 48, 54)( 49, 99)( 50, 76)( 52, 58)( 53,103)( 56, 79)
        ( 57,107)( 60, 66)( 61,111)( 62, 87)( 64, 70)( 65,115)( 68, 74)( 69,118)( 73, 94)( 77, 95)( 78, 91)( 82, 86)
        ( 84, 90)( 85,108)( 88, 97)( 89,121)( 92,113)( 93,119)( 96,102)( 98,114)(100,106)(101,122)(104,110)(105,123)
        (109,124)(112,117)(116,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 43)( 26, 32)( 27, 80)( 28, 55)( 30, 36)( 31, 81)( 34, 59)
        ( 35, 83)( 38, 42)( 39, 71)( 41, 46)( 44, 75)( 45, 72)( 48, 54)( 49, 99)( 50, 76)( 52, 58)( 53,102)( 56, 79)
        ( 57,106)( 60, 66)( 61,114)( 62, 87)( 64, 70)( 65,115)( 68, 74)( 69,118)( 73, 94)( 77, 95)( 78, 91)( 82, 86)
        ( 84, 90)( 85,107)( 88,110)( 89,121)( 92,112)( 93,119)( 96,101)( 97,122)( 98,113)(100,105)(103,109)(104,123)
        (108,124)(111,117)(116,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 62)( 16, 33)( 18, 37)( 19, 63)( 23, 48)( 24, 45)( 26, 32)( 27, 78)( 28, 55)( 30, 36)( 31, 82)( 34, 58)
        ( 35, 83)( 38, 44)( 39, 94)( 40, 66)( 42, 47)( 43, 98)( 46, 70)( 49, 54)( 50, 77)( 51, 71)( 53, 57)( 56, 74)
        ( 59, 65)( 60,110)( 61, 86)( 64, 69)( 67, 90)( 68,111)( 72,102)( 73, 99)( 75, 81)( 76,103)( 79, 85)( 80,117)
        ( 84, 89)( 87,106)( 88,118)( 91, 97)( 92,108)( 93,112)( 95,101)( 96,122)(100,114)(104,120)(105,115)(107,113)
        (109,121)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 75)( 33, 55)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 64)( 41, 47)( 42, 91)( 45, 51)( 46, 95)( 49, 54)( 50, 99)( 53, 67)( 56, 62)( 57,106)
        ( 58, 79)( 60, 66)( 61,107)( 65, 83)( 68, 74)( 69,110)( 70,100)( 72, 78)( 73,114)( 77, 82)( 80,102)( 81,115)
        ( 84, 90)( 85,104)( 86,108)( 88, 94)( 89,119)( 92, 98)( 93,122)( 96,101)( 97,113)(103,109)(105,118)(111,117)
        (112,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 74)( 33, 55)( 34, 78)
        ( 37, 43)( 38, 90)( 39, 64)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 54)( 50,102)( 53, 67)( 56, 62)( 57,109)
        ( 58, 82)( 60, 66)( 61,110)( 65, 86)( 68, 73)( 69,113)( 70,103)( 72, 77)( 75, 81)( 76,114)( 79, 85)( 80,117)
        ( 83,105)( 84,121)( 87, 93)( 88,107)( 89,111)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,104)(100,116)(106,112)
        (108,122)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 49)( 29, 35)( 30, 79)( 33, 52)( 34, 80)
        ( 37, 43)( 38, 88)( 39, 64)( 41, 47)( 42, 91)( 45, 68)( 46, 95)( 50, 71)( 51, 69)( 53, 59)( 54,106)( 55, 83)
        ( 57, 63)( 58,107)( 61, 67)( 62,108)( 65, 87)( 66,104)( 70, 99)( 72, 78)( 73,114)( 74,100)( 76, 82)( 77,118)
        ( 81, 86)( 84,102)( 85,119)( 89, 94)( 90,110)( 92, 98)( 93,123)( 96,101)( 97,117)(103,109)(105,113)(111,122)
        (112,120)(115,121)(116,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 49)( 29, 35)( 30, 78)( 33, 52)( 34, 82)
        ( 37, 43)( 38, 91)( 39, 64)( 41, 47)( 42, 94)( 45, 68)( 46, 98)( 50, 71)( 51, 69)( 53, 59)( 54,109)( 55, 86)
        ( 57, 63)( 58,110)( 61, 67)( 62,111)( 65, 90)( 66,107)( 70,102)( 72, 77)( 73,117)( 74,103)( 76, 81)( 79, 85)
        ( 80,118)( 83, 89)( 84,121)( 87,105)( 88,115)( 92, 97)( 93,113)( 95,101)( 96,123)( 99,104)(100,120)(106,112)
        (108,116)(114,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 49)( 29, 35)( 30, 79)( 33, 52)( 34, 83)
        ( 37, 43)( 38, 91)( 39, 64)( 41, 47)( 42, 94)( 45, 68)( 46, 98)( 50, 71)( 51, 69)( 53, 59)( 54,109)( 55, 87)
        ( 57, 63)( 58,110)( 61, 67)( 62,111)( 65, 90)( 66,107)( 70,102)( 72, 78)( 73,117)( 74,103)( 76, 82)( 77,118)
        ( 80, 86)( 81,121)( 84, 89)( 85,115)( 88,105)( 92, 97)( 93,113)( 95,101)( 96,123)( 99,104)(100,120)(106,112)
        (108,116)(114,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 65)( 41, 47)( 42, 95)( 45, 51)( 46, 99)( 49, 55)( 50,103)( 53, 59)( 54,107)( 57, 68)
        ( 58,108)( 61, 67)( 62, 90)( 63, 84)( 66, 88)( 69, 75)( 70,110)( 71,105)( 73, 79)( 74,114)( 77, 83)( 78,115)
        ( 81, 87)( 82,118)( 85, 93)( 86,121)( 89, 94)( 92, 98)( 96,102)( 97,122)(100,106)(101,113)(104,109)(111,117)
        (112,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 65)( 41, 47)( 42, 95)( 45, 51)( 46, 99)( 49, 55)( 50,103)( 53, 59)( 54,107)( 57, 68)
        ( 58,108)( 61, 67)( 62, 90)( 63, 84)( 66, 88)( 69, 75)( 70,110)( 71,105)( 73, 79)( 74,114)( 77, 83)( 78,117)
        ( 81, 87)( 82,118)( 85, 93)( 86,121)( 89, 94)( 92, 98)( 96,102)( 97,122)(100,106)(101,113)(104,109)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 52)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 38, 43)( 39, 67)( 41, 47)( 42, 96)( 45, 71)( 46, 99)( 50, 55)( 51, 72)( 53, 75)( 54,108)( 57, 62)
        ( 58, 65)( 59, 91)( 61, 66)( 64, 70)( 68, 95)( 69, 92)( 73,107)( 74,103)( 76, 82)( 77,114)( 78,105)( 80, 86)
        ( 81,118)( 84, 90)( 85,119)( 88, 94)( 89,122)( 93,113)( 97,102)( 98,110)(100,106)(101,117)(104,109)(111,116)
        (112,123)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 52)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 38, 43)( 39, 67)( 41, 47)( 42, 96)( 45, 71)( 46, 99)( 50, 55)( 51, 72)( 53, 75)( 54,108)( 57, 62)
        ( 58, 65)( 59, 91)( 61, 66)( 64, 70)( 68, 95)( 69, 92)( 73,107)( 74,103)( 76, 82)( 77,114)( 78,105)( 80, 86)
        ( 81,118)( 84, 90)( 85,121)( 88, 94)( 89,122)( 93,113)( 97,102)( 98,110)(100,106)(101,117)(104,109)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 46)( 23, 42)( 25, 31)( 26, 74)( 27, 54)( 29, 35)( 30, 78)( 33, 58)( 34, 82)
        ( 37, 41)( 38, 63)( 40, 45)( 43, 66)( 44, 64)( 47, 53)( 48, 93)( 49, 67)( 51, 57)( 52, 97)( 55, 70)( 56,101)
        ( 59, 65)( 60, 69)( 61, 86)( 68, 90)( 71, 77)( 72,110)( 73,105)( 75, 81)( 76,111)( 79, 85)( 80,113)( 83, 89)
        ( 84,117)( 87, 92)( 88,121)( 91, 96)( 94,100)( 95,122)( 98,104)( 99,123)(102,108)(103,119)(106,109)(107,115)
        (112,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 46)( 23, 42)( 25, 31)( 26, 74)( 27, 54)( 29, 35)( 30, 78)( 33, 58)( 34, 82)
        ( 37, 41)( 38, 63)( 40, 45)( 43, 66)( 44, 64)( 47, 53)( 48, 94)( 49, 67)( 51, 57)( 52, 97)( 55, 70)( 56,101)
        ( 59, 65)( 60, 69)( 61, 86)( 68, 90)( 71, 77)( 72,110)( 73,105)( 75, 81)( 76,111)( 79, 85)( 80,113)( 83, 89)
        ( 84,117)( 87, 93)( 88,121)( 91, 96)( 92,122)( 95,100)( 98,104)( 99,123)(102,108)(103,119)(106,109)(107,115)
        (112,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 42)( 26, 32)( 27, 77)( 28, 53)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 84)( 38, 44)( 39, 95)( 40, 68)( 43, 72)( 46, 52)( 47,103)( 48, 73)( 50, 56)( 51,106)( 54, 76)( 55,110)
        ( 58, 64)( 59, 94)( 60, 88)( 62, 67)( 63, 70)( 66, 71)( 69, 92)( 74, 99)( 75, 96)( 78, 83)( 79,114)( 81, 87)
        ( 82,118)( 85, 91)( 86,121)( 89, 97)( 90,102)( 93, 98)(100,105)(101,122)(104,109)(107,113)(108,123)(111,116)
        (112,120)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 42)( 26, 32)( 27, 76)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 38, 44)( 39, 91)( 40, 66)( 43, 68)( 46, 52)( 47, 95)( 48, 69)( 50, 56)( 51, 99)( 54, 72)( 55,103)
        ( 58, 64)( 59, 93)( 60, 87)( 62, 67)( 63, 94)( 70, 88)( 71, 92)( 73, 78)( 74,114)( 75,107)( 77, 82)( 80, 86)
        ( 81,115)( 84, 90)( 85,118)( 89, 98)( 96,102)( 97,119)(100,106)(101,122)(104,109)(105,113)(108,110)(111,117)
        (112,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 47)
        ( 15, 31)( 17, 35)( 18, 51)( 22, 26)( 23, 40)( 25, 30)( 28, 34)( 29, 41)( 32, 43)( 33, 37)( 36, 42)( 38, 55)
        ( 44, 50)( 45, 63)( 46, 56)( 48, 54)( 49, 67)( 52, 58)( 53, 71)( 57, 59)( 60, 66)( 61, 79)( 62, 72)( 64, 70)
        ( 65, 83)( 68, 74)( 69, 87)( 73, 75)( 76, 82)( 77, 95)( 78, 88)( 80, 86)( 81, 99)( 84, 90)( 85,103)( 89, 91)
        ( 92, 98)( 93,111)( 94,104)( 96,102)( 97,115)(100,106)(101,119)(105,107)(108,114)(109,122)(110,120)(112,118)
        (113,123)(116,121)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 54)( 34, 40)( 35, 84)
        ( 36, 68)( 38, 44)( 39, 88)( 42, 72)( 43, 89)( 46, 52)( 47,100)( 48, 73)( 50, 56)( 51,103)( 55, 79)( 58, 64)
        ( 59,111)( 60, 76)( 62, 67)( 63,115)( 66, 71)( 69, 80)( 70,116)( 74, 96)( 75, 92)( 77,107)( 78,104)( 81, 87)
        ( 82,121)( 83,113)( 85, 91)( 86, 94)( 90, 95)( 93,118)( 97,102)( 98,123)( 99,119)(101,106)(105,124)(108,114)
        (109,120)(110,122)(112,117),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 40)( 23, 36)( 26, 47)( 27, 43)( 29, 35)( 30, 71)( 31, 59)( 33, 39)( 34, 75)
        ( 37, 45)( 38, 66)( 42, 46)( 44, 63)( 48, 54)( 49, 79)( 50, 64)( 52, 58)( 53, 83)( 56, 62)( 57, 87)( 60, 67)
        ( 61, 91)( 65, 76)( 68, 74)( 69,100)( 70, 95)( 72, 78)( 73,103)( 77, 82)( 80, 86)( 81,104)( 84, 90)( 85,107)
        ( 88, 94)( 89,111)( 92, 98)( 93,114)( 96, 99)( 97,118)(101,106)(102,121)(105,110)(108,113)(109,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 24)(  4,  9)(  6, 11)(  7, 23)(  8, 16)( 10, 20)( 13, 19)( 14, 39)( 15, 27)
        ( 17, 31)( 18, 43)( 21, 26)( 22, 32)( 25, 30)( 28, 35)( 29, 33)( 34, 47)( 36, 42)( 37, 55)( 38, 48)( 40, 46)
        ( 41, 59)( 44, 50)( 45, 63)( 49, 51)( 52, 58)( 53, 71)( 54, 64)( 56, 62)( 57, 75)( 60, 66)( 61, 79)( 65, 67)
        ( 68, 74)( 69, 87)( 70, 80)( 72, 78)( 73, 91)( 76, 82)( 77, 95)( 81, 83)( 84, 90)( 85,103)( 86, 96)( 88, 94)
        ( 89,107)( 92, 98)( 93,111)( 97, 99)(100,106)(101,119)(102,112)(104,110)(105,122)(108,114)(109,118)(113,115)
        (116,121)(117,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 43)( 23, 40)( 25, 30)( 26, 71)( 27, 51)( 29, 34)( 32, 55)( 33, 72)( 36, 42)
        ( 37, 83)( 38, 60)( 41, 63)( 44, 50)( 45, 91)( 46, 64)( 48, 54)( 49, 95)( 52, 67)( 53, 99)( 56, 62)( 57,106)
        ( 58, 75)( 61, 79)( 65, 87)( 66, 84)( 68, 74)( 69,110)( 70,100)( 73, 78)( 76,102)( 77,111)( 80, 86)( 81,121)
        ( 82,107)( 85, 90)( 88, 94)( 89,122)( 92, 98)( 93,116)( 96,101)( 97,113)(103,109)(104,120)(105,114)(108,118)
        (112,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 35)( 22, 43)( 23, 40)( 25, 31)( 26, 71)( 27, 51)( 29, 34)( 30, 75)( 33, 55)( 36, 42)
        ( 37, 83)( 38, 60)( 41, 63)( 44, 50)( 45, 88)( 46, 64)( 48, 54)( 49, 91)( 52, 67)( 53, 95)( 56, 62)( 57,102)
        ( 58, 76)( 61, 79)( 65, 87)( 66, 84)( 68, 74)( 69,110)( 70, 96)( 72, 78)( 73,114)( 77, 98)( 80, 86)( 81,121)
        ( 82,103)( 85,106)( 89, 94)( 90,107)( 92, 97)( 93,113)( 99,105)(100,120)(101,115)(104,118)(108,112)(109,122)
        (111,117)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 35)(  8, 17)( 10, 21)( 11, 39)( 14, 20)( 15, 51)
        ( 16, 28)( 18, 32)( 19, 55)( 22, 27)( 23, 67)( 24, 43)( 26, 31)( 29, 47)( 30, 68)( 33, 38)( 34, 59)( 36, 42)
        ( 37, 76)( 40, 46)( 41, 79)( 44, 63)( 45, 83)( 48, 54)( 49, 94)( 50, 71)( 52, 58)( 53, 97)( 56, 62)( 57,101)
        ( 60, 75)( 61,105)( 64, 70)( 65,113)( 66, 87)( 69, 74)( 72, 90)( 73,114)( 77, 82)( 78,106)( 80, 86)( 81,122)
        ( 84, 89)( 85,112)( 88,109)( 91, 96)( 92, 99)( 93,117)( 95,100)( 98,104)(102,108)(103,118)(107,121)(110,116)
        (111,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 47)( 24, 43)( 26, 32)( 27, 75)( 28, 55)( 30, 36)( 31, 79)( 34, 59)
        ( 35, 83)( 38, 42)( 39, 64)( 41, 46)( 44, 67)( 45, 65)( 48, 54)( 49, 87)( 50, 68)( 52, 58)( 53, 91)( 56, 71)
        ( 57, 95)( 61, 66)( 62, 70)( 69, 84)( 72, 78)( 73,105)( 74, 98)( 76, 82)( 77,109)( 80, 86)( 81,113)( 85, 90)
        ( 88, 94)( 89,114)( 92, 97)( 93,117)( 96,101)( 99,102)(100,118)(103,108)(104,121)(106,112)(107,122)(110,116)
        (111,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 44)( 24, 40)( 26, 32)( 27, 70)( 28, 52)( 30, 36)( 31, 74)( 34, 56)
        ( 35, 78)( 39, 43)( 41, 58)( 42, 64)( 45, 51)( 46, 79)( 47, 59)( 49, 55)( 50, 82)( 53, 66)( 54, 86)( 57, 62)
        ( 61, 65)( 67, 73)( 68, 97)( 69, 90)( 71, 77)( 72,101)( 75, 81)( 76,105)( 80, 85)( 83, 89)( 84,106)( 87, 93)
        ( 88,109)( 91, 94)( 92,113)( 95,100)( 96,117)( 98,104)( 99,118)(102,108)(103,121)(107,112)(110,116)(111,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 86)( 34, 60)
        ( 35, 90)( 38, 43)( 39, 46)( 40, 71)( 42, 47)( 45, 74)( 49, 55)( 50, 62)( 51, 75)( 53, 59)( 54, 95)( 57, 78)
        ( 58, 98)( 61, 67)( 63, 94)( 65, 70)( 66, 76)( 69, 73)( 72, 77)( 79, 85)( 80,107)( 81,102)( 83, 89)( 84,109)
        ( 87, 93)( 88,113)( 91, 97)( 92,117)( 96,101)( 99,105)(100,118)(103,106)(104,121)(108,112)(110,116)(111,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 52)( 16, 28)( 18, 32)( 19, 56)( 23, 40)( 26, 31)( 27, 45)( 29, 48)( 30, 65)( 33, 39)( 34, 76)( 35, 60)
        ( 37, 43)( 38, 70)( 41, 47)( 42, 67)( 46, 64)( 49, 55)( 50, 80)( 51, 68)( 53, 59)( 54, 84)( 57, 63)( 58, 88)
        ( 61, 72)( 62, 92)( 66, 71)( 69, 77)( 73, 79)( 74,103)( 75, 96)( 78, 83)( 81, 87)( 82,104)( 85, 91)( 86,107)
        ( 89, 95)( 90,111)( 93, 99)( 94,115)( 97,100)( 98,118)(101,106)(102,121)(105,110)(108,114)(109,122)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 74)( 27, 56)( 29, 35)( 30, 78)( 33, 60)( 34, 82)
        ( 37, 43)( 38, 90)( 39, 65)( 41, 47)( 42, 94)( 45, 67)( 46, 95)( 49, 55)( 50, 97)( 51, 68)( 53, 59)( 54,101)
        ( 57, 71)( 58,105)( 61, 66)( 62, 93)( 63, 86)( 69, 87)( 70, 92)( 72, 77)( 73,109)( 75, 81)( 76,110)( 79, 85)
        ( 80,113)( 83, 89)( 84,117)( 88,100)( 91, 96)( 98,104)( 99,118)(102,108)(103,121)(106,112)(107,122)(111,116)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 43)( 15, 21)
        ( 17, 24)( 18, 47)( 22, 39)( 23, 36)( 25, 31)( 26, 63)( 27, 51)( 29, 35)( 30, 67)( 33, 38)( 34, 58)( 37, 55)
        ( 40, 46)( 41, 71)( 42, 56)( 44, 50)( 45, 75)( 48, 54)( 49, 79)( 52, 59)( 53, 83)( 57, 68)( 60, 66)( 61, 94)
        ( 62, 87)( 64, 70)( 65, 98)( 69, 74)( 72, 78)( 73, 99)( 76, 82)( 77,102)( 80, 86)( 81,106)( 84, 90)( 85,110)
        ( 88, 91)( 89,114)( 92, 97)( 93,115)( 95,101)( 96,119)(100,105)(103,109)(104,120)(107,113)(108,122)(111,117)
        (112,123)(116,118)(121,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 11)(  3,  8)(  5, 10)(  6, 22)(  7, 15)(  9, 19)( 12, 18)( 13, 27)( 14, 20)( 16, 23)
        ( 17, 31)( 21, 24)( 25, 30)( 26, 35)( 28, 34)( 29, 40)( 32, 38)( 33, 43)( 36, 39)( 37, 47)( 41, 46)( 42, 51)
        ( 44, 50)( 45, 56)( 48, 54)( 49, 59)( 52, 55)( 53, 63)( 57, 62)( 58, 67)( 60, 66)( 61, 72)( 64, 70)( 65, 75)
        ( 68, 71)( 69, 79)( 73, 78)( 74, 83)( 76, 82)( 77, 88)( 80, 86)( 81, 91)( 84, 87)( 85, 95)( 89, 94)( 90, 99)
        ( 92, 98)( 93,104)( 96,102)( 97,107)(100,103)(101,111)(105,110)(106,115)(108,114)(109,120)(112,118)(113,122)
        (116,119)(117,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 47)( 24, 44)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 55)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 67)( 41, 46)( 42, 95)( 45, 71)( 48, 54)( 49, 78)( 50, 72)( 53, 75)( 56, 62)( 57,103)
        ( 58, 83)( 60, 66)( 61,107)( 64, 70)( 65,111)( 68, 87)( 69,115)( 73, 81)( 74, 96)( 77, 82)( 80, 86)( 84, 99)
        ( 85, 97)( 88, 94)( 89,101)( 90,118)( 92, 98)( 93,102)(100,106)(104,110)(105,119)(108,114)(109,122)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 41)( 26, 31)( 27, 52)( 29, 35)( 30, 77)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 92)( 39, 68)( 42, 72)( 45, 51)( 46, 99)( 47, 73)( 49, 55)( 50,103)( 53, 76)( 54,107)( 57, 63)
        ( 58,114)( 59, 84)( 61, 67)( 62,118)( 65, 71)( 66,122)( 69, 88)( 70,123)( 74, 96)( 75, 93)( 78, 83)( 79,108)
        ( 81, 87)( 82,105)( 85,110)( 86,101)( 89, 95)( 90,116)( 91,120)( 94,112)( 97,102)( 98,113)(100,106)(104,109)
        (111,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 25, 31)( 26, 74)( 27, 52)( 29, 35)( 30, 78)( 33, 55)( 34, 82)
        ( 37, 43)( 38, 90)( 39, 67)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 54)( 50,102)( 53, 70)( 56, 62)( 57,109)
        ( 58, 83)( 60, 66)( 61,113)( 64, 69)( 65,114)( 68, 86)( 71, 77)( 72,117)( 73,103)( 75, 81)( 76,118)( 79, 85)
        ( 80,121)( 84,105)( 87, 93)( 88,111)( 89,115)( 91, 97)( 92,107)( 95,101)( 96,123)( 99,104)(100,120)(106,112)
        (108,122)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 74)( 27, 49)( 29, 35)( 30, 78)( 33, 52)( 34, 82)
        ( 37, 43)( 38, 90)( 39, 63)( 41, 47)( 42, 94)( 45, 67)( 46, 98)( 50, 70)( 51, 68)( 53, 59)( 54,109)( 55, 83)
        ( 57, 62)( 58,113)( 61, 66)( 64, 86)( 65,114)( 69,102)( 71, 77)( 72,117)( 73,103)( 75, 81)( 76,118)( 79, 85)
        ( 80,121)( 84,105)( 87, 93)( 88,111)( 89,115)( 91, 97)( 92,107)( 95,101)( 96,123)( 99,104)(100,120)(106,112)
        (108,122)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 74)( 28, 54)( 30, 36)( 31, 77)( 34, 57)
        ( 35, 81)( 38, 44)( 39, 93)( 40, 69)( 42, 48)( 43, 97)( 46, 52)( 47,101)( 50, 56)( 51,105)( 55, 73)( 58, 64)
        ( 59,111)( 60, 85)( 62, 68)( 63,115)( 66, 72)( 67,118)( 70, 89)( 71,121)( 75, 80)( 76,106)( 78, 84)( 79,103)
        ( 82, 88)( 83, 99)( 86,108)( 87, 95)( 90, 96)( 91,110)( 92,122)( 94,100)( 98,104)(102,107)(109,114)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107)(108,109,110)(111,112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 31)( 18, 35)( 19, 63)( 23, 43)( 25, 30)( 26, 51)( 28, 34)( 29, 72)( 32, 55)( 33, 75)( 36, 42)
        ( 37, 87)( 38, 67)( 40, 46)( 41, 91)( 44, 50)( 45, 95)( 48, 54)( 49, 99)( 52, 71)( 53,100)( 56, 62)( 57,107)
        ( 58, 79)( 60, 66)( 61,111)( 64, 70)( 65,115)( 68, 83)( 69,118)( 73, 78)( 74,101)( 76, 82)( 77, 97)( 80,103)
        ( 81, 93)( 84, 90)( 85,105)( 86,121)( 88, 94)( 89,106)( 92, 98)( 96,102)(104,110)(108,114)(109,122)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 37)( 19, 63)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 38, 44)( 39, 99)( 40, 67)( 42, 48)( 43,103)( 46, 71)( 47,107)( 50, 55)( 51, 72)( 54, 75)( 57, 62)
        ( 58, 91)( 60, 66)( 61,112)( 64, 70)( 65,115)( 68, 95)( 69,118)( 73, 78)( 74,108)( 76, 82)( 77,109)( 80, 86)
        ( 81,105)( 84, 90)( 85,101)( 88, 94)( 89, 97)( 92,111)( 93,122)( 96,102)( 98,121)(100,106)(104,110)(113,117)
        (114,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 76)( 28, 54)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 84)( 38, 44)( 39, 96)( 40, 68)( 42, 48)( 43,100)( 46, 52)( 47,104)( 50, 56)( 51,108)( 55, 72)( 58, 63)
        ( 59, 88)( 61, 67)( 62,112)( 65, 71)( 66,115)( 69, 92)( 70,118)( 73, 79)( 74,106)( 75,109)( 77, 83)( 78,102)
        ( 81, 87)( 82, 98)( 85, 91)( 86, 94)( 89,111)( 90,123)( 93, 99)( 95,122)( 97,103)(101,107)(105,110)(113,117)
        (114,120)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 25, 31)( 26, 73)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 92)( 39, 68)( 41, 47)( 42, 96)( 45, 51)( 46,100)( 49, 55)( 50,104)( 53, 72)( 54,105)( 57, 63)
        ( 58,109)( 59, 84)( 61, 67)( 62,112)( 65, 71)( 66,116)( 69, 88)( 70,119)( 74, 79)( 75,106)( 77, 83)( 78,102)
        ( 81, 87)( 82, 98)( 85,108)( 86, 94)( 89, 95)( 90,111)( 91,122)( 93, 99)( 97,103)(101,107)(110,115)(113,118)
        (114,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114,115)(116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 29)( 18, 33)( 19, 60)( 23, 41)( 24, 38)( 27, 32)( 28, 49)( 30, 53)( 31, 72)( 34, 40)( 35, 83)
        ( 36, 64)( 39, 67)( 42, 48)( 43, 88)( 44, 68)( 46, 52)( 47, 91)( 50, 71)( 51, 95)( 54, 59)( 55,106)( 56, 75)
        ( 58, 63)( 61, 66)( 62,107)( 65, 79)( 69, 87)( 70, 84)( 73, 78)( 74, 99)( 76,102)( 77,115)( 80, 86)( 81,122)
        ( 82,108)( 85,110)( 89, 94)( 90,111)( 92, 98)( 93,120)( 96,101)( 97,117)(100,114)(103,109)(104,124)(105,118)
        (112,119)(113,123)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 12)(  7, 35)(  8, 17)( 10, 21)( 11, 39)( 14, 20)( 15, 51)
        ( 16, 28)( 18, 32)( 19, 55)( 22, 27)( 23, 67)( 24, 43)( 26, 31)( 29, 47)( 30, 68)( 33, 38)( 34, 59)( 36, 42)
        ( 37, 76)( 40, 46)( 41, 79)( 44, 63)( 45, 83)( 48, 54)( 49, 95)( 50, 71)( 52, 58)( 53, 99)( 56, 62)( 57,103)
        ( 60, 75)( 61,107)( 64, 70)( 65, 73)( 66, 87)( 69, 74)( 72, 91)( 77, 82)( 78,110)( 80, 86)( 81,115)( 84, 90)
        ( 85,118)( 88, 94)( 89,122)( 92, 98)( 93,123)( 96,102)( 97,120)(100,106)(101,117)(104,109)(105,112)(108,113)
        (111,114)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 29)( 17, 32)( 18, 56)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 45)( 30, 48)( 33, 39)( 34, 80)( 35, 60)
        ( 37, 43)( 38, 84)( 41, 64)( 42, 88)( 46, 68)( 47, 65)( 49, 55)( 50,101)( 51, 73)( 53, 59)( 54,105)( 57, 63)
        ( 58,109)( 61, 76)( 62,110)( 66, 94)( 67, 91)( 69, 75)( 70,121)( 71, 95)( 74, 97)( 77, 83)( 78, 99)( 79,113)
        ( 81, 87)( 82,123)( 85, 90)( 86,120)( 89, 93)( 92,117)( 96,118)( 98,104)(100,122)(102,108)(103,114)(106,112)
        (107,115)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 32)( 17, 36)( 18, 56)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 45)( 29, 35)( 30, 76)( 33, 48)( 34, 77)
        ( 38, 43)( 39, 60)( 41, 64)( 42, 85)( 46, 68)( 47, 65)( 49, 55)( 50, 98)( 51, 80)( 53, 59)( 54,102)( 57, 63)
        ( 58,103)( 61, 84)( 62,106)( 66, 91)( 67, 88)( 69, 75)( 70,118)( 71, 92)( 73, 79)( 74,122)( 78, 83)( 81, 94)
        ( 82,123)( 86, 90)( 87,110)( 89,114)( 93,115)( 95,101)( 96,112)( 97,120)( 99,105)(100,108)(104,109)(107,113)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 28)( 17, 32)( 18, 56)( 22, 44)( 23, 40)( 26, 31)( 27, 45)( 29, 48)( 30, 69)( 33, 39)( 34, 77)( 35, 60)
        ( 37, 43)( 38, 80)( 41, 64)( 42, 84)( 46, 68)( 47, 65)( 49, 55)( 50, 98)( 51, 72)( 53, 59)( 54,102)( 57, 63)
        ( 58,105)( 61, 76)( 62,109)( 66, 91)( 67, 88)( 70, 75)( 71, 92)( 73, 94)( 74,119)( 78, 83)( 79,113)( 81, 87)
        ( 82,114)( 85, 90)( 86,123)( 89,117)( 93,118)( 95,101)( 96,111)( 97,121)( 99,104)(100,107)(103,108)(106,112)
        (110,116)(115,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 32)( 17, 36)( 18, 57)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 49)( 29, 35)( 30, 75)( 33, 52)( 34, 79)
        ( 37, 43)( 38, 84)( 39, 60)( 41, 47)( 42, 87)( 45, 64)( 46, 91)( 50, 68)( 51, 65)( 53, 59)( 54,105)( 55, 80)
        ( 58, 63)( 61, 83)( 62,106)( 66, 98)( 67, 95)( 69, 74)( 70,117)( 71, 99)( 73, 78)( 76, 82)( 77,118)( 81,101)
        ( 85, 90)( 86,109)( 88, 94)( 89,110)( 92, 97)( 93,121)( 96,113)(100,114)(102,108)(103,123)(104,119)(107,112)
        (111,124)(115,120)(116,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 77)( 28, 54)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 84)( 38, 44)( 39, 96)( 40, 69)( 42, 48)( 43,100)( 46, 73)( 47,104)( 50, 56)( 51,109)( 52, 74)( 55, 76)
        ( 58, 64)( 59,115)( 60, 88)( 62, 68)( 63,118)( 66, 72)( 67,122)( 70, 92)( 71,123)( 75,108)( 78, 83)( 79,110)
        ( 81, 87)( 82,106)( 85, 91)( 86,102)( 89,112)( 90, 98)( 93, 99)( 94,114)( 95,120)( 97,103)(101,107)(105,111)
        (113,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 52)( 29, 35)( 30, 77)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 92)( 39, 68)( 41, 47)( 42, 96)( 45, 72)( 46,100)( 50, 55)( 51, 73)( 53, 76)( 54, 74)( 57, 63)
        ( 58,111)( 59, 84)( 61, 67)( 62,115)( 65, 71)( 66,118)( 69, 88)( 70,119)( 75,104)( 78, 83)( 79,105)( 81, 87)
        ( 82,102)( 85,107)( 86, 98)( 89, 95)( 90,109)( 91,122)( 93, 99)( 94,110)( 97,103)(101,106)(108,114)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 57)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 99)( 40, 71)( 42, 48)( 43,103)( 46, 52)( 47,107)( 50, 56)( 51,111)( 54, 59)( 55,112)
        ( 58, 75)( 61, 66)( 62, 91)( 64, 70)( 65,116)( 68, 74)( 69,118)( 72, 95)( 73,119)( 76, 82)( 77,109)( 78,113)
        ( 80, 86)( 81,105)( 84, 90)( 85,101)( 88, 94)( 89, 97)( 92,115)( 93,123)( 96,102)( 98,122)(100,106)(104,110)
        (108,114)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 53)( 29, 35)( 30, 77)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 89)( 39, 68)( 41, 47)( 42, 92)( 45, 72)( 46, 96)( 49, 55)( 50,104)( 51, 73)( 54, 76)( 57, 63)
        ( 58,111)( 59, 84)( 61, 67)( 62,115)( 65, 71)( 66,116)( 69, 88)( 70,113)( 74,100)( 75, 97)( 78, 83)( 79,105)
        ( 81, 87)( 82,102)( 85,107)( 86,120)( 90, 95)( 91,109)( 93, 99)( 94,123)( 98,118)(101,106)(103,119)(108,114)
        (110,122)(112,117)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 62)( 23, 43)( 25, 31)( 26, 74)( 27, 51)( 29, 35)( 30, 78)( 33, 55)( 34, 81)
        ( 37, 42)( 38, 93)( 39, 66)( 41, 46)( 44, 50)( 45, 94)( 48, 54)( 49, 97)( 52, 70)( 53,101)( 56, 61)( 57,109)
        ( 58, 85)( 60, 65)( 63, 69)( 64,110)( 67, 89)( 68,111)( 71, 77)( 72,117)( 73,102)( 75, 80)( 76,121)( 79, 84)
        ( 82, 88)( 83,122)( 86,105)( 87,123)( 90, 96)( 91,115)( 92,107)( 95,100)( 98,104)( 99,116)(103,113)(106,112)
        (108,119)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 43)( 25, 31)( 26, 74)( 27, 51)( 29, 35)( 30, 78)( 33, 55)( 34, 82)
        ( 37, 42)( 38, 93)( 39, 66)( 41, 46)( 44, 50)( 45, 94)( 48, 54)( 49, 97)( 52, 70)( 53,101)( 56, 62)( 57,109)
        ( 58, 85)( 60, 65)( 61,110)( 64, 69)( 67, 89)( 68,111)( 71, 77)( 72,117)( 73,102)( 75, 81)( 76,121)( 79, 84)
        ( 80,122)( 83, 88)( 86,105)( 87,123)( 90, 96)( 91,115)( 92,107)( 95,100)( 98,104)( 99,116)(103,113)(106,112)
        (108,119)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 67)( 42, 47)( 45, 71)( 46, 99)( 49, 55)( 50,106)( 51, 72)( 54, 75)( 57, 62)
        ( 58,113)( 59, 90)( 61, 66)( 64, 70)( 65,114)( 68, 94)( 69,115)( 73,102)( 74,100)( 76, 82)( 77,117)( 78,107)
        ( 80, 85)( 81,121)( 84, 89)( 87, 93)( 88,122)( 91,109)( 92,123)( 95,101)( 96,105)( 97,111)(103,108)(104,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 67)( 42, 47)( 45, 71)( 46, 99)( 49, 55)( 50,106)( 51, 72)( 54, 75)( 57, 63)
        ( 58,113)( 59, 90)( 61, 66)( 62,114)( 65, 70)( 68, 94)( 69,115)( 73,102)( 74,100)( 76, 82)( 77,117)( 78,107)
        ( 80, 85)( 81,121)( 84, 89)( 87, 93)( 88,122)( 91,109)( 92,123)( 95,101)( 96,105)( 97,111)(103,108)(104,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 59)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 71)( 32, 51)( 33, 74)( 36, 42)
        ( 37, 86)( 38, 62)( 40, 46)( 41, 89)( 44, 66)( 45, 93)( 49, 70)( 50, 67)( 52, 58)( 53,109)( 54, 78)( 56, 61)
        ( 57,110)( 60, 65)( 63, 82)( 64,111)( 68,101)( 69, 97)( 72, 77)( 73,102)( 75, 81)( 76,114)( 79,105)( 80,117)
        ( 83, 88)( 84,122)( 85,107)( 87, 92)( 90, 96)( 91,123)( 94,100)( 95,119)( 98,104)( 99,116)(103,113)(106,112)
        (108,121)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 31)( 17, 35)( 18, 59)( 22, 47)( 23, 43)( 25, 30)( 26, 48)( 28, 34)( 29, 71)( 32, 51)( 33, 74)( 36, 42)
        ( 37, 86)( 38, 62)( 40, 46)( 41, 90)( 44, 66)( 45, 94)( 49, 70)( 50, 67)( 52, 58)( 53, 85)( 54, 78)( 56, 61)
        ( 57, 64)( 60, 65)( 63, 82)( 68,102)( 69, 98)( 72, 77)( 73,103)( 75, 81)( 76,111)( 79,106)( 80,114)( 83, 89)
        ( 84,107)( 87, 93)( 88,122)( 91, 97)( 92,120)( 95,101)( 96,116)( 99,105)(100,113)(104,110)(108,124)(109,118)
        (112,117)(115,121)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 39)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 68)( 27, 53)( 29, 35)( 30, 72)( 33, 56)( 34, 75)
        ( 37, 43)( 38, 57)( 41, 47)( 42, 83)( 45, 60)( 46, 87)( 49, 55)( 50, 95)( 51, 61)( 54, 64)( 58, 86)( 59, 79)
        ( 62, 91)( 63, 88)( 65, 71)( 66,106)( 67, 96)( 69, 74)( 70,110)( 73, 78)( 76, 82)( 77,111)( 80, 98)( 81,114)
        ( 84, 90)( 85, 99)( 89,102)( 92, 97)( 93,109)( 94,103)(100,105)(101,118)(104,121)(107,113)(108,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 45)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 86)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 98)( 40, 71)( 42, 47)( 43,101)( 46, 74)( 49, 55)( 50,109)( 51, 75)( 53, 59)( 54,113)
        ( 57, 78)( 58,114)( 61, 67)( 62,117)( 63, 90)( 65, 70)( 66, 97)( 69, 73)( 72, 94)( 76,105)( 77,102)( 79, 85)
        ( 80,121)( 81,115)( 83, 89)( 84,122)( 88, 93)( 91,107)( 92,123)( 95,100)( 96,118)( 99,104)(103,119)(106,112)
        (108,120)(110,116)(111,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 28)( 18, 32)( 19, 60)( 23, 40)( 26, 31)( 27, 48)( 29, 52)( 30, 68)( 33, 39)( 34, 79)( 35, 63)
        ( 37, 43)( 38, 83)( 41, 47)( 42, 87)( 45, 51)( 46, 91)( 49, 67)( 50, 95)( 53, 59)( 54,103)( 55, 71)( 57, 62)
        ( 58,107)( 61, 66)( 64, 75)( 65,108)( 69, 74)( 70, 96)( 72, 99)( 73,111)( 76, 82)( 77,118)( 78,105)( 80, 86)
        ( 81,121)( 84, 90)( 85,122)( 88, 94)( 89,116)( 92, 98)( 93,113)( 97,110)(100,106)(101,120)(102,114)(104,109)
        (112,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 47)( 24, 44)( 26, 31)( 27, 55)( 29, 35)( 30, 79)( 33, 59)( 34, 82)
        ( 37, 43)( 38, 93)( 39, 71)( 41, 46)( 42, 97)( 45, 74)( 48, 54)( 49,105)( 50, 75)( 52, 58)( 53,109)( 56, 78)
        ( 57,110)( 60, 66)( 61,117)( 62, 86)( 64, 70)( 65,121)( 68, 73)( 69,122)( 72, 90)( 76,101)( 77, 98)( 80, 85)
        ( 81,111)( 83, 89)( 84,107)( 87,113)( 88,103)( 91, 96)( 92,123)( 94,100)( 95,119)( 99,115)(102,108)(104,116)
        (106,112)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 12)(  7, 35)(  8, 17)( 10, 20)( 11, 39)( 14, 19)( 15, 51)
        ( 16, 27)( 18, 31)( 21, 26)( 22, 59)( 23, 43)( 25, 30)( 28, 47)( 29, 60)( 32, 38)( 33, 71)( 34, 52)( 36, 42)
        ( 37, 72)( 40, 46)( 41, 75)( 44, 55)( 45, 79)( 48, 54)( 49, 91)( 50, 63)( 53, 67)( 56, 62)( 57, 99)( 58, 83)
        ( 61, 66)( 64, 87)( 65,100)( 68, 74)( 69,106)( 70, 92)( 73, 78)( 76, 82)( 77,107)( 80, 86)( 81,110)( 84, 95)
        ( 85,114)( 88, 94)( 89,121)( 90, 97)( 93,102)( 96,101)( 98,118)(103,109)(104,112)(105,122)(108,113)(111,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 86)( 38, 44)( 39, 95)( 40, 67)( 42, 48)( 43, 98)( 46, 71)( 47,102)( 50, 54)( 51, 72)( 53, 58)( 56, 75)
        ( 57, 73)( 60, 66)( 61,113)( 62, 90)( 65, 70)( 68, 94)( 69,114)( 74,106)( 76, 82)( 77,117)( 78,107)( 80, 85)
        ( 81,121)( 84, 89)( 87, 93)( 88,122)( 91,109)( 92,123)( 96,101)( 97,115)( 99,105)(100,111)(103,108)(104,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 87)( 38, 44)( 39, 95)( 40, 67)( 42, 48)( 43, 98)( 46, 71)( 47,102)( 50, 54)( 51, 72)( 53, 58)( 56, 75)
        ( 57, 73)( 60, 66)( 61,113)( 62, 90)( 65, 70)( 68, 94)( 69,114)( 74,106)( 76, 82)( 77,117)( 78,107)( 80, 86)
        ( 81,121)( 84, 89)( 85,122)( 88, 93)( 91,109)( 92,123)( 96,101)( 97,115)( 99,105)(100,111)(103,108)(104,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 78)( 28, 56)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 85)( 38, 44)( 39, 94)( 40, 68)( 42, 48)( 43, 97)( 46, 71)( 47,101)( 50, 55)( 51, 72)( 53, 58)( 54,106)
        ( 57, 74)( 60, 66)( 61,113)( 62, 89)( 64, 70)( 65,114)( 69, 93)( 73,105)( 75, 81)( 76,117)( 77,107)( 79, 84)
        ( 80,121)( 83, 88)( 86, 92)( 87,122)( 90,109)( 91,123)( 95,100)( 96,115)( 98,104)( 99,111)(102,108)(103,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)( 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 78)( 28, 56)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 44)( 39, 94)( 40, 68)( 42, 48)( 43, 97)( 46, 71)( 47,101)( 50, 55)( 51, 72)( 53, 58)( 54,106)
        ( 57, 74)( 60, 66)( 61,113)( 62, 89)( 64, 70)( 65,114)( 69, 93)( 73,105)( 75, 81)( 76,117)( 77,107)( 79, 85)
        ( 80,121)( 83, 88)( 84,122)( 87, 92)( 90,109)( 91,123)( 95,100)( 96,115)( 98,104)( 99,111)(102,108)(103,120)
        (110,116)(112,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)( 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 82)( 28, 55)( 30, 36)( 31, 86)( 34, 59)
        ( 35, 90)( 38, 44)( 39,102)( 40, 71)( 42, 48)( 43,106)( 46, 75)( 47,110)( 50, 54)( 51, 76)( 53, 58)( 56, 79)
        ( 57, 77)( 60, 66)( 61,118)( 62, 94)( 64, 70)( 65,119)( 68, 74)( 69,121)( 72, 98)( 73,122)( 78,114)( 80, 85)
        ( 81,115)( 83, 89)( 84,112)( 87, 93)( 88,108)( 91, 97)( 92,104)( 95,117)( 96,100)( 99,105)(101,123)(103,109)
        (107,113)(111,116)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 81)( 28, 56)( 30, 36)( 31, 85)( 34, 59)
        ( 35, 89)( 38, 44)( 39,101)( 40, 71)( 42, 48)( 43,105)( 46, 75)( 47,109)( 50, 55)( 51, 76)( 53, 58)( 54,114)
        ( 57, 78)( 60, 66)( 61,118)( 62, 93)( 64, 70)( 65,121)( 68, 74)( 69,122)( 72, 97)( 73,123)( 77,113)( 79, 84)
        ( 80,115)( 82, 88)( 83,111)( 86, 92)( 87,107)( 90, 96)( 91,103)( 94,117)( 95, 99)( 98,104)(100,120)(102,108)
        (106,112)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 54)
        ( 15, 25)( 17, 28)( 18, 58)( 22, 40)( 23, 36)( 26, 50)( 27, 46)( 29, 35)( 30, 75)( 31, 62)( 33, 39)( 34, 78)
        ( 37, 66)( 38, 82)( 41, 45)( 42, 67)( 44, 49)( 47, 70)( 48, 68)( 51, 57)( 52, 93)( 53, 71)( 55, 61)( 56, 97)
        ( 59, 65)( 60,101)( 63, 74)( 64,105)( 69, 86)( 72, 89)( 73, 87)( 76, 81)( 77,109)( 79, 85)( 80,114)( 83, 88)
        ( 84, 92)( 90, 96)( 91,115)( 94,100)( 95,117)( 98,104)( 99,118)(102,108)(103,121)(106,112)(107,122)(110,113)
        (111,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 43)( 25, 31)( 26, 71)( 27, 51)( 29, 35)( 30, 75)( 33, 55)( 34, 79)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 88)( 44, 50)( 45, 91)( 48, 54)( 49, 95)( 52, 67)( 53, 99)( 56, 62)( 57,109)
        ( 58, 83)( 60, 66)( 61,110)( 65, 87)( 68, 74)( 69,117)( 70,102)( 72, 78)( 73,121)( 76, 82)( 77,122)( 80, 86)
        ( 81,123)( 84,105)( 85,119)( 89, 94)( 90,111)( 92, 98)( 93,107)( 96,101)( 97,116)(100,104)(103,113)(106,112)
        (108,115)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 44)( 25, 31)( 26, 68)( 27, 52)( 29, 35)( 30, 69)( 33, 56)( 34, 72)
        ( 37, 43)( 38, 80)( 39, 62)( 41, 47)( 42, 84)( 45, 51)( 46, 88)( 49, 55)( 50, 92)( 53, 64)( 54, 96)( 57, 63)
        ( 58, 83)( 59, 76)( 65, 71)( 66,110)( 67, 99)( 70, 75)( 73, 79)( 74,111)( 77,102)( 78,114)( 81, 87)( 82,103)
        ( 85, 91)( 86,118)( 89, 95)( 90,121)( 93, 98)( 94,109)( 97,101)(100,106)(104,120)(105,115)(107,113)(108,122)
        (112,117)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 28)( 18, 32)( 19, 60)( 23, 40)( 26, 31)( 27, 48)( 29, 52)( 30, 65)( 33, 39)( 34, 76)( 35, 61)
        ( 37, 43)( 38, 79)( 41, 47)( 42, 83)( 45, 51)( 46, 87)( 49, 64)( 50, 91)( 53, 59)( 54,101)( 55, 68)( 57, 63)
        ( 58,105)( 62, 72)( 66, 71)( 67, 94)( 69, 97)( 70,110)( 73, 78)( 74,121)( 75,106)( 77, 82)( 80, 86)( 81,122)
        ( 84, 90)( 85,115)( 88, 93)( 89,112)( 92, 96)( 95,109)( 98,104)( 99,119)(100,113)(102,108)(103,120)(107,117)
        (111,116)(114,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 85)( 28, 57)( 30, 36)( 31, 89)( 34, 61)
        ( 35, 90)( 38, 44)( 39,101)( 40, 73)( 42, 48)( 43,105)( 46, 77)( 47, 84)( 50, 56)( 51,110)( 52, 78)( 54, 60)
        ( 55,111)( 58, 81)( 59, 80)( 62, 68)( 63, 99)( 64, 93)( 66, 72)( 67,112)( 70, 76)( 71,116)( 74, 97)( 75,119)
        ( 79,109)( 82, 88)( 83,106)( 86, 92)( 87,122)( 91, 96)( 94,103)( 95,123)( 98,104)(100,115)(102,108)(107,124)
        (113,118)(114,120)(117,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111)(112,113,114,115)(116,117,118)(119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 53)( 30, 36)( 31, 84)( 34, 57)
        ( 35, 85)( 38, 44)( 39, 96)( 40, 68)( 42, 48)( 43, 99)( 46, 72)( 47,103)( 51, 56)( 52, 73)( 54, 76)( 55,112)
        ( 58, 64)( 59, 95)( 60, 88)( 62, 67)( 63, 70)( 66, 71)( 69, 92)( 74,111)( 75,107)( 77, 83)( 78,118)( 79,109)
        ( 81, 87)( 82,122)( 86, 91)( 89,114)( 90,123)( 93, 98)( 94,115)( 97,102)(100,106)(101,116)(104,110)(105,121)
        (108,113)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 49)( 24, 45)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 86)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 95)( 40, 71)( 42, 48)( 43, 98)( 46, 74)( 47,102)( 50, 55)( 51, 75)( 53, 59)( 54, 76)
        ( 57, 78)( 58,107)( 61, 66)( 62,114)( 63, 90)( 65, 70)( 68, 73)( 69,115)( 72, 94)( 77,106)( 79, 85)( 80,118)
        ( 81,108)( 83, 89)( 84,122)( 88, 93)( 91,110)( 92,123)( 96,101)( 97,116)( 99,105)(100,112)(103,109)(104,121)
        (111,117)(113,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)( 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96, 97)
        ( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 52)( 30, 35)( 31, 84)( 34, 56)
        ( 37, 43)( 38, 89)( 39, 68)( 41, 47)( 42, 92)( 45, 72)( 46, 96)( 50, 55)( 51, 73)( 53, 76)( 54,105)( 57, 63)
        ( 58,111)( 59, 85)( 61, 67)( 62,115)( 65, 71)( 66,116)( 69, 88)( 70,113)( 74,104)( 75,100)( 77, 83)( 78,118)
        ( 79,102)( 81, 87)( 82,121)( 86,107)( 90, 95)( 91,109)( 93, 99)( 94,123)( 97,103)( 98,120)(101,106)(108,114)
        (110,122)(112,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 71)( 41, 47)( 42, 95)( 45, 51)( 46, 99)( 49, 55)( 50,103)( 53, 59)( 54,107)( 57, 75)
        ( 58,108)( 61, 67)( 62,114)( 63, 83)( 65, 70)( 66,118)( 69, 74)( 72, 87)( 73,119)( 77, 82)( 78,105)( 80, 86)
        ( 81,101)( 84,110)( 85, 97)( 88, 94)( 89,112)( 90,122)( 92, 98)( 93,113)( 96,102)(100,106)(104,109)(111,117)
        (115,121)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 68)( 41, 47)( 42, 95)( 45, 71)( 46, 99)( 50, 55)( 51, 72)( 53, 75)( 54,108)( 57, 63)
        ( 58,114)( 59, 83)( 61, 67)( 62,118)( 65, 70)( 66,121)( 69, 87)( 73,107)( 74,103)( 77, 82)( 78,105)( 80, 86)
        ( 81,101)( 84,110)( 85, 97)( 88, 94)( 89,112)( 90,122)( 92, 98)( 93,113)( 96,102)(100,106)(104,109)(111,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 55)( 29, 35)( 30, 80)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 95)( 39, 71)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 54)( 50, 76)( 52, 58)( 53, 77)( 56, 79)
        ( 57,108)( 60, 66)( 61,115)( 62, 87)( 64, 70)( 65,118)( 68, 74)( 69,122)( 72, 91)( 73,123)( 78,107)( 81, 86)
        ( 82,109)( 84, 90)( 85,105)( 88,111)( 89,101)( 92, 98)( 93,113)( 94,120)( 96,102)( 97,114)(100,106)(104,110)
        (112,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 77)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 92)( 39, 72)( 41, 47)( 42, 96)( 45, 51)( 46,100)( 49, 55)( 50,104)( 53, 59)( 54,108)( 57, 76)
        ( 58,109)( 61, 67)( 62,114)( 63, 84)( 65, 71)( 66,118)( 69, 75)( 70,119)( 73, 88)( 74,122)( 78, 83)( 79,106)
        ( 81, 87)( 82,102)( 85,111)( 86, 98)( 89, 95)( 90,116)( 91,123)( 93, 99)( 94,113)( 97,103)(101,107)(105,110)
        (112,117)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 38, 43)( 39, 68)( 41, 47)( 42, 92)( 45, 72)( 46, 95)( 49, 55)( 50,103)( 51, 73)( 54, 76)( 57, 63)
        ( 58,110)( 59, 88)( 61, 67)( 62,114)( 65, 71)( 66,115)( 69, 91)( 70,112)( 74,102)( 75, 99)( 77, 82)( 78,104)
        ( 80, 86)( 81,119)( 84, 90)( 85,121)( 89,106)( 93, 98)( 94,108)( 96,101)( 97,123)(100,117)(105,118)(107,113)
        (109,122)(111,116)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 46)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 60)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 49)( 30, 36)( 31, 80)( 34, 53)
        ( 35, 81)( 39, 44)( 40, 64)( 42, 68)( 43, 89)( 47, 52)( 48, 69)( 50, 72)( 51, 96)( 54, 59)( 55,103)( 56, 84)
        ( 58, 63)( 61, 67)( 62,104)( 65, 88)( 66,107)( 70, 95)( 71, 92)( 73, 79)( 74,118)( 75, 97)( 77, 83)( 78,122)
        ( 82, 87)( 85, 99)( 86,123)( 90, 94)( 91,110)( 93,114)( 98,115)(100,106)(101,112)(102,120)(105,109)(108,113)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 46)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 49)( 30, 36)( 31, 80)( 34, 53)
        ( 35, 81)( 39, 44)( 40, 64)( 42, 68)( 43, 89)( 47, 52)( 48, 69)( 50, 72)( 51, 96)( 54, 60)( 55,103)( 56, 84)
        ( 58, 63)( 59,106)( 62, 67)( 65, 88)( 66,107)( 70, 95)( 71, 92)( 73, 79)( 74,118)( 75, 97)( 77, 83)( 78,122)
        ( 82, 87)( 85, 99)( 86,123)( 90, 94)( 91,110)( 93,114)( 98,115)(100,105)(101,112)(102,120)(104,109)(108,113)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 49)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 77)
        ( 37, 43)( 38, 88)( 39, 61)( 41, 47)( 42, 89)( 45, 64)( 46, 92)( 50, 55)( 51, 65)( 53, 68)( 54,100)( 57, 63)
        ( 58,107)( 59, 80)( 62, 84)( 66, 99)( 67, 96)( 69, 75)( 70,114)( 71,101)( 73, 79)( 74,118)( 78, 83)( 81,103)
        ( 82,119)( 85, 91)( 86,121)( 87,108)( 90, 95)( 93, 98)( 94,122)( 97,110)(102,111)(104,109)(105,124)(106,116)
        (112,117)(113,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 82)( 28, 56)( 30, 36)( 31, 86)( 34, 59)
        ( 35, 87)( 38, 43)( 39, 98)( 40, 70)( 42, 47)( 45, 74)( 46, 99)( 49, 55)( 50,106)( 51, 75)( 53, 58)( 54,107)
        ( 57, 78)( 60, 66)( 61,114)( 62, 90)( 64, 69)( 65,115)( 68, 73)( 71, 94)( 72,116)( 76,102)( 77,100)( 79, 85)
        ( 80,118)( 81,108)( 83, 89)( 84,122)( 88, 93)( 91,110)( 92,123)( 95,101)( 96,105)( 97,112)(103,109)(104,121)
        (111,117)(113,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 56)( 29, 35)( 30, 75)( 33, 59)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 64)( 41, 47)( 42, 91)( 45, 51)( 46, 94)( 49, 55)( 50, 98)( 53, 58)( 54,102)( 57, 67)
        ( 60, 66)( 61, 86)( 62, 79)( 65, 83)( 68, 74)( 69,114)( 70,103)( 72, 78)( 73,118)( 77, 82)( 80,106)( 81,119)
        ( 84, 90)( 85,107)( 88, 93)( 89,121)( 92, 97)( 95,101)( 96,122)( 99,105)(100,113)(104,110)(108,124)(109,116)
        (111,117)(112,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 50)( 30, 36)( 31, 80)( 34, 53)
        ( 35, 81)( 39, 44)( 40, 64)( 42, 68)( 43, 89)( 46, 52)( 47, 96)( 48, 69)( 51, 72)( 54, 60)( 55,103)( 56, 84)
        ( 58, 63)( 59,106)( 62, 67)( 65, 88)( 66,107)( 70, 95)( 71, 92)( 73, 79)( 74,118)( 75, 97)( 77, 83)( 78,122)
        ( 82, 87)( 85, 99)( 86,123)( 90, 94)( 91,110)( 93,114)( 98,115)(100,105)(101,112)(102,120)(104,109)(108,113)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 53)( 29, 35)( 30, 75)( 33, 56)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 61)( 41, 47)( 42, 88)( 45, 64)( 46, 91)( 49, 55)( 50, 99)( 51, 65)( 54, 67)( 57, 63)
        ( 58,107)( 59, 79)( 62, 83)( 66, 95)( 68, 74)( 69,114)( 70,100)( 72, 78)( 73,118)( 77, 82)( 80,103)( 81,119)
        ( 84, 90)( 85,121)( 86,108)( 89, 94)( 92, 98)( 93,122)( 96,102)( 97,113)(101,110)(104,109)(105,124)(106,116)
        (111,117)(112,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 39)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 67)( 27, 56)( 29, 35)( 30, 71)( 33, 59)( 34, 75)
        ( 37, 43)( 38, 60)( 41, 47)( 42, 82)( 45, 51)( 46, 86)( 49, 55)( 50, 90)( 53, 58)( 54, 94)( 57, 63)( 61, 85)
        ( 62, 79)( 64, 70)( 65,106)( 66, 95)( 68, 74)( 69,110)( 72, 78)( 73,111)( 76, 81)( 77,114)( 80, 98)( 83, 89)
        ( 84, 99)( 87, 93)( 88,118)( 91, 97)( 92,105)( 96,102)(100,121)(101,115)(103,109)(104,119)(107,113)(108,124)
        (112,117)(116,122)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 39)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 68)( 27, 53)( 29, 35)( 30, 72)( 33, 56)( 34, 75)
        ( 37, 43)( 38, 57)( 41, 47)( 42, 83)( 45, 60)( 46, 87)( 49, 55)( 50, 95)( 51, 61)( 54, 64)( 58, 86)( 59, 79)
        ( 62, 94)( 63, 91)( 65, 71)( 66,106)( 67, 96)( 69, 74)( 70,110)( 73, 78)( 76, 82)( 77,111)( 80, 98)( 81,114)
        ( 84, 90)( 85, 99)( 88, 93)( 89,121)( 92,102)( 97,103)(100,124)(101,117)(104,109)(105,122)(107,113)(108,119)
        (112,116)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 39)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 67)( 27, 53)( 29, 35)( 30, 71)( 33, 56)( 34, 74)
        ( 37, 43)( 38, 57)( 41, 47)( 42, 82)( 45, 60)( 46, 86)( 49, 55)( 50, 94)( 51, 61)( 54, 63)( 58, 85)( 59, 78)
        ( 62, 90)( 64, 70)( 65,106)( 66, 95)( 68, 73)( 69,110)( 72, 77)( 75, 81)( 76,111)( 79, 98)( 80,114)( 83, 89)
        ( 84, 99)( 87, 93)( 88,118)( 91, 97)( 92,105)( 96,102)(100,121)(101,115)(103,109)(104,119)(107,113)(108,124)
        (112,117)(116,122)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 82)( 28, 56)( 30, 35)( 31, 86)( 34, 59)
        ( 37, 43)( 38, 91)( 39, 70)( 41, 47)( 42, 94)( 45, 74)( 46, 98)( 49, 55)( 50,106)( 51, 75)( 53, 58)( 54,107)
        ( 57, 78)( 60, 66)( 61,114)( 62, 87)( 64, 69)( 65,118)( 68, 73)( 71, 90)( 72,119)( 76,102)( 77, 99)( 79, 85)
        ( 80,104)( 81,108)( 83, 89)( 84,123)( 88,110)( 92, 97)( 93,116)( 95,101)( 96,112)(100,121)(103,109)(105,122)
        (111,117)(113,124)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 56)( 29, 35)( 30, 72)( 33, 59)( 34, 75)
        ( 37, 43)( 38, 83)( 39, 64)( 41, 47)( 42, 86)( 45, 51)( 46, 90)( 49, 55)( 50, 94)( 53, 58)( 54, 98)( 57, 67)
        ( 60, 66)( 61,106)( 62, 79)( 65, 82)( 68, 74)( 69,114)( 70, 99)( 73, 78)( 76, 81)( 77,115)( 80,102)( 84, 89)
        ( 85,107)( 87, 93)( 88,119)( 91, 97)( 92,121)( 95,101)( 96,113)(100,110)(103,109)(104,123)(105,116)(108,118)
        (111,117)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 67)( 24, 51)( 26, 32)( 27, 71)( 30, 55)( 31, 74)( 34, 39)( 35, 56)
        ( 37, 43)( 38, 83)( 41, 59)( 42, 86)( 45, 50)( 46, 94)( 47, 60)( 49, 54)( 52, 63)( 53, 95)( 57, 82)( 58, 78)
        ( 61, 90)( 62, 87)( 64, 70)( 65,106)( 66, 96)( 68, 73)( 69,110)( 72, 77)( 75, 81)( 76,111)( 79, 98)( 80,114)
        ( 84, 89)( 85, 99)( 88,102)( 91, 97)( 92,109)( 93,103)(100,105)(101,118)(104,121)(107,113)(108,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 52)( 30, 36)( 31, 84)( 34, 56)
        ( 35, 87)( 38, 43)( 39, 98)( 40, 68)( 42, 47)( 45, 72)( 46, 99)( 50, 55)( 51, 73)( 53, 76)( 54,106)( 57, 63)
        ( 58,113)( 59, 90)( 61, 67)( 62,117)( 65, 71)( 66,118)( 69, 94)( 70,119)( 74,105)( 75,102)( 77, 83)( 78,112)
        ( 79,107)( 81, 86)( 82, 92)( 85, 89)( 88, 93)( 91,109)( 95,101)( 96,124)( 97,115)(100,104)(103,121)(108,122)
        (110,116)(111,123)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 35)( 22, 47)( 23, 43)( 25, 31)( 26, 71)( 27, 52)( 29, 34)( 30, 75)( 33, 55)( 36, 42)
        ( 37, 82)( 38, 60)( 40, 46)( 41, 86)( 44, 63)( 45, 90)( 48, 54)( 49, 98)( 50, 64)( 53, 67)( 56, 62)( 57,105)
        ( 58, 76)( 61, 79)( 65, 97)( 66, 94)( 68, 74)( 69,113)( 70, 99)( 72, 78)( 73,114)( 77,101)( 80, 85)( 81,106)
        ( 83, 89)( 84,118)( 87, 93)( 88,119)( 91, 96)( 92,121)( 95,109)(100,110)(102,108)(103,123)(104,115)(107,117)
        (111,116)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 48)( 29, 35)( 30, 75)( 31, 63)( 33, 39)( 34, 76)
        ( 37, 43)( 38, 79)( 41, 47)( 42, 83)( 45, 50)( 46, 87)( 49, 67)( 52, 58)( 53, 95)( 54, 68)( 56, 62)( 57, 98)
        ( 60, 66)( 61,102)( 64, 71)( 65,106)( 69, 91)( 70, 88)( 72, 78)( 73,121)( 74,109)( 77, 82)( 80, 86)( 81,122)
        ( 84, 90)( 85,116)( 89,113)( 92, 97)( 93,119)( 94,114)( 96,101)( 99,105)(100,120)(103,108)(104,111)(107,112)
        (110,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 45)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 76)
        ( 37, 64)( 38, 79)( 41, 47)( 42, 87)( 43, 65)( 46, 67)( 49, 55)( 50, 95)( 51, 68)( 53, 59)( 54, 98)( 57, 63)
        ( 58,102)( 61, 71)( 62,106)( 66, 83)( 69, 91)( 70, 88)( 72, 78)( 73,121)( 74,109)( 77, 82)( 80, 86)( 81,122)
        ( 84, 90)( 85,116)( 89,113)( 92, 97)( 93,119)( 94,114)( 96,101)( 99,105)(100,120)(103,108)(104,111)(107,112)
        (110,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 62)( 16, 32)( 18, 36)( 19, 66)( 23, 46)( 24, 43)( 26, 31)( 27, 54)( 29, 35)( 30, 78)( 33, 58)( 34, 81)
        ( 37, 42)( 38, 69)( 40, 45)( 41, 90)( 44, 73)( 47, 53)( 48, 97)( 49, 74)( 51, 57)( 52,101)( 55, 77)( 56,105)
        ( 59, 65)( 60,113)( 61, 85)( 63, 68)( 64,114)( 67, 72)( 70, 89)( 71,115)( 75, 93)( 76, 91)( 79, 84)( 80,106)
        ( 82, 88)( 83,118)( 86,109)( 87,121)( 92,111)( 94,100)( 95,122)( 96,112)( 98,104)( 99,123)(102,108)(103,120)
        (107,117)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45)( 46, 47, 48, 49)
        ( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 31)( 17, 35)( 18, 52)( 22, 43)( 23, 39)( 25, 30)( 26, 67)( 27, 44)( 29, 34)( 32, 47)( 33, 68)( 37, 42)
        ( 38, 55)( 40, 59)( 41, 76)( 45, 63)( 46, 60)( 48, 54)( 49, 91)( 50, 71)( 53, 58)( 56, 75)( 57, 92)( 61, 83)
        ( 62, 79)( 64, 70)( 65,107)( 66, 84)( 69, 74)( 72, 87)( 73,108)( 77, 82)( 78, 95)( 80, 99)( 81,115)( 85,103)
        ( 86,100)( 88, 94)( 89,122)( 90,111)( 93, 98)( 96,114)( 97,123)(101,106)(102,116)(104,110)(105,121)(109,113)
        (112,118)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 44)( 26, 32)( 27, 82)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 70)( 41, 46)( 42, 95)( 45, 74)( 48, 54)( 49,102)( 50, 75)( 52, 58)( 53,106)( 56, 78)
        ( 57,110)( 60, 66)( 61,100)( 62, 90)( 64, 69)( 65,114)( 68, 73)( 71, 94)( 72,115)( 76, 98)( 77, 96)( 79, 85)
        ( 80,122)( 81,111)( 84, 89)( 87, 93)( 88,123)( 91,104)( 92,120)( 97,116)( 99,105)(101,117)(103,109)(107,113)
        (108,121)(112,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 80)( 34, 60)
        ( 35, 83)( 38, 44)( 39, 94)( 40, 69)( 42, 48)( 43, 98)( 46, 72)( 47,102)( 50, 55)( 51,110)( 52, 73)( 54, 59)
        ( 57, 75)( 58,111)( 61, 67)( 62,117)( 63, 87)( 65, 71)( 66, 93)( 70, 90)( 74,106)( 76, 82)( 77,121)( 78,108)
        ( 81, 86)( 84, 89)( 85,122)( 88,113)( 91, 97)( 92,118)( 95,101)( 96,119)( 99,105)(100,115)(103,109)(104,124)
        (107,112)(114,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 31, 56)( 34, 40)( 35, 87)
        ( 36, 68)( 38, 44)( 39, 91)( 42, 72)( 43, 94)( 46, 51)( 47,102)( 48, 73)( 50, 55)( 53, 75)( 54,103)( 57, 63)
        ( 58,109)( 59, 80)( 61, 67)( 62,113)( 65, 71)( 66,114)( 69, 83)( 70,117)( 74, 98)( 76, 82)( 77,121)( 78,100)
        ( 81,105)( 84, 90)( 85,107)( 86,118)( 88, 93)( 89,123)( 92, 97)( 95,101)( 96,124)( 99,104)(106,112)(108,122)
        (110,116)(111,119)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 30)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 31, 55)( 34, 40)( 35, 87)
        ( 36, 67)( 38, 44)( 39, 91)( 42, 71)( 43, 95)( 46, 51)( 47, 72)( 49, 54)( 50,102)( 53, 75)( 56, 62)( 57,109)
        ( 58, 80)( 60, 66)( 61,110)( 64, 70)( 65,113)( 68, 83)( 69,114)( 73,101)( 74, 98)( 76, 82)( 77,121)( 78,103)
        ( 81,105)( 84, 90)( 85,107)( 86,115)( 88, 94)( 89,123)( 92, 97)( 93,120)( 96,100)( 99,117)(104,118)(106,112)
        (108,122)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 37)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 30, 36)( 31, 80)( 34, 55)
        ( 35, 83)( 39, 44)( 40, 67)( 42, 71)( 43, 91)( 46, 51)( 47, 72)( 49, 54)( 50, 98)( 53, 75)( 56, 62)( 57,105)
        ( 58, 87)( 60, 66)( 61,106)( 64, 70)( 65,109)( 68, 90)( 69,110)( 73, 97)( 74, 94)( 76, 82)( 77,121)( 78, 99)
        ( 81, 86)( 84, 89)( 85,122)( 88,101)( 92, 96)( 93,113)( 95,117)(100,118)(102,108)(103,115)(104,123)(107,112)
        (111,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 47)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 66)( 24, 51)( 26, 32)( 27, 70)( 30, 54)( 31, 74)( 34, 39)( 35, 55)
        ( 37, 43)( 38, 83)( 41, 58)( 42, 86)( 45, 50)( 46, 59)( 48, 53)( 49, 94)( 52, 62)( 56, 82)( 57, 78)( 60, 93)
        ( 61, 90)( 63, 69)( 64,105)( 65, 95)( 67, 73)( 68,109)( 71, 77)( 72,110)( 75, 81)( 76,113)( 79, 97)( 80,114)
        ( 84, 89)( 85, 98)( 87, 92)( 88,122)( 91,101)( 96,102)( 99,121)(100,117)(103,108)(104,123)(106,112)(107,119)
        (111,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 45)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 44)( 39, 96)( 40, 69)( 42, 47)( 43, 99)( 46, 72)( 49, 55)( 50,103)( 51, 73)( 53, 59)( 54,107)
        ( 57, 76)( 58,111)( 61, 67)( 62,101)( 63, 91)( 65, 71)( 66, 98)( 70, 95)( 74, 92)( 75,100)( 77, 82)( 78,114)
        ( 80, 86)( 81,118)( 84, 90)( 85,121)( 88, 94)( 89,122)( 93,106)( 97,102)(104,110)(105,123)(108,113)(109,120)
        (112,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 41)( 26, 32)( 27, 80)( 28, 52)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 87)( 39, 43)( 40, 68)( 42, 72)( 45, 51)( 46, 99)( 47, 73)( 49, 55)( 50,103)( 53, 76)( 54,107)( 57, 63)
        ( 58, 97)( 59, 91)( 61, 67)( 62,113)( 65, 71)( 66,114)( 69, 75)( 70,115)( 74, 95)( 77, 82)( 78,121)( 79,110)
        ( 81, 86)( 84, 90)( 85,122)( 88, 94)( 89,123)( 92,101)( 93,119)( 96,102)( 98,116)(100,106)(104,109)(105,120)
        (108,112)(111,117)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 23)( 10, 39)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 24)( 17, 27)( 18, 55)( 22, 35)( 25, 47)( 26, 43)( 28, 34)( 29, 67)( 30, 56)( 32, 38)( 33, 68)( 36, 42)
        ( 37, 71)( 40, 46)( 41, 75)( 44, 59)( 45, 79)( 48, 54)( 49, 90)( 50, 60)( 52, 58)( 53, 94)( 57, 63)( 61, 86)
        ( 62, 83)( 64, 70)( 65,106)( 66, 95)( 69, 74)( 72, 78)( 73,107)( 76, 82)( 77,110)( 80, 85)( 81,114)( 84, 98)
        ( 87, 93)( 88,121)( 89, 99)( 91, 97)( 92,122)( 96,102)(100,117)(101,115)(103,109)(104,119)(105,123)(108,113)
        (111,116)(112,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 12)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 28)( 17, 32)( 18, 56)( 22, 44)( 23, 40)( 26, 31)( 27, 45)( 29, 48)( 30, 69)( 33, 39)( 34, 79)( 35, 60)
        ( 37, 43)( 38, 80)( 41, 64)( 42, 83)( 46, 68)( 47, 65)( 49, 55)( 50, 99)( 51, 72)( 53, 59)( 54,103)( 57, 63)
        ( 58,107)( 61, 75)( 62,108)( 66, 91)( 67, 87)( 70, 74)( 71, 92)( 73, 95)( 76, 82)( 77,114)( 78,109)( 81, 86)
        ( 84, 90)( 85,115)( 88,111)( 89,118)( 93, 98)( 94,112)( 96,102)( 97,123)(100,106)(101,120)(104,110)(105,117)
        (113,122)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 65)( 41, 47)( 42, 94)( 45, 68)( 46, 98)( 49, 55)( 50,106)( 51, 69)( 53, 59)( 54,107)
        ( 57, 71)( 58,108)( 61, 67)( 62,114)( 63, 83)( 66, 87)( 70,102)( 72, 78)( 73,117)( 74,104)( 77, 82)( 80, 86)
        ( 81,118)( 84,110)( 85,121)( 88, 93)( 89,115)( 91, 97)( 92,112)( 95,101)( 96,123)( 99,105)(100,120)(103,109)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 56)( 29, 35)( 30, 79)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 90)( 39, 65)( 41, 47)( 42, 94)( 45, 68)( 46, 98)( 49, 55)( 50,106)( 51, 69)( 53, 59)( 54,107)
        ( 57, 71)( 58,108)( 61, 67)( 62,114)( 63, 84)( 66, 87)( 70,102)( 72, 78)( 73,117)( 74,104)( 76, 82)( 77,118)
        ( 80, 86)( 81,121)( 85,110)( 88, 93)( 89,115)( 91, 97)( 92,112)( 95,101)( 96,123)( 99,105)(100,120)(103,109)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 55)( 29, 35)( 30, 79)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 90)( 39, 64)( 41, 47)( 42, 94)( 45, 67)( 46, 98)( 49, 54)( 50,107)( 51, 68)( 53, 58)( 56, 71)
        ( 57,108)( 60, 66)( 61,114)( 62, 84)( 65, 87)( 69,106)( 70,102)( 72, 78)( 73,117)( 74,104)( 76, 82)( 77,118)
        ( 80, 86)( 81,121)( 85,110)( 88, 93)( 89,115)( 91, 97)( 92,112)( 95,101)( 96,123)( 99,105)(100,120)(103,109)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 79)( 28, 56)( 30, 35)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 90)( 39, 69)( 41, 47)( 42, 94)( 45, 72)( 46, 98)( 49, 55)( 50,106)( 51, 73)( 53, 59)( 54,107)
        ( 57, 75)( 58,108)( 61, 67)( 62,114)( 63, 83)( 65, 71)( 66,118)( 70, 87)( 74,102)( 76, 82)( 77,121)( 78,104)
        ( 81, 86)( 84,110)( 85,122)( 88, 93)( 89,119)( 91, 97)( 92,116)( 95,101)( 96,112)( 99,105)(100,124)(103,109)
        (111,117)(113,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 35)( 31, 83)( 34, 60)
        ( 37, 43)( 38, 90)( 39, 69)( 41, 47)( 42, 94)( 45, 72)( 46, 98)( 49, 55)( 50,106)( 51, 73)( 53, 59)( 54,107)
        ( 57, 75)( 58,108)( 61, 67)( 62,114)( 63, 84)( 65, 71)( 66,118)( 70, 87)( 74,102)( 76, 82)( 77,121)( 78,104)
        ( 80, 86)( 81,122)( 85,110)( 88, 93)( 89,119)( 91, 97)( 92,116)( 95,101)( 96,112)( 99,105)(100,124)(103,109)
        (111,117)(113,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 82)( 28, 55)( 30, 35)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 91)( 39, 70)( 41, 47)( 42, 94)( 45, 74)( 46, 98)( 49, 54)( 50, 75)( 52, 58)( 53,107)( 56, 78)
        ( 57,108)( 60, 66)( 61,114)( 62, 86)( 64, 69)( 65,118)( 68, 73)( 71, 90)( 72,119)( 76,106)( 77,102)( 79, 85)
        ( 80,121)( 81,104)( 84, 89)( 87,110)( 88,122)( 92, 97)( 93,116)( 95,101)( 96,112)( 99,105)(100,124)(103,109)
        (111,117)(113,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 82)( 28, 55)( 30, 35)( 31, 86)( 34, 59)
        ( 37, 43)( 38, 91)( 39, 70)( 41, 47)( 42, 94)( 45, 74)( 46, 98)( 49, 54)( 50, 75)( 52, 58)( 53,107)( 56, 78)
        ( 57,108)( 60, 66)( 61,114)( 62, 87)( 64, 69)( 65,118)( 68, 73)( 71, 90)( 72,119)( 76,106)( 77,102)( 79, 85)
        ( 80,121)( 81,104)( 83, 89)( 84,122)( 88,110)( 92, 97)( 93,116)( 95,101)( 96,112)( 99,105)(100,124)(103,109)
        (111,117)(113,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 81)( 28, 55)( 30, 35)( 33, 59)( 34, 82)
        ( 37, 43)( 38, 93)( 39, 70)( 41, 47)( 42, 97)( 45, 73)( 46,101)( 49, 54)( 50,110)( 51, 74)( 53, 58)( 56, 77)
        ( 57,111)( 60, 66)( 61,117)( 62, 85)( 64, 69)( 65, 92)( 68, 72)( 71, 89)( 75,109)( 76,105)( 78, 84)( 79,121)
        ( 80,107)( 83, 88)( 86,113)( 87,122)( 90, 96)( 91,118)( 94,100)( 95,119)( 98,104)( 99,115)(102,108)(103,124)
        (106,112)(114,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)( 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 77)( 34, 40)( 35, 88)
        ( 36, 69)( 38, 44)( 39, 91)( 42, 73)( 43, 95)( 46, 52)( 47,103)( 48, 74)( 50, 56)( 51,104)( 54, 76)( 55,105)
        ( 58, 64)( 59,111)( 60, 80)( 62, 68)( 63,115)( 66, 72)( 67,116)( 70, 84)( 71,119)( 75, 99)( 78, 83)( 79,101)
        ( 81,107)( 82, 97)( 85, 90)( 86,109)( 87,122)( 89, 94)( 92, 98)( 93,110)( 96,102)(100,106)(108,114)(112,118)
        (113,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 62)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 57)( 30, 36)( 31, 84)( 34, 61)
        ( 35, 88)( 38, 44)( 39,100)( 40, 69)( 42, 48)( 43,104)( 46, 73)( 47,108)( 50, 56)( 51,115)( 52, 74)( 54, 60)
        ( 55,116)( 58, 76)( 59,117)( 63, 68)( 64, 92)( 66, 72)( 67, 93)( 70, 96)( 71,119)( 75,111)( 77, 83)( 78,106)
        ( 79,113)( 81, 87)( 82,102)( 85, 91)( 86, 98)( 89, 95)( 90,123)( 94,121)( 97,103)( 99,122)(101,107)(105,110)
        (109,114)(112,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 52)( 30, 56)( 31, 77)( 34, 40)( 35, 88)
        ( 36, 68)( 38, 44)( 39, 91)( 42, 72)( 43, 95)( 46, 51)( 47, 73)( 49, 55)( 50,104)( 53, 76)( 54,105)( 57, 63)
        ( 58,111)( 59, 80)( 61, 67)( 62,115)( 65, 71)( 66,118)( 69, 84)( 70,119)( 74,103)( 75, 99)( 78, 83)( 79,101)
        ( 81,107)( 82, 97)( 85, 90)( 86,109)( 87,122)( 89, 94)( 92, 98)( 93,110)( 96,102)(100,106)(108,114)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 84)( 34, 60)
        ( 35, 88)( 38, 44)( 39, 99)( 40, 68)( 42, 48)( 43,103)( 46, 72)( 47,107)( 50, 55)( 51, 73)( 53, 59)( 54,115)
        ( 57, 76)( 58,116)( 62, 67)( 63, 92)( 65, 71)( 66,119)( 69, 95)( 70,120)( 74,114)( 75,110)( 77, 83)( 78,105)
        ( 79,112)( 81, 87)( 82,101)( 85, 91)( 86, 97)( 89, 94)( 90,123)( 93,118)( 96,102)( 98,122)(100,106)(104,109)
        (108,113)(111,117)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 52)( 30, 56)( 31, 77)( 34, 40)( 35, 88)
        ( 36, 68)( 38, 44)( 39, 91)( 42, 72)( 43, 95)( 46, 51)( 47,104)( 48, 73)( 50, 55)( 53, 76)( 54,105)( 57, 63)
        ( 58,111)( 59, 80)( 61, 67)( 62,115)( 65, 71)( 66,118)( 69, 84)( 70,121)( 74,103)( 75, 99)( 78, 83)( 79,101)
        ( 81,107)( 82, 97)( 85, 90)( 86,109)( 87,122)( 89, 94)( 92, 98)( 93,110)( 96,102)(100,106)(108,114)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 84)( 34, 60)
        ( 35, 88)( 38, 44)( 39, 99)( 40, 68)( 42, 48)( 43,103)( 46, 72)( 47,107)( 50, 55)( 51,115)( 52, 73)( 54, 59)
        ( 57, 76)( 58,116)( 62, 67)( 63, 92)( 65, 71)( 66,119)( 69, 95)( 70,121)( 74,114)( 75,110)( 77, 83)( 78,105)
        ( 79,112)( 81, 87)( 82,101)( 85, 91)( 86, 97)( 89, 94)( 90,123)( 93,118)( 96,102)( 98,122)(100,106)(104,109)
        (108,113)(111,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 56)( 30, 36)( 31, 82)( 34, 60)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 70)( 42, 47)( 45, 51)( 46, 99)( 49, 55)( 50,102)( 53, 59)( 54,106)( 57, 74)
        ( 58,109)( 61, 66)( 62, 72)( 63, 90)( 65, 69)( 68, 73)( 71, 94)( 75, 81)( 76,117)( 77,110)( 79, 85)( 80,121)
        ( 83, 89)( 84,122)( 87, 93)( 88,123)( 91, 97)( 92,119)( 95,101)( 96,115)(100,105)(103,108)(104,116)(107,112)
        (111,113)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 75)( 33, 55)( 34, 79)
        ( 37, 42)( 38, 60)( 40, 46)( 41, 88)( 44, 63)( 45, 91)( 48, 54)( 49,102)( 50, 64)( 53, 67)( 56, 62)( 57,110)
        ( 58, 83)( 61, 87)( 65, 99)( 66, 95)( 68, 74)( 69,117)( 70,103)( 72, 78)( 73,121)( 76, 82)( 77,122)( 80, 86)
        ( 81,123)( 84,106)( 85,119)( 89, 94)( 90,111)( 92, 98)( 93,108)( 96,101)( 97,116)(100,105)(104,113)(107,112)
        (109,115)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 48)( 24, 44)( 26, 31)( 27, 53)( 29, 35)( 30, 73)( 33, 56)( 34, 76)
        ( 37, 43)( 38, 85)( 39, 64)( 41, 47)( 42, 88)( 45, 68)( 46, 92)( 49, 55)( 50,103)( 51, 69)( 54, 72)( 57, 63)
        ( 58,111)( 59, 80)( 62, 67)( 65, 84)( 66,112)( 70,100)( 71, 96)( 74, 79)( 75,104)( 77, 83)( 78,115)( 81,107)
        ( 82,118)( 86, 91)( 87,109)( 89, 95)( 90,123)( 93, 99)( 94,120)( 97,102)( 98,117)(101,106)(105,114)(108,113)
        (110,122)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 48)( 24, 44)( 26, 31)( 27, 53)( 29, 35)( 30, 72)( 33, 56)( 34, 75)
        ( 37, 43)( 38, 87)( 39, 64)( 41, 47)( 42, 91)( 45, 67)( 46, 95)( 49, 55)( 50,106)( 51, 68)( 54, 71)( 57, 63)
        ( 58, 86)( 59, 79)( 62, 66)( 65, 83)( 69,103)( 70, 99)( 73, 78)( 74,107)( 76, 82)( 77,115)( 80,110)( 81,118)
        ( 84, 90)( 85,111)( 88, 94)( 89,112)( 92, 98)( 93,123)( 96,102)( 97,120)(100,105)(101,117)(104,109)(108,114)
        (113,122)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 61)( 23, 48)( 24, 44)( 26, 31)( 27, 75)( 28, 52)( 30, 35)( 33, 56)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 64)( 41, 47)( 42, 90)( 45, 67)( 46, 94)( 50, 55)( 51, 68)( 53, 71)( 54,103)( 57, 63)
        ( 58, 86)( 59, 79)( 62, 66)( 65, 83)( 69,102)( 70, 98)( 72, 78)( 73,117)( 74,105)( 77, 82)( 80,109)( 81,118)
        ( 84, 89)( 85,110)( 88, 93)( 91, 97)( 92,111)( 95,101)( 96,122)( 99,107)(100,116)(104,108)(106,113)(112,121)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 81)( 28, 53)( 31, 57)( 34, 40)( 35, 88)
        ( 36, 69)( 38, 44)( 39, 92)( 42, 73)( 43, 96)( 46, 52)( 47,103)( 48, 74)( 50, 56)( 51,107)( 54, 77)( 55,108)
        ( 58, 64)( 59,114)( 60, 82)( 62, 68)( 63,118)( 66, 72)( 67,119)( 70, 85)( 71,116)( 75, 99)( 76, 97)( 78, 84)
        ( 79,121)( 80,105)( 83,110)( 86, 91)( 87,112)( 89, 95)( 90,123)( 93, 98)( 94,102)(100,106)(101,124)(104,109)
        (111,117)(113,122)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 77)( 28, 53)( 31, 57)( 34, 40)( 35, 84)
        ( 36, 69)( 38, 44)( 39, 88)( 42, 48)( 43, 92)( 46, 52)( 47, 95)( 50, 56)( 51, 99)( 54, 73)( 55,100)( 58, 64)
        ( 59,110)( 60, 78)( 62, 68)( 63,114)( 66, 72)( 67,115)( 70, 81)( 71,112)( 74, 80)( 75,121)( 76,103)( 79,106)
        ( 82, 87)( 83,108)( 85, 91)( 86,123)( 89, 94)( 90,119)( 93, 98)( 96,102)( 97,120)(101,105)(104,117)(107,113)
        (109,122)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 32)( 18, 36)( 19, 59)( 23, 44)( 24, 40)( 26, 31)( 27, 75)( 28, 48)( 30, 35)( 33, 52)( 34, 76)
        ( 38, 43)( 39, 63)( 41, 67)( 42, 84)( 46, 51)( 47, 68)( 49, 71)( 50, 92)( 53, 58)( 54,102)( 55, 79)( 57, 62)
        ( 60, 66)( 61,103)( 64, 83)( 65,106)( 69, 91)( 70, 87)( 72, 78)( 73,118)( 74, 94)( 77, 82)( 80, 98)( 81,119)
        ( 85, 90)( 86,110)( 88, 96)( 89,117)( 93, 97)( 95,114)( 99,105)(100,108)(101,122)(104,109)(107,113)(111,116)
        (112,123)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 64)( 24, 49)( 26, 32)( 27, 68)( 30, 52)( 31, 72)( 34, 39)( 35, 53)
        ( 37, 43)( 38, 81)( 41, 56)( 42, 84)( 45, 51)( 46, 95)( 47, 57)( 50, 60)( 54, 80)( 55, 76)( 58, 92)( 59, 88)
        ( 61, 67)( 62,106)( 63, 96)( 65, 71)( 66,110)( 69, 75)( 70,111)( 73, 79)( 74,114)( 77, 99)( 78,117)( 82, 87)
        ( 83,100)( 85, 91)( 86,122)( 89, 94)( 90,105)( 93, 98)( 97,102)(101,121)(103,109)(104,123)(107,113)(108,119)
        (112,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 71)( 27, 51)( 29, 34)( 32, 55)( 33, 72)( 36, 42)
        ( 37, 80)( 38, 60)( 40, 46)( 41, 83)( 44, 63)( 45, 87)( 49, 54)( 50, 64)( 52, 67)( 53, 96)( 56, 62)( 57,106)
        ( 58, 75)( 61, 79)( 65, 95)( 66, 91)( 68, 74)( 69,114)( 70, 98)( 73, 78)( 76,102)( 77,115)( 81, 86)( 82,107)
        ( 84, 90)( 85,119)( 88, 94)( 89,121)( 92,100)( 93,113)( 97,101)( 99,110)(103,109)(104,123)(105,116)(108,118)
        (111,117)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 71)( 27, 55)( 29, 34)( 32, 59)( 33, 72)( 36, 42)
        ( 37, 80)( 38, 64)( 40, 46)( 41, 83)( 44, 50)( 45, 87)( 48, 54)( 49, 91)( 52, 58)( 53, 95)( 56, 67)( 57, 96)
        ( 60, 66)( 61,106)( 62, 75)( 65, 79)( 68, 74)( 69,114)( 70, 99)( 73, 78)( 76,102)( 77,115)( 81, 86)( 82,107)
        ( 84, 90)( 85,119)( 88, 94)( 89,121)( 92, 98)( 93,113)( 97,101)(100,110)(103,109)(104,123)(105,116)(108,118)
        (111,117)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 60)( 23, 47)( 24, 43)( 26, 31)( 27, 75)( 28, 51)( 30, 35)( 33, 55)( 34, 76)
        ( 37, 42)( 38, 63)( 40, 46)( 41, 84)( 44, 67)( 45, 87)( 49, 54)( 50, 68)( 52, 71)( 53, 96)( 56, 62)( 57,106)
        ( 58, 79)( 61, 66)( 64, 83)( 65,107)( 69, 95)( 70, 91)( 72, 78)( 73,117)( 74, 99)( 77, 82)( 80,102)( 81,118)
        ( 85, 90)( 86,110)( 88, 94)( 89,122)( 92, 98)( 93,116)( 97,101)(100,113)(103,109)(104,124)(105,119)(108,112)
        (111,121)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 36)( 19, 60)( 23, 47)( 24, 43)( 26, 32)( 27, 75)( 28, 51)( 30, 35)( 31, 79)( 34, 55)
        ( 37, 42)( 38, 63)( 40, 46)( 41, 84)( 44, 67)( 45, 87)( 49, 54)( 50, 68)( 52, 71)( 53, 96)( 56, 62)( 57,106)
        ( 58, 80)( 61, 66)( 64, 83)( 65,107)( 69, 95)( 70, 91)( 72, 78)( 73,117)( 74, 99)( 76, 82)( 77,118)( 81,102)
        ( 85, 90)( 86,110)( 88, 94)( 89,122)( 92, 98)( 93,116)( 97,101)(100,113)(103,109)(104,124)(105,119)(108,112)
        (111,121)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 47)( 24, 43)( 26, 31)( 27, 75)( 28, 55)( 30, 35)( 33, 59)( 34, 76)
        ( 37, 42)( 38, 67)( 40, 46)( 41, 84)( 44, 50)( 45, 87)( 48, 54)( 49, 91)( 52, 58)( 53, 95)( 56, 71)( 57, 98)
        ( 60, 66)( 61,106)( 62, 79)( 65, 70)( 68, 83)( 69,107)( 72, 78)( 73,117)( 74, 99)( 77, 82)( 80,102)( 81,118)
        ( 85, 90)( 86,110)( 88, 94)( 89,122)( 92, 97)( 93,116)( 96,101)(100,113)(103,109)(104,124)(105,119)(108,112)
        (111,121)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 47)( 24, 43)( 26, 31)( 27, 75)( 28, 52)( 30, 35)( 33, 55)( 34, 76)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 84)( 44, 67)( 45, 87)( 48, 54)( 49, 98)( 50, 68)( 53, 71)( 56, 62)( 57,106)
        ( 58, 79)( 60, 66)( 61,109)( 65, 83)( 69, 95)( 70, 91)( 72, 78)( 73,117)( 74, 99)( 77, 82)( 80,102)( 81,118)
        ( 85, 90)( 86,110)( 88, 94)( 89,122)( 92, 97)( 93,116)( 96,101)(100,113)(103,108)(104,124)(105,119)(107,112)
        (111,121)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 36)( 19, 63)( 23, 47)( 24, 43)( 26, 32)( 27, 75)( 28, 52)( 30, 35)( 31, 79)( 34, 55)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 84)( 44, 67)( 45, 87)( 48, 54)( 49, 98)( 50, 68)( 53, 71)( 56, 62)( 57,106)
        ( 58, 80)( 60, 66)( 61,109)( 65, 83)( 69, 95)( 70, 91)( 72, 78)( 73,117)( 74, 99)( 76, 82)( 77,118)( 81,102)
        ( 85, 90)( 86,110)( 88, 94)( 89,122)( 92, 97)( 93,116)( 96,101)(100,113)(103,108)(104,124)(105,119)(107,112)
        (111,121)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 44)( 24, 40)( 27, 32)( 28, 52)( 30, 56)( 31, 73)( 34, 39)( 35, 68)
        ( 37, 43)( 38, 81)( 41, 47)( 42, 84)( 45, 51)( 46, 88)( 49, 55)( 50, 92)( 53, 72)( 54, 93)( 57, 63)( 58,103)
        ( 59, 76)( 61, 67)( 62,104)( 65, 71)( 66,107)( 69, 80)( 70,110)( 74, 79)( 75, 96)( 77, 99)( 78,118)( 82, 87)
        ( 83,114)( 85, 91)( 86,123)( 89, 95)( 90,120)( 94, 98)( 97,117)(100,106)(101,112)(102,121)(105,109)(108,113)
        (111,116)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 44)( 24, 40)( 27, 32)( 28, 52)( 30, 56)( 31, 73)( 34, 39)( 35, 68)
        ( 37, 43)( 38, 81)( 41, 47)( 42, 84)( 45, 51)( 46, 88)( 49, 55)( 50, 92)( 53, 72)( 54, 95)( 57, 63)( 58,103)
        ( 59, 76)( 61, 67)( 62,106)( 65, 71)( 66,107)( 69, 80)( 70,110)( 74, 79)( 75, 96)( 77, 99)( 78,118)( 82, 87)
        ( 83,114)( 85, 91)( 86,123)( 89, 94)( 90,120)( 93, 98)( 97,117)(100,105)(101,112)(102,121)(104,109)(108,113)
        (111,116)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 29)( 18, 33)( 19, 61)( 23, 45)( 24, 41)( 27, 32)( 28, 50)( 30, 53)( 31, 73)( 34, 40)( 35, 84)
        ( 36, 64)( 38, 44)( 39, 88)( 42, 68)( 43, 92)( 46, 52)( 47,103)( 48, 69)( 51, 72)( 54, 60)( 55, 83)( 56, 76)
        ( 58, 63)( 59, 66)( 62, 67)( 65, 80)( 70,100)( 71, 96)( 74, 79)( 75,104)( 77,107)( 78,112)( 81, 87)( 82,108)
        ( 85, 91)( 86,119)( 89, 95)( 90,122)( 93, 99)( 94,117)( 97,102)( 98,114)(101,106)(105,111)(109,121)(110,115)
        (113,118)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 39)( 23, 35)( 26, 47)( 27, 43)( 29, 34)( 30, 59)( 32, 38)( 33, 72)( 36, 63)
        ( 37, 75)( 41, 46)( 42, 64)( 44, 67)( 45, 84)( 48, 54)( 49, 94)( 50, 68)( 52, 58)( 53, 98)( 56, 62)( 57,102)
        ( 60, 71)( 61,103)( 65, 83)( 66, 79)( 69, 90)( 70, 86)( 73, 78)( 74,106)( 76, 82)( 77,115)( 80, 88)( 81,113)
        ( 85, 89)( 87,110)( 91, 97)( 92,118)( 93,111)( 95,101)( 96,119)( 99,105)(100,122)(104,109)(107,114)(108,123)
        (112,116)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 77)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 90)( 39, 69)( 41, 47)( 42, 94)( 45, 72)( 46, 98)( 49, 55)( 50,106)( 51, 73)( 53, 59)( 54,110)
        ( 57, 76)( 58,111)( 61, 67)( 62,117)( 63, 84)( 65, 71)( 66,121)( 70, 87)( 74,102)( 75, 99)( 78, 83)( 79,108)
        ( 81, 86)( 82,104)( 85,113)( 88, 93)( 89,122)( 91, 97)( 92,123)( 95,101)( 96,119)(100,115)(103,109)(105,116)
        (107,112)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 77)
        ( 37, 64)( 38, 80)( 42, 47)( 43, 65)( 45, 68)( 46, 89)( 49, 55)( 50, 99)( 51, 69)( 53, 59)( 54,102)( 57, 63)
        ( 58,106)( 61, 72)( 62,107)( 66, 88)( 67, 84)( 70, 95)( 71, 91)( 73, 79)( 74,121)( 75,110)( 78, 83)( 81, 87)
        ( 82,122)( 85, 93)( 86,116)( 90, 94)( 92,113)( 96,101)( 97,119)( 98,114)(100,105)(103,109)(104,120)(108,112)
        (111,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 77)
        ( 37, 64)( 38, 80)( 42, 47)( 43, 65)( 45, 68)( 46, 89)( 49, 55)( 50, 99)( 51, 69)( 53, 59)( 54,102)( 57, 63)
        ( 58,106)( 61, 72)( 62,109)( 66, 88)( 67, 84)( 70, 95)( 71, 91)( 73, 79)( 74,121)( 75,110)( 78, 83)( 81, 87)
        ( 82,122)( 85, 93)( 86,116)( 90, 94)( 92,113)( 96,101)( 97,119)( 98,114)(100,105)(103,108)(104,120)(107,112)
        (111,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 80)
        ( 37, 64)( 38, 83)( 42, 47)( 43, 65)( 45, 68)( 46, 92)( 49, 55)( 50,102)( 51, 69)( 53, 59)( 54,103)( 57, 63)
        ( 58,106)( 61, 72)( 62,110)( 66, 91)( 67, 87)( 70, 98)( 71, 94)( 73, 79)( 74,117)( 75,111)( 77, 82)( 78,121)
        ( 81, 86)( 84, 90)( 85,122)( 88, 96)( 89,116)( 93, 97)( 95,113)( 99,105)(100,119)(101,114)(104,109)(107,112)
        (108,120)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 45)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 80)
        ( 37, 64)( 38, 83)( 41, 47)( 42, 94)( 43, 65)( 46, 68)( 49, 55)( 50,102)( 51, 69)( 53, 59)( 54,106)( 57, 63)
        ( 58,110)( 61, 72)( 62,111)( 66, 91)( 67, 87)( 70, 98)( 71, 95)( 73, 79)( 74,117)( 75,108)( 77, 82)( 78,121)
        ( 81, 86)( 84, 90)( 85,122)( 88, 93)( 89,116)( 92, 97)( 96,113)( 99,105)(100,119)(101,114)(103,109)(104,120)
        (107,112)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 82)( 28, 56)( 30, 35)( 33, 59)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 70)( 41, 47)( 42, 95)( 45, 74)( 46, 98)( 49, 55)( 50,106)( 51, 75)( 53, 58)( 54,110)
        ( 57, 78)( 60, 66)( 61, 93)( 62, 86)( 64, 69)( 65, 72)( 68, 73)( 71, 90)( 76,102)( 77, 99)( 79, 85)( 80,121)
        ( 81,111)( 84, 89)( 87,114)( 88,122)( 91, 97)( 92,115)( 96,101)(100,116)(103,109)(104,123)(105,117)(107,113)
        (108,120)(112,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 52)( 29, 55)( 30, 68)( 33, 39)( 34, 79)( 35, 60)
        ( 37, 43)( 38, 82)( 41, 63)( 42, 86)( 45, 51)( 46, 94)( 47, 64)( 49, 54)( 50, 98)( 53, 67)( 56, 62)( 57,106)
        ( 58, 71)( 61, 75)( 65, 90)( 66, 87)( 69, 74)( 70, 99)( 72,102)( 73,114)( 76, 81)( 77,121)( 78,107)( 80, 85)
        ( 83, 89)( 84,122)( 88,109)( 91, 97)( 92,119)( 93,110)( 95,101)( 96,116)(100,113)(103,108)(104,124)(105,117)
        (111,118)(112,123)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 60)( 23, 47)( 24, 43)( 26, 31)( 27, 75)( 28, 52)( 30, 35)( 33, 55)( 34, 76)
        ( 37, 42)( 38, 63)( 40, 46)( 41, 84)( 44, 67)( 45, 87)( 48, 54)( 49, 98)( 50, 68)( 53, 71)( 56, 62)( 57,106)
        ( 58, 79)( 61, 66)( 64, 83)( 65,107)( 69, 94)( 70, 91)( 72, 78)( 73,122)( 74, 99)( 77, 82)( 80,102)( 81,123)
        ( 85, 90)( 86,110)( 88, 93)( 89,111)( 92,114)( 95,101)( 96,121)( 97,115)(100,118)(103,109)(104,116)(105,120)
        (108,113)(112,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 45)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 79)
        ( 37, 63)( 38, 80)( 41, 47)( 42, 90)( 43, 64)( 46, 67)( 49, 55)( 50, 98)( 51, 68)( 53, 59)( 54,101)( 57, 62)
        ( 58,105)( 61, 71)( 65, 86)( 66, 83)( 69, 94)( 70, 91)( 72, 78)( 73,121)( 74,106)( 76, 82)( 77,112)( 81, 85)
        ( 84,109)( 87, 93)( 88,116)( 89,110)( 92,113)( 95,100)( 96,119)( 97,114)( 99,104)(102,108)(103,120)(107,117)
        (111,122)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 23)( 11, 45)( 12, 21)( 14, 19)
        ( 15, 57)( 16, 30)( 18, 34)( 22, 41)( 24, 29)( 25, 65)( 26, 49)( 28, 33)( 31, 53)( 32, 66)( 35, 40)( 36, 58)
        ( 38, 44)( 39, 74)( 42, 48)( 43, 77)( 46, 52)( 47, 81)( 50, 61)( 51, 85)( 54, 60)( 55, 97)( 56, 69)( 59, 73)
        ( 62, 68)( 63,105)( 64, 89)( 67, 72)( 70, 93)( 71,106)( 75, 80)( 76, 98)( 78, 84)( 79,110)( 82, 88)( 83,113)
        ( 86, 92)( 87,117)( 90,101)( 91,118)( 94,100)( 95,121)( 96,107)( 99,109)(102,108)(103,124)(104,119)(111,116)
        (112,122)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29)( 30, 31, 32, 33)( 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)
        ( 45, 46, 47, 48)( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 23)( 11, 45)( 12, 21)( 14, 19)
        ( 15, 57)( 16, 31)( 18, 34)( 22, 41)( 24, 30)( 25, 65)( 26, 49)( 28, 33)( 29, 69)( 32, 53)( 35, 40)( 36, 58)
        ( 38, 44)( 39, 74)( 42, 48)( 43, 77)( 46, 52)( 47, 81)( 50, 61)( 51, 85)( 54, 60)( 55, 97)( 56, 70)( 59, 73)
        ( 62, 68)( 63,105)( 64, 89)( 66, 72)( 67,106)( 71, 93)( 75, 80)( 76, 98)( 78, 84)( 79,110)( 82, 88)( 83,113)
        ( 86, 92)( 87,117)( 90,101)( 91,118)( 94,100)( 95,121)( 96,107)( 99,109)(102,108)(103,124)(104,119)(111,116)
        (112,122)(114,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33)( 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)
        ( 45, 46, 47, 48)( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 41)( 26, 32)( 27, 75)( 28, 52)( 30, 36)( 31, 79)( 34, 56)
        ( 35, 83)( 38, 43)( 39, 65)( 42, 68)( 45, 51)( 46, 62)( 47, 69)( 49, 55)( 50, 58)( 53, 71)( 54, 88)( 57, 63)
        ( 59, 87)( 61, 67)( 66, 70)( 72, 78)( 73, 98)( 74, 91)( 76, 82)( 77,102)( 80, 86)( 81,106)( 84, 90)( 85,110)
        ( 89, 94)( 92, 95)( 93,111)( 96,101)( 97,114)( 99,105)(100,119)(103,109)(104,120)(107,113)(108,122)(112,117)
        (115,118)(116,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 78)( 31, 63)( 33, 39)( 34, 79)
        ( 37, 67)( 38, 82)( 41, 46)( 42, 90)( 43, 68)( 45, 50)( 48, 70)( 49, 91)( 52, 58)( 53,101)( 54, 71)( 56, 62)
        ( 57,105)( 60, 66)( 61,106)( 64, 74)( 65,109)( 69, 86)( 72, 97)( 73, 94)( 75, 81)( 76,121)( 77,110)( 80, 85)
        ( 83, 89)( 84,122)( 87, 93)( 88,116)( 92, 96)( 95,113)( 98,104)( 99,119)(100,114)(102,108)(103,120)(107,112)
        (111,117)(115,123)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 48)( 29, 35)( 30, 78)( 31, 63)( 33, 39)( 34, 79)
        ( 37, 67)( 38, 82)( 41, 47)( 42, 90)( 43, 68)( 45, 50)( 46, 93)( 49, 70)( 52, 58)( 53,101)( 54, 71)( 56, 62)
        ( 57,105)( 60, 66)( 61,106)( 64, 74)( 65,109)( 69, 86)( 72, 97)( 73, 94)( 75, 81)( 76,122)( 77,113)( 80, 85)
        ( 83, 89)( 84,123)( 87, 92)( 88,120)( 91, 96)( 95,117)( 98,104)( 99,115)(100,118)(102,108)(103,111)(107,112)
        (110,116)(114,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 47)( 24, 44)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 87)( 38, 43)( 39, 67)( 41, 46)( 42, 68)( 45, 71)( 48, 54)( 49, 92)( 50, 72)( 52, 58)( 53, 95)( 56, 75)
        ( 57, 99)( 60, 66)( 61, 73)( 62, 91)( 65, 70)( 69, 74)( 76, 82)( 77,110)( 78,103)( 80, 86)( 81,111)( 84, 90)
        ( 85,114)( 88, 94)( 89,118)( 93, 98)( 96,102)( 97,119)(100,105)(101,122)(104,106)(107,113)(108,116)(109,123)
        (112,117)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 44)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 87)( 38, 43)( 39, 68)( 41, 46)( 42, 96)( 45, 71)( 48, 54)( 49, 92)( 50, 72)( 52, 58)( 53, 99)( 56, 75)
        ( 57,103)( 60, 66)( 61, 73)( 62, 91)( 64, 70)( 65, 98)( 69, 95)( 74, 97)( 76, 82)( 77,111)( 78,107)( 80, 86)
        ( 81,114)( 84, 90)( 85,115)( 88, 94)( 89,118)( 93,102)(100,106)(101,119)(104,109)(105,122)(108,110)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 53)( 31, 57)( 34, 40)( 35, 87)
        ( 36, 68)( 38, 44)( 39, 91)( 42, 72)( 43, 95)( 46, 52)( 47,107)( 48, 73)( 50, 56)( 51,108)( 54, 76)( 55,105)
        ( 58, 64)( 59,114)( 60, 81)( 62, 67)( 63,118)( 66, 71)( 69, 84)( 70,119)( 74,103)( 75, 99)( 77, 83)( 78,122)
        ( 79,101)( 82,110)( 85, 90)( 86,120)( 88, 94)( 89,116)( 92, 98)( 93,112)( 96,102)( 97,124)(100,106)(104,109)
        (111,117)(113,123)(115,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 53)( 31, 57)( 34, 40)( 35, 87)
        ( 36, 69)( 38, 44)( 39, 91)( 42, 72)( 43, 95)( 46, 52)( 47,104)( 48, 73)( 50, 56)( 51,105)( 54, 76)( 55,107)
        ( 58, 64)( 59,114)( 60, 81)( 62, 68)( 63,118)( 66, 71)( 67,119)( 70, 84)( 74,103)( 75, 99)( 77, 83)( 78,122)
        ( 79,101)( 82,110)( 85, 90)( 86,120)( 88, 94)( 89,116)( 92, 98)( 93,112)( 96,102)( 97,124)(100,108)(106,109)
        (111,117)(113,123)(115,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 72)( 41, 47)( 42, 98)( 45, 75)( 46,102)( 49, 55)( 50,111)( 51, 76)( 53, 59)( 54,112)
        ( 57, 79)( 58,114)( 61, 67)( 62,118)( 63, 87)( 65, 71)( 66,121)( 69, 74)( 70,122)( 73, 91)( 77,110)( 78,106)
        ( 81, 86)( 82,108)( 84, 90)( 85,104)( 88,117)( 89,100)( 92, 97)( 93,123)( 95,101)( 96,120)( 99,105)(103,109)
        (107,115)(113,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 95)( 39, 72)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 55)( 50,112)( 51, 76)( 53, 59)( 54,114)
        ( 57, 79)( 58,115)( 61, 67)( 62,119)( 63, 87)( 65, 71)( 66,122)( 69, 74)( 70, 94)( 73, 91)( 77,111)( 78,107)
        ( 81, 86)( 82,109)( 84, 90)( 85,105)( 88,118)( 89,101)( 92, 98)( 93,123)( 96,102)( 97,121)(100,106)(104,110)
        (108,116)(113,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 57)( 30, 36)( 31, 83)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 99)( 40, 72)( 42, 48)( 43,103)( 46, 75)( 47,107)( 50, 56)( 51,116)( 52, 76)( 54, 60)
        ( 55,118)( 58, 79)( 59,119)( 62, 67)( 63, 91)( 65, 71)( 66,123)( 69, 74)( 70, 98)( 73, 95)( 77,115)( 78,111)
        ( 81, 86)( 82,113)( 84, 90)( 85,109)( 88, 94)( 89,105)( 92,122)( 93,101)( 96,102)( 97,124)(100,106)(104,110)
        (108,114)(112,120)(117,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 68)( 42, 47)( 45, 72)( 46, 99)( 49, 55)( 50,106)( 51, 73)( 53, 59)( 54,107)
        ( 57, 75)( 58,110)( 61, 67)( 62, 70)( 63, 90)( 66, 71)( 69, 94)( 74,102)( 76, 82)( 77,118)( 78,111)( 80, 85)
        ( 81,122)( 84, 89)( 87, 93)( 88,123)( 91, 97)( 92,120)( 95,101)( 96,116)(100,105)(103,109)(104,117)(108,113)
        (112,114)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 67)( 42, 47)( 45, 71)( 46, 99)( 49, 54)( 50, 72)( 52, 58)( 53,107)( 56, 75)
        ( 57,110)( 60, 66)( 61, 69)( 62, 90)( 65, 70)( 68, 94)( 73,106)( 74,102)( 76, 82)( 77,118)( 78,111)( 80, 85)
        ( 81,122)( 84, 89)( 87, 93)( 88,123)( 91, 97)( 92,120)( 95,101)( 96,116)(100,105)(103,109)(104,117)(108,113)
        (112,114)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 67)( 41, 47)( 42, 94)( 45, 71)( 46, 98)( 49, 54)( 50, 72)( 52, 58)( 53,107)( 56, 75)
        ( 57,110)( 60, 66)( 61, 69)( 62, 83)( 65, 70)( 68, 87)( 73,106)( 74,102)( 77, 82)( 78,111)( 80, 86)( 81,115)
        ( 84, 90)( 85,118)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,120)(103,109)(104,117)(108,113)
        (112,114)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 67)( 41, 47)( 42, 94)( 45, 71)( 46, 98)( 49, 55)( 50,107)( 51, 72)( 53, 58)( 54,110)
        ( 57, 75)( 60, 66)( 61, 69)( 62, 83)( 65, 70)( 68, 87)( 73,106)( 74,102)( 77, 82)( 78,111)( 80, 86)( 81,115)
        ( 84, 90)( 85,118)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,120)(103,109)(104,117)(108,113)
        (112,114)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 56)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 67)( 41, 47)( 42, 91)( 45, 71)( 46, 94)( 49, 55)( 50,103)( 51, 72)( 53, 58)( 54,106)
        ( 57, 75)( 60, 66)( 61,114)( 62, 87)( 65, 70)( 68, 90)( 69,115)( 73,102)( 74, 98)( 76, 81)( 77,107)( 79, 85)
        ( 80,118)( 83, 89)( 84,121)( 88,110)( 92, 97)( 93,112)( 95,101)( 96,123)( 99,105)(100,120)(104,109)(108,117)
        (111,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 27, 32)( 28, 52)( 30, 56)( 31, 75)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 90)( 42, 70)( 43, 93)( 46, 51)( 47, 71)( 49, 55)( 50,102)( 53, 74)( 54,103)( 57, 62)
        ( 58,113)( 59, 78)( 61, 66)( 64, 69)( 65,114)( 68, 82)( 72,101)( 73, 97)( 76, 81)( 77,105)( 79,109)( 80,118)
        ( 83, 89)( 84,111)( 85,115)( 87, 92)( 88,122)( 91, 96)( 94,100)( 95,123)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 31, 56)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 90)( 42, 71)( 43, 94)( 46, 51)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,103)( 57, 62)
        ( 58,113)( 59, 80)( 61, 66)( 64, 70)( 65,114)( 68, 83)( 69,115)( 73,101)( 74, 97)( 76, 82)( 77,121)( 78,105)
        ( 81,109)( 84, 89)( 85,111)( 87, 93)( 88,123)( 91, 96)( 92,119)( 95,100)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 31, 56)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 90)( 42, 71)( 43, 94)( 46, 51)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,103)( 57, 63)
        ( 58,113)( 59, 80)( 61, 66)( 62,114)( 65, 70)( 68, 83)( 69,115)( 73,101)( 74, 97)( 76, 82)( 77,121)( 78,105)
        ( 81,109)( 84, 89)( 85,111)( 87, 93)( 88,123)( 91, 96)( 92,119)( 95,100)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 78)( 28, 52)( 31, 56)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 90)( 42, 70)( 43, 94)( 46, 51)( 47,102)( 48, 71)( 50, 55)( 53, 74)( 54,103)( 57, 62)
        ( 58,113)( 59, 79)( 61, 66)( 64, 69)( 65,114)( 68, 82)( 72,101)( 73, 97)( 75, 81)( 76,121)( 77,105)( 80,109)
        ( 83, 89)( 84,111)( 85,115)( 87, 93)( 88,123)( 91, 96)( 92,119)( 95,100)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 27, 32)( 28, 52)( 30, 56)( 31, 76)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 90)( 42, 71)( 43, 93)( 46, 51)( 47,102)( 48, 72)( 50, 55)( 53, 75)( 54,103)( 57, 62)
        ( 58,113)( 59, 79)( 61, 66)( 64, 70)( 65,114)( 68, 83)( 69,115)( 73,101)( 74, 97)( 77, 82)( 78,105)( 80,109)
        ( 81,118)( 84, 89)( 85,111)( 87, 92)( 88,122)( 91, 96)( 94,100)( 95,123)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 76)( 34, 40)( 35, 86)
        ( 36, 68)( 38, 44)( 39, 90)( 42, 71)( 43, 94)( 46, 52)( 47,105)( 48, 72)( 50, 56)( 51,106)( 54, 75)( 55,107)
        ( 58, 63)( 59,113)( 60, 79)( 62, 67)( 65, 70)( 66,114)( 69, 83)( 73,101)( 74, 98)( 77, 82)( 78,103)( 80,109)
        ( 81,119)( 84, 89)( 85,115)( 87, 93)( 88,111)( 91, 97)( 92,122)( 95,100)( 96,123)( 99,117)(102,108)(104,118)
        (110,116)(112,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 78)( 28, 52)( 31, 56)( 34, 40)( 35, 85)
        ( 36, 67)( 38, 44)( 39, 89)( 42, 70)( 43, 93)( 46, 51)( 47,102)( 48, 71)( 50, 55)( 53, 74)( 54,103)( 57, 62)
        ( 58,113)( 59, 79)( 61, 66)( 64, 69)( 65,114)( 68, 82)( 72,101)( 73, 97)( 75, 81)( 76,121)( 77,105)( 80,109)
        ( 83, 88)( 84,115)( 86, 92)( 87,111)( 90, 96)( 91,123)( 94,100)( 95,119)( 98,107)( 99,120)(104,108)(106,117)
        (110,116)(112,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 71)( 27, 52)( 30, 56)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 82)( 41, 64)( 42, 86)( 45, 51)( 46, 94)( 47, 65)( 49, 55)( 50, 95)( 53, 67)( 54, 98)( 57, 63)
        ( 58,106)( 59, 72)( 62, 75)( 66, 90)( 68, 74)( 69,113)( 70, 99)( 73,102)( 76, 81)( 77,117)( 78,107)( 80, 85)
        ( 83, 89)( 84,118)( 87, 93)( 88,121)( 91, 97)( 92,112)( 96,101)(100,109)(103,108)(104,120)(105,114)(110,116)
        (111,122)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 30)( 18, 33)( 19, 61)( 23, 41)( 24, 37)( 26, 32)( 27, 77)( 28, 49)( 31, 53)( 35, 40)( 36, 65)
        ( 38, 69)( 39, 82)( 42, 48)( 43, 92)( 44, 70)( 46, 52)( 47, 93)( 50, 73)( 51, 94)( 54, 60)( 55,100)( 56, 78)
        ( 58, 64)( 59,104)( 62, 68)( 63,107)( 66, 81)( 67,110)( 71, 88)( 72, 85)( 74, 80)( 75,122)( 76, 90)( 79, 96)
        ( 83, 87)( 84,114)( 86,118)( 89, 95)( 91,119)( 97,103)( 98,116)( 99,123)(101,106)(102,112)(105,109)(108,113)
        (111,117)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 71)( 27, 51)( 30, 55)( 33, 39)( 34, 78)( 35, 60)
        ( 37, 43)( 38, 82)( 41, 63)( 42, 86)( 45, 50)( 46, 64)( 48, 54)( 49, 95)( 52, 67)( 53, 96)( 56, 62)( 57,106)
        ( 58, 72)( 61, 75)( 65, 94)( 66, 90)( 68, 74)( 69,114)( 70, 98)( 73,102)( 76, 81)( 77,107)( 79, 85)( 80,118)
        ( 83, 89)( 84,119)( 87, 93)( 88,121)( 91,100)( 92,113)( 97,101)( 99,110)(103,109)(104,123)(105,115)(108,117)
        (111,116)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 71)( 27, 51)( 30, 55)( 33, 39)( 34, 79)( 35, 60)
        ( 37, 43)( 38, 82)( 41, 63)( 42, 86)( 45, 50)( 46, 95)( 47, 64)( 49, 54)( 52, 67)( 53, 96)( 56, 62)( 57,106)
        ( 58, 72)( 61, 75)( 65, 94)( 66, 90)( 68, 74)( 69,114)( 70, 98)( 73,102)( 76, 81)( 77,118)( 78,107)( 80, 85)
        ( 83, 89)( 84,119)( 87, 93)( 88,121)( 91,100)( 92,113)( 97,101)( 99,110)(103,109)(104,123)(105,115)(108,117)
        (111,116)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 71)( 27, 52)( 30, 56)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 82)( 41, 64)( 42, 86)( 45, 51)( 46, 94)( 47, 65)( 49, 55)( 50, 95)( 53, 67)( 54, 98)( 57, 63)
        ( 58,106)( 59, 72)( 62, 75)( 66, 90)( 68, 74)( 69,114)( 70, 99)( 73,102)( 76, 81)( 77,118)( 78,107)( 80, 85)
        ( 83, 89)( 84,119)( 87, 93)( 88,121)( 91, 97)( 92,113)( 96,101)(100,110)(103,109)(104,123)(105,115)(108,117)
        (111,116)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 30)( 18, 33)( 19, 62)( 23, 44)( 24, 40)( 26, 32)( 27, 78)( 28, 51)( 31, 55)( 34, 39)( 35, 66)
        ( 37, 43)( 38, 83)( 41, 70)( 42, 86)( 45, 50)( 46, 71)( 48, 54)( 49, 95)( 52, 74)( 53, 98)( 56, 61)( 57,106)
        ( 58, 79)( 60, 65)( 63, 69)( 64,107)( 67, 82)( 68,110)( 72, 94)( 73, 90)( 75, 81)( 76,118)( 77, 99)( 80,102)
        ( 84, 89)( 85,111)( 87, 93)( 88,122)( 91, 97)( 92,117)( 96,101)(100,114)(103,109)(104,124)(105,119)(108,113)
        (112,121)(115,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 26, 32)( 27, 76)( 28, 49)( 31, 52)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 81)( 42, 48)( 43, 89)( 44, 69)( 46, 51)( 47, 92)( 50, 72)( 53, 59)( 54,100)( 55, 77)( 57, 63)
        ( 58,104)( 61, 67)( 62,107)( 65, 80)( 66,110)( 70, 88)( 71, 84)( 73, 79)( 74,122)( 75, 93)( 78, 96)( 82, 87)
        ( 83,114)( 85, 91)( 86,121)( 90, 95)( 94,118)( 97,103)( 98,116)( 99,123)(101,106)(102,112)(105,109)(108,113)
        (111,117)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 30)( 18, 33)( 19, 63)( 23, 44)( 24, 40)( 26, 32)( 27, 78)( 28, 52)( 31, 55)( 34, 39)( 35, 67)
        ( 37, 43)( 38, 83)( 41, 70)( 42, 86)( 45, 51)( 46, 95)( 47, 71)( 49, 54)( 50, 98)( 53, 74)( 56, 62)( 57,106)
        ( 58, 79)( 60, 66)( 61,107)( 64, 69)( 65,110)( 68, 82)( 72, 94)( 73, 90)( 75, 81)( 76,118)( 77, 99)( 80,102)
        ( 84, 89)( 85,111)( 87, 93)( 88,122)( 91, 97)( 92,117)( 96,101)(100,114)(103,109)(104,124)(105,119)(108,113)
        (112,121)(115,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 78)( 31, 63)( 33, 39)( 34, 82)
        ( 37, 66)( 38, 85)( 41, 46)( 42, 67)( 44, 50)( 45, 94)( 48, 70)( 49, 95)( 52, 58)( 53,105)( 54, 71)( 56, 62)
        ( 57,106)( 60, 65)( 61,109)( 64, 74)( 68, 93)( 69, 89)( 72,101)( 73, 97)( 75, 81)( 76,118)( 77,110)( 79, 84)
        ( 80,121)( 83, 88)( 86, 92)( 87,122)( 90, 99)( 91,116)( 96,100)( 98,113)(102,108)(103,120)(104,114)(107,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 60)( 22, 48)( 23, 44)( 25, 31)( 26, 74)( 27, 55)( 29, 35)( 30, 78)( 33, 59)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 63)( 41, 47)( 42, 94)( 45, 66)( 46, 98)( 49, 54)( 50, 67)( 52, 58)( 53,106)( 56, 70)
        ( 57,107)( 61, 65)( 62, 82)( 64, 86)( 68,105)( 69,101)( 71, 77)( 72,117)( 73,109)( 75, 81)( 76,121)( 80, 85)
        ( 83, 89)( 84,122)( 87, 93)( 88,123)( 91, 97)( 92,119)( 95,100)( 96,115)( 99,104)(102,111)(103,116)(108,112)
        (110,113)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 78)( 31, 63)( 33, 39)( 34, 82)
        ( 37, 67)( 38, 85)( 41, 46)( 42, 68)( 44, 50)( 45, 94)( 48, 71)( 49, 95)( 52, 58)( 53,105)( 54, 72)( 56, 62)
        ( 57,106)( 60, 66)( 61,109)( 64, 75)( 65,110)( 69, 93)( 70, 89)( 73,101)( 74, 97)( 76, 81)( 77,113)( 79, 84)
        ( 80,122)( 83, 88)( 86, 92)( 87,123)( 90, 99)( 91,120)( 96,100)( 98,117)(102,108)(103,115)(104,118)(107,112)
        (111,116)(114,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 78)( 31, 63)( 33, 39)( 34, 82)
        ( 37, 67)( 38, 85)( 41, 46)( 42, 94)( 43, 68)( 45, 50)( 48, 71)( 49, 95)( 52, 58)( 53,105)( 54, 72)( 56, 62)
        ( 57,106)( 60, 66)( 61,109)( 64, 75)( 65,110)( 69, 93)( 70, 89)( 73,101)( 74, 97)( 76, 81)( 77,113)( 79, 84)
        ( 80,122)( 83, 88)( 86, 92)( 87,123)( 90, 99)( 91,120)( 96,100)( 98,117)(102,108)(103,115)(104,118)(107,112)
        (111,116)(114,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 73)( 34, 40)( 35, 81)
        ( 36, 68)( 38, 44)( 39, 83)( 42, 48)( 43, 87)( 46, 52)( 47, 91)( 50, 56)( 51, 95)( 54, 72)( 55, 99)( 58, 63)
        ( 59,109)( 60, 76)( 62, 67)( 65, 71)( 66,110)( 69, 80)( 70,113)( 74, 79)( 75,102)( 77,106)( 78,118)( 82, 86)
        ( 84, 90)( 85,114)( 88, 94)( 89,123)( 92, 98)( 93,120)( 96,101)( 97,104)(100,105)(103,117)(107,112)(108,121)
        (111,116)(115,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 58)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 77)( 31, 62)( 33, 39)( 34, 81)
        ( 37, 66)( 38, 85)( 41, 46)( 42, 67)( 44, 50)( 45, 94)( 48, 70)( 49, 95)( 52, 57)( 53,105)( 54, 71)( 56, 61)
        ( 59, 65)( 60,106)( 63, 74)( 64,109)( 68, 93)( 69, 89)( 72,101)( 73, 97)( 75, 80)( 76,110)( 78, 84)( 79,118)
        ( 82, 88)( 83,121)( 86, 92)( 87,122)( 90, 99)( 91,116)( 96,100)( 98,113)(102,108)(103,120)(104,114)(107,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 58)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 77)( 31, 62)( 33, 39)( 34, 81)
        ( 37, 66)( 38, 85)( 41, 46)( 42, 94)( 43, 67)( 45, 50)( 48, 70)( 49, 95)( 52, 57)( 53,105)( 54, 71)( 56, 61)
        ( 59, 65)( 60,106)( 63, 74)( 64,109)( 68, 93)( 69, 89)( 72,101)( 73, 97)( 75, 80)( 76,110)( 78, 84)( 79,118)
        ( 82, 88)( 83,121)( 86, 92)( 87,122)( 90, 99)( 91,116)( 96,100)( 98,113)(102,108)(103,120)(104,114)(107,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 86)( 38, 43)( 39, 68)( 41, 47)( 42, 95)( 45, 71)( 46, 98)( 49, 55)( 50,106)( 51, 72)( 53, 59)( 54,110)
        ( 57, 75)( 58,113)( 61, 67)( 62, 97)( 63, 90)( 66, 70)( 69, 94)( 73,102)( 74, 99)( 76, 82)( 77,118)( 78,114)
        ( 80, 85)( 81,121)( 84, 89)( 87, 93)( 88,122)( 91,100)( 92,105)( 96,101)(103,109)(104,123)(107,112)(108,120)
        (111,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 48)( 24, 44)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 78)( 34, 56)
        ( 35, 82)( 38, 43)( 39, 94)( 40, 64)( 42, 47)( 45, 67)( 46, 95)( 49, 55)( 50,105)( 51, 68)( 54, 71)( 57, 62)
        ( 58, 93)( 59, 86)( 61, 66)( 65, 90)( 69,102)( 70, 98)( 72, 77)( 73,121)( 74,106)( 76, 81)( 79, 85)( 80,122)
        ( 83, 89)( 84,123)( 87,109)( 88,119)( 91, 97)( 92,110)( 96,101)( 99,113)(100,111)(103,108)(104,114)(107,117)
        (112,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 60)( 23, 45)( 24, 41)( 26, 32)( 27, 75)( 28, 50)( 30, 36)( 31, 79)( 34, 53)
        ( 35, 82)( 39, 44)( 40, 64)( 42, 67)( 43, 91)( 46, 52)( 47,101)( 48, 68)( 51, 71)( 54, 59)( 55,109)( 56, 86)
        ( 58, 63)( 61, 66)( 62,110)( 65, 90)( 69, 98)( 70, 94)( 72, 78)( 73,121)( 74,102)( 76, 81)( 77,122)( 80, 85)
        ( 83, 89)( 84,123)( 87,105)( 88,119)( 92, 97)( 93,111)( 95,113)( 96,107)( 99,104)(100,114)(103,117)(106,112)
        (108,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 65)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 91)( 39, 68)( 41, 47)( 42, 92)( 45, 71)( 46, 95)( 49, 55)( 50,103)( 51, 72)( 53, 59)( 54,107)
        ( 57, 75)( 58,108)( 61, 67)( 62, 90)( 63, 83)( 66, 70)( 69, 87)( 73, 99)( 74, 96)( 77, 82)( 78,111)( 80, 86)
        ( 81,119)( 84,114)( 85,122)( 88, 94)( 89,115)( 93, 98)( 97,116)(100,106)(101,123)(102,117)(104,110)(105,121)
        (109,113)(112,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 47)( 24, 43)( 26, 31)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 67)( 40, 46)( 41, 88)( 44, 71)( 45, 91)( 48, 54)( 49, 99)( 50, 72)( 52, 58)( 53,103)( 56, 75)
        ( 57,106)( 60, 66)( 61,114)( 62, 83)( 65, 70)( 68, 87)( 69,115)( 73, 95)( 74, 92)( 77, 82)( 78,107)( 80, 86)
        ( 81,119)( 84,110)( 85,122)( 89, 94)( 90,116)( 93,112)( 96,102)( 97,123)( 98,113)(100,105)(101,121)(104,109)
        (108,118)(111,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 81)( 28, 57)( 30, 36)( 31, 84)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 96)( 40, 70)( 42, 48)( 43, 99)( 46, 73)( 47,102)( 50, 56)( 51,110)( 52, 74)( 54, 60)
        ( 55,114)( 58, 77)( 59,117)( 62, 68)( 63,108)( 64, 91)( 66, 72)( 67,121)( 71, 95)( 75,106)( 76,103)( 78, 83)
        ( 79, 89)( 80,118)( 82, 86)( 85, 90)( 88, 94)( 92,112)( 93,119)( 97,101)( 98,122)(100,105)(104,123)(107,113)
        (109,124)(111,116)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 54)( 30, 36)( 31, 83)( 34, 57)
        ( 35, 86)( 38, 44)( 39, 95)( 40, 68)( 42, 48)( 43, 96)( 46, 72)( 47, 98)( 50, 56)( 51,109)( 52, 73)( 55, 76)
        ( 58, 64)( 59,117)( 60, 90)( 62, 67)( 63,121)( 66, 71)( 69, 94)( 70,122)( 74,106)( 75,102)( 77, 82)( 78, 88)
        ( 79,110)( 81, 85)( 84, 89)( 87, 93)( 91,113)( 92,111)( 97,101)( 99,105)(100,123)(103,115)(104,119)(107,112)
        (108,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 80)( 28, 54)( 30, 36)( 31, 83)( 34, 57)
        ( 35, 86)( 38, 44)( 39, 95)( 40, 68)( 42, 48)( 43, 96)( 46, 72)( 47, 98)( 50, 56)( 51,110)( 52, 73)( 55, 76)
        ( 58, 64)( 59,117)( 60, 90)( 62, 67)( 63,121)( 66, 71)( 69, 94)( 70,122)( 74,106)( 75,102)( 77, 82)( 78, 88)
        ( 79,111)( 81, 85)( 84, 89)( 87, 93)( 91,114)( 92,112)( 97,101)( 99,105)(100,123)(103,109)(104,119)(107,113)
        (108,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 51)( 28, 34)( 29, 68)( 32, 55)( 33, 71)( 36, 42)
        ( 37, 82)( 38, 60)( 40, 46)( 41, 83)( 44, 63)( 45, 86)( 49, 54)( 50, 64)( 52, 67)( 53, 95)( 56, 62)( 57,105)
        ( 58, 75)( 61, 78)( 65, 94)( 66, 90)( 69, 74)( 70, 98)( 72, 77)( 73,114)( 76,101)( 79, 85)( 80,118)( 81,106)
        ( 84, 89)( 87, 93)( 88,119)( 91,109)( 92,121)( 96,100)( 97,110)( 99,113)(102,108)(103,123)(104,115)(107,117)
        (111,116)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 47)( 24, 43)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 55)( 34, 79)
        ( 37, 42)( 38, 67)( 40, 46)( 41, 68)( 44, 71)( 45, 86)( 48, 54)( 49, 97)( 50, 72)( 53, 75)( 56, 62)( 57,105)
        ( 58, 83)( 60, 66)( 61,106)( 64, 70)( 65,109)( 69, 89)( 73, 94)( 74, 90)( 77, 82)( 78, 98)( 80, 85)( 81,118)
        ( 84,101)( 87, 93)( 88,110)( 91,113)( 92,121)( 95,100)( 96,114)( 99,117)(102,108)(103,123)(104,119)(107,112)
        (111,124)(115,120)(116,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 80)( 31, 64)( 33, 39)( 34, 84)
        ( 37, 68)( 38, 88)( 41, 47)( 42, 95)( 43, 69)( 45, 51)( 46, 99)( 49, 72)( 50,100)( 53, 59)( 54,110)( 55, 73)
        ( 57, 63)( 58,114)( 61, 67)( 62,115)( 65, 76)( 66,112)( 70, 91)( 71, 89)( 74,106)( 75,103)( 77, 83)( 78,121)
        ( 79,108)( 81, 87)( 82,122)( 85, 90)( 86, 94)( 92, 98)( 93,123)( 96,102)( 97,120)(101,105)(104,117)(107,113)
        (109,118)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 73)( 31, 60)( 33, 39)( 34, 76)
        ( 37, 64)( 38, 80)( 42, 47)( 43, 65)( 45, 68)( 46, 88)( 49, 55)( 50, 98)( 51, 69)( 53, 59)( 54, 99)( 57, 63)
        ( 58,102)( 61, 72)( 62,105)( 66, 87)( 67, 83)( 70, 94)( 71, 91)( 74, 79)( 75,109)( 77, 82)( 78,122)( 81, 86)
        ( 84,113)( 85,123)( 89, 93)( 90,114)( 92,117)( 95,101)( 96,107)( 97,118)(100,104)(103,108)(106,112)(110,121)
        (111,119)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 72)( 31, 57)( 33, 39)( 34, 76)
        ( 37, 60)( 38, 80)( 42, 47)( 43, 61)( 45, 64)( 46, 88)( 49, 55)( 50, 98)( 51, 65)( 53, 59)( 54,101)( 58, 68)
        ( 62, 87)( 63, 83)( 66, 94)( 67, 91)( 69, 75)( 70,114)( 71,102)( 73, 79)( 74,117)( 77, 82)( 78,121)( 81, 86)
        ( 84,105)( 85,122)( 89, 93)( 90,106)( 92,109)( 95,100)( 96,116)( 97,110)( 99,104)(103,113)(107,112)(108,123)
        (111,119)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 41)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 48)( 27, 44)( 29, 35)( 30, 72)( 31, 57)( 33, 39)( 34, 76)
        ( 37, 60)( 38, 80)( 42, 47)( 43, 61)( 45, 64)( 46, 88)( 49, 55)( 50, 98)( 51, 65)( 53, 59)( 54,102)( 58, 68)
        ( 62, 87)( 63, 83)( 66, 94)( 67, 91)( 69, 75)( 70,113)( 71,103)( 73, 79)( 74,117)( 77, 82)( 78,121)( 81, 86)
        ( 84,105)( 85,122)( 89, 93)( 90,106)( 92,109)( 95,101)( 96,115)( 97,110)( 99,104)(100,116)(107,112)(108,123)
        (111,119)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 79)
        ( 37, 64)( 38, 83)( 41, 47)( 42, 91)( 43, 65)( 45, 51)( 46, 95)( 49, 68)( 50, 98)( 53, 59)( 54,106)( 55, 69)
        ( 58, 63)( 61, 72)( 62,107)( 66, 87)( 67, 84)( 70,102)( 71, 99)( 73, 78)( 74,110)( 76, 82)( 77,118)( 80, 86)
        ( 81,121)( 85, 90)( 88, 94)( 89,122)( 92, 97)( 93,116)( 96,101)(100,113)(103,109)(104,120)(105,114)(108,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 46)( 23, 43)( 25, 31)( 26, 74)( 27, 54)( 29, 35)( 30, 78)( 33, 58)( 34, 82)
        ( 37, 42)( 38, 63)( 40, 45)( 41, 91)( 44, 66)( 47, 53)( 48, 87)( 49, 67)( 51, 57)( 52, 93)( 55, 70)( 56, 97)
        ( 59, 65)( 60, 68)( 61, 86)( 64, 90)( 69, 92)( 71, 77)( 72,109)( 73,101)( 75, 81)( 76,110)( 79, 85)( 80,113)
        ( 83, 89)( 84,117)( 88, 96)( 94,100)( 95,118)( 98,104)( 99,121)(102,105)(103,122)(106,112)(107,115)(108,123)
        (111,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45)
        ( 46, 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 47)( 24, 44)( 26, 32)( 27, 75)( 28, 55)( 30, 36)( 31, 78)( 34, 59)
        ( 35, 82)( 38, 43)( 39, 67)( 41, 46)( 42, 91)( 45, 70)( 48, 54)( 49, 94)( 50, 71)( 52, 58)( 53, 98)( 56, 74)
        ( 57,102)( 60, 66)( 61, 93)( 62, 86)( 65, 69)( 68, 90)( 72, 87)( 73, 92)( 76, 81)( 77,106)( 79, 85)( 80,111)
        ( 83, 89)( 84,114)( 88, 97)( 95,101)( 96,115)( 99,105)(100,118)(103,109)(104,121)(107,110)(108,122)(112,117)
        (113,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 11)(  3,  8)(  5, 19)(  6, 31)(  7, 15)(  9, 23)( 10, 20)( 12, 18)( 13, 46)( 14, 24)
        ( 16, 27)( 17, 49)( 21, 38)( 22, 34)( 25, 42)( 26, 39)( 28, 33)( 29, 69)( 30, 53)( 32, 37)( 35, 57)( 36, 70)
        ( 40, 61)( 41, 58)( 43, 48)( 44, 85)( 45, 62)( 47, 52)( 50, 56)( 51, 86)( 54, 65)( 55, 89)( 59, 77)( 60, 73)
        ( 63, 81)( 64, 78)( 66, 72)( 67,106)( 68, 93)( 71, 76)( 74, 97)( 75,107)( 79,101)( 80, 98)( 82, 88)( 83,118)
        ( 84,102)( 87, 92)( 90, 96)( 91,119)( 94,105)( 95,121)( 99,113)(100,109)(103,117)(104,114)(108,112)(110,116)
        (111,122)(115,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33)( 34, 35, 36, 37)( 38, 39, 40, 41)( 42, 43, 44, 45)
        ( 46, 47, 48)( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 20)(  4,  9)(  6, 12)(  7, 27)(  8, 14)( 10, 16)( 11, 31)( 15, 24)( 17, 23)
        ( 18, 43)( 19, 35)( 21, 26)( 22, 47)( 25, 30)( 28, 34)( 29, 48)( 32, 38)( 33, 51)( 36, 39)( 37, 55)( 40, 46)
        ( 41, 67)( 42, 59)( 44, 50)( 45, 71)( 49, 54)( 52, 58)( 53, 72)( 56, 62)( 57, 75)( 60, 63)( 61, 79)( 64, 70)
        ( 65, 91)( 66, 83)( 68, 74)( 69, 95)( 73, 78)( 76, 82)( 77, 96)( 80, 86)( 81, 99)( 84, 87)( 85,103)( 88, 94)
        ( 89,112)( 90,107)( 92, 98)( 93,115)( 97,102)(100,106)(101,116)(104,110)(105,119)(108,111)(109,122)(113,118)
        (114,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 52)( 31, 56)( 34, 40)( 35, 84)
        ( 36, 65)( 38, 44)( 39, 88)( 42, 68)( 43, 92)( 46, 51)( 47, 69)( 49, 55)( 50,100)( 53, 72)( 54,102)( 57, 63)
        ( 58,113)( 59, 77)( 61, 67)( 62,114)( 66, 80)( 70, 99)( 71, 95)( 73, 79)( 74,121)( 75,106)( 78,109)( 81, 87)
        ( 82,111)( 83,115)( 85, 91)( 86,123)( 89, 94)( 90,119)( 93, 98)( 96,104)( 97,120)(101,105)(103,108)(107,117)
        (110,116)(112,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 26, 32)( 27, 76)( 28, 48)( 31, 52)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 81)( 42, 47)( 43, 69)( 45, 51)( 46, 89)( 49, 72)( 50, 91)( 53, 59)( 54,102)( 55, 77)( 57, 63)
        ( 58,103)( 61, 67)( 62,106)( 65, 80)( 66,110)( 70, 88)( 71, 84)( 73, 79)( 74,121)( 75, 95)( 78, 98)( 82, 87)
        ( 83,114)( 85, 93)( 86,120)( 90, 94)( 92, 97)( 96,117)( 99,105)(100,108)(101,122)(104,109)(107,113)(111,116)
        (112,123)(115,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 52)( 30, 36)( 31, 84)( 34, 56)
        ( 35, 85)( 39, 44)( 40, 68)( 42, 72)( 43, 88)( 46, 51)( 47, 73)( 49, 55)( 50, 96)( 53, 76)( 54, 98)( 57, 63)
        ( 58,105)( 59, 82)( 61, 67)( 62,109)( 65, 71)( 66,113)( 69, 87)( 70,114)( 74, 95)( 75, 91)( 77, 83)( 78,108)
        ( 79,102)( 81, 86)( 89, 94)( 90,117)( 92,100)( 93,124)( 97,101)( 99,104)(103,121)(106,112)(107,122)(110,116)
        (111,119)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 51)( 27, 47)( 29, 35)( 30, 76)( 31, 63)( 33, 39)( 34, 79)
        ( 37, 67)( 38, 83)( 41, 46)( 42, 68)( 44, 50)( 45, 92)( 48, 71)( 49, 94)( 52, 58)( 53,105)( 54, 72)( 56, 62)
        ( 57,106)( 60, 66)( 61,109)( 64, 75)( 65,110)( 69, 91)( 70, 87)( 73,101)( 74, 98)( 77, 82)( 78,113)( 80, 86)
        ( 81,122)( 84, 90)( 85,123)( 88, 96)( 89,120)( 93, 97)( 95,100)( 99,117)(102,108)(103,115)(104,118)(107,112)
        (111,116)(114,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 52)( 30, 36)( 31, 83)( 34, 56)
        ( 35, 84)( 39, 44)( 40, 68)( 42, 72)( 43, 92)( 46, 51)( 47,102)( 48, 73)( 50, 55)( 53, 76)( 54,103)( 57, 63)
        ( 58,113)( 59, 87)( 61, 67)( 62,117)( 65, 71)( 66,118)( 69, 91)( 70,119)( 74, 98)( 75, 95)( 77, 82)( 78,106)
        ( 80, 86)( 81,122)( 85, 90)( 88,109)( 89,123)( 93, 97)( 94,115)( 96,111)( 99,105)(100,124)(101,112)(104,108)
        (107,121)(110,116)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 57)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 84)( 38, 44)( 39, 92)( 40, 68)( 42, 48)( 43, 93)( 46, 72)( 47, 95)( 50, 56)( 51,106)( 52, 73)( 54, 59)
        ( 55,109)( 58, 76)( 61, 67)( 62,117)( 63, 87)( 66, 71)( 69, 91)( 70,118)( 74,102)( 75, 99)( 77, 82)( 78,110)
        ( 80, 86)( 81,122)( 85, 90)( 88,113)( 89,123)( 94, 98)( 96,101)( 97,119)(100,115)(103,108)(104,124)(105,116)
        (107,112)(111,121)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 29)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 27, 32)( 28, 48)( 30, 52)( 31, 73)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 81)( 42, 47)( 43, 91)( 44, 69)( 46, 51)( 49, 72)( 50, 92)( 53, 59)( 54,102)( 55, 76)( 57, 63)
        ( 58,103)( 61, 67)( 62,106)( 65, 80)( 66,107)( 70, 87)( 71, 84)( 74, 79)( 75, 95)( 77, 98)( 78,119)( 82, 86)
        ( 83,110)( 85,114)( 88, 94)( 89,121)( 90,115)( 93, 97)( 96,118)( 99,105)(100,112)(101,122)(104,109)(108,113)
        (111,117)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 60)( 23, 43)( 25, 31)( 26, 67)( 27, 51)( 29, 35)( 30, 71)( 33, 55)( 34, 75)
        ( 37, 42)( 38, 83)( 39, 61)( 41, 46)( 44, 50)( 45, 84)( 48, 54)( 49, 87)( 52, 63)( 53, 91)( 56, 62)( 57, 86)
        ( 58, 79)( 64, 70)( 65,103)( 66, 95)( 68, 74)( 69,104)( 72, 78)( 73,107)( 76, 82)( 77,111)( 80, 89)( 81,115)
        ( 85, 90)( 88, 94)( 92, 98)( 93,116)( 96, 99)( 97,119)(100,106)(101,109)(102,122)(105,110)(108,114)(112,118)
        (113,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 95)( 39, 71)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 55)( 50,112)( 51, 76)( 53, 59)( 54,115)
        ( 57, 79)( 58,118)( 61, 67)( 62, 93)( 63, 87)( 65, 70)( 66,122)( 69, 74)( 72, 91)( 73,123)( 77,111)( 78,107)
        ( 81, 86)( 82,109)( 84, 90)( 85,105)( 88, 97)( 89,101)( 92, 98)( 94,124)( 96,102)(100,106)(104,110)(108,119)
        (113,117)(114,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 35)( 31, 87)( 34, 60)
        ( 37, 43)( 38, 95)( 39, 71)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 55)( 50,112)( 51, 76)( 53, 59)( 54,115)
        ( 57, 79)( 58,118)( 61, 67)( 62, 93)( 63, 88)( 65, 70)( 66,122)( 69, 74)( 72, 91)( 73,123)( 77,111)( 78,107)
        ( 80, 86)( 81,105)( 82,109)( 84, 90)( 85,101)( 89, 97)( 92, 98)( 94,124)( 96,102)(100,106)(104,110)(108,119)
        (113,117)(114,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 95)( 39, 72)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 55)( 50,114)( 51, 76)( 53, 59)( 54,115)
        ( 57, 79)( 58,118)( 61, 67)( 62, 93)( 63, 87)( 65, 71)( 66,122)( 69, 74)( 70,123)( 73, 91)( 77,111)( 78,107)
        ( 81, 86)( 82,109)( 84, 90)( 85,105)( 88, 97)( 89,101)( 92, 98)( 94,124)( 96,102)(100,106)(104,110)(108,119)
        (112,117)(113,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 35)( 31, 87)( 34, 60)
        ( 37, 43)( 38, 95)( 39, 72)( 41, 47)( 42, 99)( 45, 75)( 46,103)( 49, 55)( 50,114)( 51, 76)( 53, 59)( 54,115)
        ( 57, 79)( 58,118)( 61, 67)( 62, 93)( 63, 88)( 65, 71)( 66,122)( 69, 74)( 70,123)( 73, 91)( 77,111)( 78,107)
        ( 80, 86)( 81,105)( 82,109)( 84, 90)( 85,101)( 89, 97)( 92, 98)( 94,124)( 96,102)(100,106)(104,110)(108,119)
        (112,117)(113,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 65)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 77)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 68)( 41, 47)( 42, 95)( 45, 72)( 46, 99)( 49, 55)( 50,108)( 51, 73)( 53, 59)( 54,111)
        ( 57, 76)( 58,114)( 61, 67)( 62,121)( 63, 84)( 66, 71)( 69, 88)( 70,122)( 74,107)( 75,103)( 78, 83)( 79,105)
        ( 81, 87)( 82,101)( 85,118)( 86, 97)( 89, 94)( 90,123)( 92, 98)( 93,120)( 96,102)(100,106)(104,115)(109,113)
        (110,116)(112,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 83)( 28, 56)( 30, 35)( 33, 60)( 34, 84)
        ( 37, 43)( 38, 91)( 39, 72)( 41, 47)( 42, 94)( 45, 75)( 46, 98)( 49, 55)( 50,107)( 51, 76)( 53, 59)( 54,110)
        ( 57, 79)( 58,113)( 61, 67)( 62,117)( 63, 85)( 65, 71)( 66,121)( 69, 74)( 70, 90)( 73, 87)( 77,106)( 78,102)
        ( 80, 86)( 81,120)( 82,104)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,119)(103,114)(108,112)
        (109,115)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 35)( 31, 84)( 34, 60)
        ( 37, 43)( 38, 91)( 39, 72)( 41, 47)( 42, 94)( 45, 75)( 46, 98)( 49, 55)( 50,107)( 51, 76)( 53, 59)( 54,110)
        ( 57, 79)( 58,113)( 61, 67)( 62,117)( 63, 85)( 65, 71)( 66,121)( 69, 74)( 70, 90)( 73, 87)( 77,106)( 78,102)
        ( 80, 86)( 81,120)( 82,104)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,119)(103,114)(108,112)
        (109,115)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 83)( 28, 56)( 30, 35)( 33, 60)( 34, 84)
        ( 37, 43)( 38, 88)( 39, 72)( 41, 47)( 42, 91)( 45, 75)( 46, 95)( 49, 55)( 50,106)( 51, 76)( 53, 59)( 54,107)
        ( 57, 79)( 58,110)( 61, 67)( 62,114)( 63, 85)( 65, 71)( 66,118)( 69, 74)( 70,122)( 73, 87)( 77,103)( 78, 99)
        ( 80, 86)( 81,117)( 82,101)( 89, 94)( 90,123)( 92, 98)( 93,120)( 96,102)( 97,116)(100,111)(104,109)(105,112)
        (108,113)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 35)( 31, 84)( 34, 60)
        ( 37, 43)( 38, 88)( 39, 72)( 41, 47)( 42, 91)( 45, 75)( 46, 95)( 49, 55)( 50,106)( 51, 76)( 53, 59)( 54,107)
        ( 57, 79)( 58,110)( 61, 67)( 62,114)( 63, 85)( 65, 71)( 66,118)( 69, 74)( 70,122)( 73, 87)( 77,103)( 78, 99)
        ( 80, 86)( 81,117)( 82,101)( 89, 94)( 90,123)( 92, 98)( 93,120)( 96,102)( 97,116)(100,111)(104,109)(105,112)
        (108,113)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 71)( 41, 47)( 42, 95)( 45, 75)( 46, 98)( 49, 55)( 50,107)( 51, 76)( 53, 59)( 54,109)
        ( 57, 79)( 58,113)( 61, 66)( 62, 69)( 63, 87)( 65, 70)( 68, 74)( 72, 91)( 73, 88)( 77,106)( 78,102)( 81, 86)
        ( 82,114)( 84, 90)( 85,122)( 89,120)( 92, 97)( 93,117)( 96,101)( 99,105)(100,118)(103,111)(104,124)(108,112)
        (110,116)(115,121)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 73)( 27, 54)( 29, 34)( 32, 58)( 33, 74)( 36, 42)
        ( 37, 81)( 38, 63)( 40, 46)( 41, 85)( 44, 65)( 45, 89)( 48, 53)( 49,101)( 50, 66)( 52, 57)( 55, 69)( 56,102)
        ( 59, 64)( 60, 84)( 61, 77)( 67, 97)( 68, 93)( 70, 76)( 71,117)( 72,105)( 75, 80)( 78,109)( 79,118)( 82, 88)
        ( 83,110)( 86, 92)( 87,111)( 90, 96)( 91,122)( 94,100)( 95,116)( 98,104)( 99,107)(103,108)(106,113)(112,121)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64)( 65, 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 62)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 73)( 34, 40)( 35, 83)
        ( 36, 65)( 38, 44)( 39, 87)( 42, 69)( 43, 90)( 46, 52)( 47, 98)( 48, 70)( 50, 56)( 51,102)( 54, 72)( 55,103)
        ( 58, 64)( 59,114)( 60, 76)( 63, 68)( 66, 80)( 67,115)( 71, 94)( 74, 79)( 75,106)( 77,110)( 78,118)( 81, 86)
        ( 82,112)( 84, 89)( 85,122)( 88, 93)( 91, 97)( 92,123)( 95,101)( 96,120)( 99,105)(100,108)(104,109)(107,117)
        (111,116)(113,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 62)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 53)( 31, 57)( 34, 40)( 35, 83)
        ( 36, 65)( 38, 44)( 39, 87)( 42, 69)( 43, 91)( 46, 52)( 47, 98)( 48, 70)( 50, 56)( 51,102)( 54, 72)( 55,103)
        ( 58, 64)( 59,114)( 60, 77)( 63, 68)( 66, 80)( 67,115)( 71, 94)( 73, 79)( 74,121)( 75,106)( 78,110)( 81, 86)
        ( 82,112)( 84, 90)( 85,123)( 88, 93)( 89,119)( 92, 97)( 95,101)( 96,120)( 99,105)(100,108)(104,109)(107,117)
        (111,116)(113,122)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 63)( 23, 45)( 24, 41)( 27, 32)( 28, 52)( 30, 56)( 31, 76)( 34, 40)( 35, 84)
        ( 36, 67)( 38, 44)( 39, 87)( 42, 71)( 43, 90)( 46, 51)( 47,102)( 48, 72)( 50, 55)( 53, 75)( 54,103)( 57, 62)
        ( 58,114)( 59, 79)( 61, 66)( 64, 70)( 65,115)( 68, 83)( 69,112)( 73, 98)( 74, 94)( 77, 82)( 78,106)( 80,110)
        ( 81,122)( 85, 89)( 86,117)( 88, 93)( 91, 97)( 92,118)( 95,101)( 96,124)( 99,105)(100,108)(104,109)(107,121)
        (111,116)(113,120)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 67)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 79)( 33, 60)( 34, 82)
        ( 37, 43)( 38, 94)( 39, 70)( 41, 47)( 42, 95)( 45, 74)( 46, 98)( 49, 55)( 50,107)( 51, 75)( 53, 59)( 54,108)
        ( 57, 78)( 58,110)( 61, 66)( 62, 72)( 63, 86)( 65, 69)( 68, 73)( 71, 90)( 76,106)( 77,102)( 80, 85)( 81,114)
        ( 83, 89)( 84,118)( 87, 93)( 88,121)( 91, 97)( 92,122)( 96,101)( 99,105)(100,123)(103,112)(104,120)(109,113)
        (111,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 87)( 34, 60)
        ( 35, 90)( 38, 43)( 39,102)( 40, 71)( 42, 47)( 45, 75)( 46,103)( 49, 55)( 50,111)( 51, 76)( 53, 59)( 54,113)
        ( 57, 79)( 58,117)( 61, 67)( 62,101)( 63, 94)( 65, 70)( 66, 73)( 69, 74)( 72, 98)( 77,110)( 78,106)( 80, 86)
        ( 81, 96)( 82,118)( 84, 89)( 85, 92)( 88, 93)( 91, 97)( 95,121)( 99,105)(100,122)(104,109)(107,115)(108,123)
        (112,116)(114,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 94)( 39, 71)( 41, 47)( 42, 95)( 45, 75)( 46, 98)( 49, 55)( 50,110)( 51, 76)( 53, 59)( 54,111)
        ( 57, 79)( 58,108)( 61, 67)( 62, 93)( 63, 87)( 65, 70)( 66, 73)( 69, 74)( 72, 90)( 77,106)( 78,102)( 81, 86)
        ( 82,113)( 84, 89)( 85,122)( 88,117)( 91, 97)( 92,118)( 96,101)( 99,105)(100,119)(103,115)(104,124)(107,112)
        (109,116)(114,121)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 53)( 31, 57)( 34, 40)( 35, 88)
        ( 36, 68)( 38, 44)( 39, 91)( 42, 72)( 43, 95)( 46, 52)( 47,107)( 48, 73)( 50, 56)( 51,108)( 54, 76)( 55,105)
        ( 58, 64)( 59, 87)( 60, 81)( 62, 67)( 63, 70)( 66, 71)( 69, 84)( 74,103)( 75, 99)( 77, 83)( 78,121)( 79,110)
        ( 82,114)( 85, 90)( 86,115)( 89, 94)( 92, 98)( 93,116)( 96,102)( 97,123)(100,112)(101,120)(104,109)(106,113)
        (111,118)(117,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 80)
        ( 37, 64)( 38, 83)( 41, 47)( 42, 92)( 43, 65)( 45, 51)( 46, 94)( 49, 68)( 50, 98)( 53, 59)( 54,106)( 55, 69)
        ( 58, 63)( 61, 72)( 62,107)( 66, 91)( 67, 87)( 70,102)( 71, 99)( 73, 79)( 74,118)( 75,110)( 77, 82)( 78,121)
        ( 81, 86)( 84, 90)( 85,122)( 88, 96)( 89,116)( 93, 97)( 95,101)(100,113)(103,109)(104,120)(105,114)(108,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 61)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 56)( 29, 35)( 30, 75)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 87)( 39, 62)( 41, 47)( 42, 90)( 45, 64)( 46, 94)( 49, 55)( 50,103)( 51, 65)( 53, 59)( 54,105)
        ( 57, 68)( 58,109)( 63, 83)( 66,102)( 67, 98)( 69, 74)( 70,110)( 72, 78)( 73,114)( 76, 82)( 77,117)( 80, 86)
        ( 81,121)( 84, 89)( 85,122)( 88, 93)( 91, 97)( 92,123)( 95,101)( 96,119)( 99,107)(100,116)(104,108)(106,112)
        (111,113)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 33)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 56)( 29, 35)( 30, 76)( 34, 63)( 37, 43)
        ( 38, 83)( 39, 60)( 41, 47)( 42, 87)( 45, 64)( 46, 91)( 49, 55)( 50,103)( 51, 65)( 53, 59)( 54,104)( 57, 68)
        ( 58,101)( 61, 80)( 62, 77)( 66, 99)( 67, 95)( 69, 75)( 70,117)( 71,106)( 73, 79)( 74,121)( 78,112)( 81, 86)
        ( 82,110)( 84, 90)( 85,123)( 88, 94)( 89,119)( 92, 98)( 93,115)( 96,108)( 97,116)(100,105)(102,109)(107,113)
        (111,122)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 79)
        ( 37, 64)( 38, 83)( 41, 47)( 42, 92)( 43, 65)( 45, 51)( 46, 93)( 49, 68)( 50, 95)( 53, 59)( 54,106)( 55, 69)
        ( 58, 63)( 61, 72)( 62,107)( 66, 91)( 67, 87)( 70,102)( 71, 99)( 73, 78)( 74,110)( 76, 82)( 77,118)( 80, 86)
        ( 81,121)( 84, 90)( 85,122)( 88, 97)( 89,116)( 94, 98)( 96,101)(100,113)(103,109)(104,120)(105,114)(108,112)
        (111,117)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 36)( 19, 67)( 23, 47)( 24, 43)( 26, 32)( 27, 81)( 28, 55)( 30, 35)( 31, 82)( 34, 59)
        ( 37, 42)( 38, 70)( 40, 46)( 41, 86)( 44, 74)( 45, 89)( 48, 54)( 49, 97)( 50, 75)( 52, 58)( 53,101)( 56, 77)
        ( 57,102)( 60, 66)( 61,109)( 62, 83)( 64, 69)( 65,113)( 68, 73)( 71, 85)( 72,114)( 76, 93)( 78, 84)( 79,112)
        ( 80,105)( 87, 92)( 88,117)( 90, 96)( 91,118)( 94,100)( 95,124)( 98,104)( 99,107)(103,108)(106,121)(110,116)
        (111,122)(115,120)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 62)( 16, 32)( 18, 36)( 19, 66)( 23, 47)( 24, 43)( 26, 31)( 27, 82)( 28, 54)( 30, 35)( 33, 58)( 34, 83)
        ( 37, 42)( 38, 70)( 40, 46)( 41, 87)( 44, 74)( 45, 89)( 48, 53)( 49,101)( 50, 75)( 52, 57)( 55, 78)( 56,102)
        ( 59, 65)( 60,109)( 61, 84)( 63, 69)( 64,113)( 67, 73)( 68,114)( 71, 86)( 72,117)( 76, 97)( 77, 93)( 79, 85)
        ( 80,112)( 81,105)( 88, 92)( 90, 96)( 91,118)( 94,100)( 95,124)( 98,104)( 99,107)(103,108)(106,121)(110,116)
        (111,122)(115,120)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 32)( 27, 80)( 28, 52)( 30, 35)( 31, 81)( 34, 56)
        ( 38, 43)( 39, 68)( 41, 72)( 42, 85)( 45, 51)( 46, 93)( 47, 73)( 49, 55)( 50, 94)( 53, 76)( 54, 96)( 57, 63)
        ( 58,103)( 59, 82)( 61, 67)( 62,107)( 65, 71)( 66,111)( 69, 84)( 70,114)( 74, 92)( 75, 88)( 77, 83)( 78,106)
        ( 79,100)( 86, 91)( 87,117)( 89, 98)( 90,124)( 95, 99)( 97,102)(101,121)(104,110)(105,122)(108,113)(109,119)
        (112,116)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 79)
        ( 37, 64)( 38, 83)( 41, 47)( 42, 95)( 43, 65)( 45, 51)( 46, 96)( 49, 68)( 50, 93)( 53, 59)( 54,106)( 55, 69)
        ( 58, 63)( 61, 72)( 62,107)( 66, 91)( 67, 87)( 70,102)( 71, 98)( 73, 78)( 74,110)( 76, 82)( 77,111)( 80, 86)
        ( 81,118)( 84, 90)( 85,122)( 88,100)( 89,117)( 92, 97)( 94,101)( 99,114)(103,109)(104,120)(105,115)(108,113)
        (112,121)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 33)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 56)( 29, 35)( 30, 76)( 34, 63)( 37, 43)
        ( 38, 83)( 39, 60)( 41, 47)( 42, 87)( 45, 64)( 46, 91)( 49, 55)( 50,103)( 51, 65)( 53, 59)( 54,104)( 57, 68)
        ( 58,101)( 61, 80)( 62, 77)( 66, 99)( 67, 95)( 69, 75)( 70,117)( 71,106)( 73, 79)( 74,121)( 78,113)( 81, 86)
        ( 82,110)( 84, 90)( 85,111)( 88, 94)( 89,123)( 92, 98)( 93,119)( 96,108)( 97,116)(100,105)(102,109)(107,114)
        (112,122)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 33)( 22, 48)( 23, 44)( 25, 31)( 26, 72)( 27, 56)( 29, 35)( 30, 76)( 34, 63)( 37, 43)
        ( 38, 83)( 39, 60)( 41, 47)( 42, 87)( 45, 64)( 46, 91)( 49, 55)( 50,100)( 51, 65)( 53, 59)( 54,101)( 57, 68)
        ( 58,103)( 61, 80)( 62, 77)( 66, 99)( 67, 95)( 69, 75)( 70,117)( 71,107)( 73, 79)( 74,121)( 78,113)( 81, 86)
        ( 82,110)( 84, 90)( 85,111)( 88, 94)( 89,123)( 92, 98)( 93,119)( 96,105)( 97,116)(102,106)(104,109)(108,114)
        (112,122)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 16)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 35)( 18, 60)( 22, 47)( 23, 43)( 25, 31)( 26, 75)( 27, 55)( 29, 34)( 30, 79)( 33, 59)( 36, 42)
        ( 37, 84)( 38, 63)( 40, 46)( 41, 87)( 44, 67)( 45, 91)( 48, 54)( 49,100)( 50, 68)( 52, 58)( 53,101)( 56, 71)
        ( 57,103)( 61, 66)( 62, 80)( 64, 83)( 65,111)( 69, 99)( 70, 95)( 72, 78)( 73,117)( 74,107)( 76, 82)( 77,121)
        ( 81,110)( 85, 90)( 86,112)( 88, 94)( 89,123)( 92, 98)( 93,119)( 96,105)( 97,116)(102,106)(104,109)(108,114)
        (113,122)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 73)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 89)( 39, 65)( 41, 47)( 42, 91)( 45, 68)( 46, 95)( 49, 55)( 50,103)( 51, 69)( 53, 59)( 54,107)
        ( 57, 72)( 58,111)( 61, 67)( 62, 93)( 63, 84)( 66, 88)( 70, 99)( 71, 96)( 74, 79)( 75,114)( 77, 83)( 78,119)
        ( 81, 87)( 82,122)( 85, 97)( 86,102)( 90, 94)( 92, 98)(100,106)(101,123)(104,110)(105,121)(108,113)(109,116)
        (112,117)(115,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 68)( 42, 71)( 43, 92)( 46, 52)( 47,102)( 48, 72)( 50, 56)( 51,103)( 54, 75)( 55,106)
        ( 58, 63)( 59,114)( 60, 87)( 62, 67)( 65, 70)( 66,115)( 69, 91)( 73, 98)( 74, 95)( 76, 82)( 77,122)( 78,107)
        ( 81, 86)( 84, 90)( 85,123)( 88,110)( 89,120)( 93, 97)( 94,116)( 96,112)( 99,105)(100,121)(101,113)(104,109)
        (108,118)(111,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 71)( 27, 52)( 29, 34)( 32, 55)( 33, 72)( 36, 42)
        ( 37, 83)( 38, 60)( 40, 46)( 41, 86)( 44, 63)( 45, 90)( 48, 54)( 49,102)( 50, 64)( 53, 67)( 56, 62)( 57,110)
        ( 58, 75)( 61, 79)( 65, 98)( 66, 94)( 68, 74)( 69,118)( 70,103)( 73, 78)( 76,106)( 77,119)( 80, 85)( 81, 88)
        ( 82,111)( 84, 89)( 87, 93)( 91, 97)( 92,112)( 95,114)( 96,108)( 99,105)(100,123)(101,115)(104,117)(107,113)
        (109,121)(116,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 84)( 34, 60)
        ( 35, 87)( 38, 43)( 39, 71)( 41, 47)( 42, 96)( 45, 75)( 46, 98)( 49, 55)( 50,109)( 51, 76)( 53, 59)( 54,110)
        ( 57, 79)( 58,113)( 61, 67)( 62,117)( 63, 91)( 65, 70)( 66,121)( 69, 74)( 72, 95)( 73,122)( 77,105)( 78,102)
        ( 80, 86)( 81, 89)( 82,114)( 85, 90)( 88, 94)( 92,107)( 93,115)( 97,101)( 99,104)(100,123)(103,119)(106,112)
        (108,120)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 79)( 28, 52)( 30, 35)( 33, 56)( 34, 80)
        ( 37, 43)( 38, 86)( 39, 67)( 41, 47)( 42, 87)( 45, 71)( 46, 90)( 50, 55)( 51, 72)( 53, 75)( 54, 99)( 57, 63)
        ( 58,106)( 59, 77)( 61, 66)( 62,110)( 65, 70)( 68, 82)( 69,111)( 73, 98)( 74, 94)( 76, 81)( 78,102)( 83, 89)
        ( 84, 92)( 85,114)( 88, 93)( 91, 97)( 95,118)( 96,115)(100,105)(101,119)(103,109)(104,120)(107,113)(108,123)
        (112,117)(116,124)(121,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 54)
        ( 15, 25)( 17, 28)( 18, 58)( 22, 39)( 23, 35)( 26, 50)( 27, 47)( 29, 34)( 30, 78)( 31, 62)( 33, 38)( 36, 66)
        ( 37, 79)( 40, 46)( 41, 87)( 42, 67)( 44, 49)( 45, 90)( 48, 70)( 51, 57)( 52, 97)( 53, 71)( 55, 61)( 56,101)
        ( 59, 65)( 60,102)( 63, 74)( 64,105)( 68, 86)( 69, 82)( 72, 94)( 73, 91)( 75, 81)( 76,121)( 77,106)( 80, 85)
        ( 83,109)( 84,122)( 88, 93)( 89,110)( 92,113)( 95,100)( 96,114)( 98,104)( 99,120)(103,108)(107,117)(111,116)
        (112,123)(115,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 74)( 27, 55)( 29, 35)( 30, 78)( 33, 59)( 34, 82)
        ( 37, 42)( 38, 90)( 39, 64)( 41, 46)( 44, 66)( 45, 91)( 48, 54)( 49, 94)( 50, 67)( 52, 58)( 53, 98)( 56, 70)
        ( 57,102)( 60, 65)( 61, 93)( 62, 86)( 68, 87)( 69, 92)( 71, 77)( 72,110)( 73,103)( 75, 81)( 76,111)( 79, 85)
        ( 80,114)( 83, 89)( 84,118)( 88, 97)( 95,101)( 96,119)( 99,105)(100,122)(104,106)(107,113)(108,116)(109,123)
        (112,117)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 56)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 49)( 29, 52)( 30, 65)( 33, 39)( 34, 76)( 35, 57)
        ( 37, 43)( 38, 79)( 41, 60)( 42, 83)( 45, 51)( 46, 95)( 47, 61)( 50, 64)( 53, 59)( 54,103)( 55, 68)( 58, 72)
        ( 62, 91)( 63, 87)( 66, 71)( 67, 96)( 69, 99)( 70,112)( 73, 78)( 74,121)( 75,104)( 77, 82)( 80, 86)( 81,122)
        ( 84, 90)( 85,123)( 88,107)( 89,119)( 92, 98)( 93,115)( 94,108)( 97,111)(100,106)(101,109)(102,114)(105,117)
        (110,120)(113,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 44)( 26, 32)( 27, 82)( 28, 55)( 30, 36)( 31, 86)( 34, 59)
        ( 35, 90)( 38, 43)( 39, 70)( 41, 46)( 42, 71)( 45, 74)( 48, 54)( 49, 61)( 50, 75)( 52, 58)( 53, 95)( 56, 78)
        ( 57, 98)( 60, 66)( 62, 94)( 64, 69)( 65, 76)( 68, 73)( 72, 77)( 79, 85)( 80,109)( 81,102)( 83, 89)( 84,110)
        ( 87, 93)( 88,113)( 91, 97)( 92,117)( 96,101)( 99,105)(100,118)(103,106)(104,121)(107,112)(108,122)(111,116)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 46)( 16, 33)( 18, 37)( 19, 56)( 23, 44)( 24, 41)( 26, 32)( 27, 64)( 28, 52)( 30, 36)( 31, 68)( 34, 50)
        ( 35, 72)( 38, 43)( 39, 57)( 42, 58)( 45, 51)( 47, 59)( 49, 55)( 53, 60)( 54, 73)( 61, 67)( 62, 84)( 63, 76)
        ( 65, 71)( 66, 88)( 69, 75)( 70, 92)( 74, 79)( 77, 80)( 78, 93)( 81, 87)( 82,103)( 83, 96)( 85, 91)( 86,107)
        ( 89, 95)( 90,111)( 94, 99)( 97,100)( 98,112)(101,106)(102,115)(104,110)(105,120)(108,114)(109,122)(113,118)
        (116,119)(117,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 41)( 26, 32)( 27, 72)( 28, 52)( 30, 36)( 31, 76)( 34, 56)
        ( 35, 80)( 38, 43)( 39, 65)( 42, 47)( 45, 51)( 46, 66)( 49, 55)( 50, 62)( 53, 68)( 54, 58)( 57, 63)( 59, 84)
        ( 61, 67)( 69, 75)( 70, 92)( 71, 85)( 73, 79)( 74, 96)( 77, 83)( 78,100)( 81, 87)( 82,104)( 86, 88)( 89, 95)
        ( 90,111)( 91,105)( 93, 99)( 94,114)( 97,103)( 98,118)(101,107)(102,121)(106,108)(109,113)(110,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 64)( 23, 44)( 24, 42)( 26, 32)( 27, 72)( 28, 52)( 30, 36)( 31, 76)( 34, 56)
        ( 35, 80)( 38, 43)( 39, 47)( 40, 65)( 45, 51)( 46, 66)( 49, 55)( 50, 62)( 53, 68)( 54, 58)( 57, 63)( 59, 84)
        ( 61, 67)( 69, 75)( 70, 92)( 71, 85)( 73, 79)( 74, 96)( 77, 83)( 78,100)( 81, 87)( 82,104)( 86, 88)( 89, 95)
        ( 90,111)( 91,105)( 93, 99)( 94,114)( 97,103)( 98,118)(101,107)(102,121)(106,108)(109,113)(110,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 41)( 24, 39)( 26, 32)( 27, 72)( 28, 49)( 30, 36)( 31, 76)( 34, 53)
        ( 35, 80)( 40, 65)( 42, 48)( 43, 63)( 44, 66)( 46, 52)( 47, 59)( 50, 68)( 51, 55)( 54, 60)( 56, 84)( 58, 64)
        ( 62, 67)( 69, 75)( 70, 92)( 71, 85)( 73, 79)( 74, 96)( 77, 83)( 78,100)( 81, 87)( 82,104)( 86, 88)( 89, 95)
        ( 90,111)( 91,105)( 93, 99)( 94,114)( 97,103)( 98,118)(101,107)(102,121)(106,108)(109,113)(110,122)(112,117)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 81)( 28, 57)( 30, 36)( 31, 85)( 34, 61)
        ( 35, 88)( 38, 44)( 39, 97)( 40, 70)( 42, 48)( 43,100)( 46, 73)( 47,104)( 50, 56)( 51,115)( 52, 74)( 54, 60)
        ( 55,118)( 58, 77)( 59,121)( 62, 68)( 63,102)( 64, 92)( 66, 72)( 67, 99)( 71, 96)( 75,112)( 76,108)( 78, 84)
        ( 79, 94)( 80,110)( 82, 87)( 83, 90)( 86, 91)( 89, 95)( 93,106)( 98,103)(101,107)(105,111)(109,122)(113,117)
        (114,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110,111)(112,113,114)(115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 81)( 28, 53)( 31, 57)( 34, 40)( 35, 85)
        ( 36, 69)( 38, 44)( 39, 88)( 42, 73)( 43, 92)( 46, 52)( 47,103)( 48, 74)( 50, 56)( 51,106)( 54, 77)( 55,109)
        ( 58, 64)( 59,113)( 60, 82)( 62, 68)( 63,117)( 66, 72)( 67,121)( 70, 84)( 71,122)( 75,100)( 76, 96)( 78, 83)
        ( 79,116)( 80, 98)( 86, 91)( 87,123)( 89, 95)( 90,119)( 93, 99)( 94,115)( 97,110)(101,105)(102,111)(104,108)
        (107,112)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 80)( 31, 64)( 33, 39)( 34, 84)
        ( 37, 68)( 38, 88)( 41, 47)( 42, 99)( 43, 69)( 45, 51)( 46,102)( 49, 72)( 50,105)( 53, 59)( 54,113)( 55, 73)
        ( 57, 63)( 58,117)( 61, 67)( 62,121)( 65, 76)( 66,122)( 70, 96)( 71, 92)( 74,109)( 75, 94)( 77, 83)( 78,119)
        ( 79,123)( 81, 87)( 82,115)( 85, 91)( 86,111)( 89, 95)( 90,112)( 93,106)( 97,101)( 98,107)(100,104)(103,108)
        (110,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 68)( 41, 72)( 42, 88)( 45, 51)( 46, 95)( 47, 73)( 49, 55)( 50, 99)( 53, 75)( 54,102)( 57, 63)
        ( 58,113)( 59, 83)( 61, 67)( 62,114)( 65, 71)( 66,115)( 69, 87)( 70,111)( 74, 91)( 77, 82)( 78,105)( 80, 86)
        ( 81,122)( 84,109)( 85,119)( 89, 94)( 90,117)( 92, 98)( 93,124)( 96,101)( 97,107)(100,104)(103,108)(106,121)
        (110,116)(112,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 55)( 29, 35)( 30, 72)( 33, 59)( 34, 75)
        ( 37, 43)( 38, 83)( 39, 65)( 41, 47)( 42, 87)( 45, 67)( 46, 91)( 49, 54)( 50,102)( 51, 68)( 53, 58)( 56, 71)
        ( 57,103)( 60, 66)( 61, 86)( 62, 79)( 69, 99)( 70, 95)( 73, 78)( 74,106)( 76, 82)( 77,118)( 80,110)( 81,121)
        ( 84, 90)( 85,111)( 88, 94)( 89,112)( 92, 98)( 93,123)( 96,114)( 97,120)(100,105)(101,115)(104,109)(107,117)
        (108,116)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 51)( 29, 55)( 30, 68)( 33, 39)( 34, 79)( 35, 60)
        ( 37, 43)( 38, 83)( 41, 63)( 42, 87)( 45, 50)( 46, 64)( 48, 54)( 49, 96)( 52, 67)( 53, 99)( 56, 62)( 57, 78)
        ( 58, 71)( 61, 75)( 65, 95)( 66, 91)( 69, 74)( 70,102)( 72,106)( 73,114)( 76, 82)( 77,107)( 80, 86)( 81,121)
        ( 84, 90)( 85,122)( 88, 94)( 89,119)( 92,110)( 93,116)( 97,101)( 98,111)(100,105)(103,113)(104,112)(108,124)
        (109,117)(115,120)(118,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 52)( 29, 56)( 30, 68)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 83)( 41, 64)( 42, 87)( 45, 51)( 46, 95)( 47, 65)( 49, 55)( 50, 99)( 53, 67)( 54,102)( 57, 63)
        ( 58,110)( 59, 71)( 62, 75)( 66, 91)( 69, 74)( 70,105)( 72,109)( 73,114)( 76, 82)( 77,121)( 78,111)( 80, 86)
        ( 81,122)( 84, 90)( 85,123)( 88, 94)( 89,119)( 92, 98)( 93,116)( 96,101)( 97,107)(100,104)(103,108)(106,113)
        (112,117)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 52)( 31, 56)( 34, 40)( 35, 83)
        ( 36, 65)( 38, 44)( 39, 84)( 42, 68)( 43, 87)( 46, 51)( 47, 69)( 49, 55)( 50, 96)( 53, 72)( 54, 99)( 57, 63)
        ( 58,106)( 59, 77)( 61, 67)( 62,110)( 66, 79)( 70, 95)( 71, 91)( 73, 78)( 74,109)( 75,102)( 80, 86)( 81,122)
        ( 82,111)( 85, 90)( 88, 94)( 89,123)( 92,114)( 93,120)( 97,101)( 98,115)(100,105)(103,117)(104,116)(107,113)
        (108,118)(112,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 80)( 28, 52)( 31, 56)( 34, 40)( 35, 84)
        ( 36, 68)( 38, 44)( 39, 85)( 42, 72)( 43, 87)( 46, 51)( 47, 98)( 48, 73)( 50, 55)( 53, 76)( 54, 99)( 57, 63)
        ( 58,106)( 59, 81)( 61, 67)( 62,110)( 65, 71)( 66,111)( 69, 83)( 70,114)( 74, 95)( 75, 91)( 77, 82)( 78,109)
        ( 79,102)( 86, 90)( 88, 94)( 89,115)( 92,118)( 93,124)( 96,101)( 97,119)(100,105)(103,121)(104,120)(107,113)
        (108,122)(112,117)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 64)( 33, 39)( 34, 80)
        ( 37, 68)( 38, 83)( 41, 47)( 42, 91)( 43, 69)( 45, 51)( 46, 95)( 49, 71)( 50, 98)( 53, 59)( 54,109)( 55, 72)
        ( 57, 63)( 58,113)( 61, 67)( 62,114)( 65, 75)( 66,115)( 70, 87)( 73,105)( 74,101)( 76, 82)( 77,121)( 78,111)
        ( 81, 86)( 84, 90)( 85,122)( 88, 94)( 89,120)( 92, 97)( 93,103)( 96,100)( 99,104)(102,117)(106,112)(107,124)
        (108,118)(110,116)(119,123),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 73)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 80)
        ( 37, 43)( 38, 91)( 39, 65)( 41, 47)( 42, 95)( 45, 68)( 46, 99)( 49, 55)( 50,111)( 51, 69)( 53, 59)( 54,114)
        ( 57, 72)( 58,118)( 61, 67)( 62,123)( 63, 84)( 66, 88)( 70,107)( 71,103)( 74, 79)( 75,105)( 77, 83)( 78,101)
        ( 81, 87)( 82, 97)( 85,122)( 86, 93)( 89, 94)( 90,124)( 92, 98)( 96,102)(100,106)(104,119)(108,113)(109,116)
        (110,120)(112,117)(115,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 83)( 28, 57)( 30, 36)( 31, 84)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 95)( 40, 72)( 42, 48)( 43, 98)( 46, 75)( 47,102)( 50, 56)( 51,114)( 52, 76)( 54, 60)
        ( 55,117)( 58, 79)( 59,121)( 62, 68)( 63,100)( 64, 90)( 66, 71)( 67, 97)( 70, 74)( 73, 94)( 77,110)( 78,106)
        ( 80, 86)( 81, 92)( 82,108)( 85, 89)( 88, 93)( 91,104)( 96,101)( 99,105)(103,109)(107,122)(111,116)(112,119)
        (113,123)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 53)( 12, 22)( 14, 20)
        ( 15, 65)( 16, 33)( 18, 37)( 19, 69)( 23, 49)( 24, 45)( 26, 32)( 27, 83)( 28, 57)( 30, 36)( 31, 86)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 95)( 40, 72)( 42, 48)( 43, 98)( 46, 75)( 47,102)( 50, 56)( 51,114)( 52, 76)( 54, 60)
        ( 55,117)( 58, 79)( 59,121)( 62, 68)( 63,100)( 64, 90)( 66, 71)( 67, 97)( 70, 74)( 73, 94)( 77,110)( 78,106)
        ( 80, 85)( 81, 92)( 82,108)( 84, 89)( 88, 93)( 91,104)( 96,101)( 99,105)(103,109)(107,122)(111,116)(112,119)
        (113,123)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 78)( 34, 40)( 35, 89)
        ( 36, 69)( 38, 44)( 39, 93)( 42, 73)( 43, 96)( 46, 52)( 47,108)( 48, 74)( 50, 56)( 51,111)( 54, 77)( 55,115)
        ( 58, 64)( 59, 87)( 60, 81)( 62, 68)( 63,119)( 66, 72)( 67,122)( 70, 85)( 71,123)( 75,104)( 76,100)( 79, 84)
        ( 80,102)( 82, 91)( 83, 98)( 86, 92)( 88,121)( 90, 95)( 94, 99)( 97,103)(101,116)(105,110)(106,113)(107,117)
        (109,114)(112,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 30)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 81)( 28, 53)( 31, 57)( 34, 40)( 35, 89)
        ( 36, 69)( 38, 44)( 39, 93)( 42, 73)( 43, 97)( 46, 52)( 47,108)( 48, 74)( 50, 56)( 51,111)( 54, 77)( 55,115)
        ( 58, 64)( 59, 87)( 60, 82)( 62, 68)( 63,119)( 66, 72)( 67,122)( 70, 85)( 71,123)( 75,104)( 76,100)( 78, 84)
        ( 79, 95)( 80,102)( 83, 91)( 86, 92)( 88,121)( 90, 96)( 94, 99)( 98,103)(101,116)(105,110)(106,113)(107,117)
        (109,114)(112,118)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113,114)(115,116,117,118)(119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 76)( 34, 40)( 35, 86)
        ( 36, 68)( 38, 44)( 39, 90)( 42, 71)( 43, 94)( 46, 52)( 47,106)( 48, 72)( 50, 56)( 51,109)( 54, 75)( 55,113)
        ( 58, 63)( 59, 79)( 61, 67)( 62,118)( 65, 70)( 66,121)( 69, 83)( 73,102)( 74, 98)( 77, 82)( 78,100)( 80,117)
        ( 81, 96)( 84, 89)( 85,122)( 87, 93)( 88,123)( 91, 97)( 92,120)( 95,101)( 99,114)(103,108)(104,111)(105,115)
        (107,112)(110,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 90)( 39, 68)( 41, 47)( 42, 94)( 45, 71)( 46, 98)( 49, 55)( 50,110)( 51, 72)( 53, 59)( 54,113)
        ( 57, 75)( 58,117)( 62, 67)( 63, 83)( 65, 70)( 66,122)( 69, 87)( 73,106)( 74,102)( 77, 82)( 78,104)( 80, 86)
        ( 81,100)( 84,121)( 85, 96)( 88, 93)( 89,123)( 91, 97)( 92,124)( 95,101)( 99,105)(103,118)(107,112)(108,115)
        (109,119)(111,116)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 55)( 28, 34)( 29, 71)( 32, 59)( 33, 74)( 36, 42)
        ( 37, 82)( 38, 64)( 40, 46)( 41, 86)( 44, 66)( 45, 90)( 48, 54)( 49,102)( 50, 67)( 52, 58)( 53,103)( 56, 70)
        ( 57,106)( 60, 65)( 61, 85)( 62, 78)( 68, 98)( 69, 94)( 72, 77)( 73,109)( 75, 81)( 76,118)( 79,113)( 80,121)
        ( 83, 89)( 84,114)( 87, 93)( 88,115)( 91, 97)( 92,123)( 95,101)( 96,120)( 99,105)(100,111)(104,108)(107,112)
        (110,117)(116,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 55)( 28, 34)( 29, 71)( 32, 59)( 33, 74)( 36, 42)
        ( 37, 82)( 38, 64)( 40, 46)( 41, 86)( 44, 66)( 45, 90)( 48, 54)( 49,102)( 50, 67)( 52, 58)( 53,105)( 56, 70)
        ( 57,106)( 60, 65)( 61, 85)( 62, 78)( 68, 98)( 69, 94)( 72, 77)( 73,109)( 75, 81)( 76,118)( 79,113)( 80,121)
        ( 83, 89)( 84,114)( 87, 93)( 88,115)( 91, 97)( 92,123)( 95,101)( 96,120)( 99,104)(100,111)(103,108)(107,112)
        (110,117)(116,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 50)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 74)( 27, 54)( 29, 35)( 30, 78)( 33, 58)( 34, 81)
        ( 37, 42)( 38, 63)( 40, 46)( 41, 90)( 44, 66)( 45, 93)( 48, 53)( 49, 67)( 51, 57)( 52,102)( 55, 70)( 56,105)
        ( 59, 65)( 60,117)( 61, 85)( 64, 89)( 68,101)( 69, 97)( 71, 77)( 72, 87)( 73,109)( 75, 80)( 76, 83)( 79, 84)
        ( 82, 88)( 86,113)( 91, 96)( 92,118)( 94,100)( 95,119)( 98,121)( 99,115)(103,108)(104,122)(106,112)(107,123)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49)( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 65)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 68)( 42, 47)( 45, 71)( 46, 99)( 49, 55)( 50,110)( 51, 72)( 53, 59)( 54,111)
        ( 57, 75)( 58,114)( 61, 67)( 62, 97)( 63, 90)( 66, 70)( 69, 94)( 73,106)( 74,102)( 76, 82)( 77, 92)( 78,117)
        ( 80, 85)( 81, 88)( 84, 89)( 87, 93)( 91,121)( 95,101)( 96,122)(100,105)(103,109)(104,123)(107,113)(108,119)
        (112,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 86)( 38, 43)( 39, 98)( 40, 68)( 42, 47)( 45, 71)( 46, 99)( 49, 55)( 50,110)( 51, 72)( 53, 59)( 54,113)
        ( 57, 75)( 58,114)( 61, 66)( 62, 97)( 63, 90)( 65, 70)( 69, 94)( 73,106)( 74,102)( 76, 82)( 77, 92)( 78,117)
        ( 80, 85)( 81, 88)( 84, 89)( 87, 93)( 91,121)( 95,101)( 96,122)(100,105)(103,109)(104,123)(107,112)(108,119)
        (111,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 79)( 28, 53)( 30, 36)( 31, 83)( 34, 57)
        ( 35, 86)( 39, 44)( 40, 68)( 42, 71)( 43, 95)( 46, 52)( 47,103)( 48, 72)( 50, 56)( 51,106)( 54, 75)( 55,107)
        ( 58, 63)( 59,118)( 60, 90)( 62, 67)( 65, 70)( 66,119)( 69, 94)( 73,102)( 74, 98)( 76, 82)( 77, 92)( 78,110)
        ( 80, 85)( 81, 88)( 84, 89)( 87, 93)( 91,114)( 96,101)( 97,120)( 99,122)(100,116)(104,109)(105,123)(108,113)
        (111,117)(112,124)(115,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 58)( 16, 29)( 18, 33)( 19, 62)( 23, 44)( 24, 40)( 27, 32)( 28, 51)( 30, 55)( 31, 74)( 34, 39)( 35, 66)
        ( 37, 43)( 38, 82)( 41, 69)( 42, 85)( 45, 50)( 46, 70)( 48, 54)( 49, 94)( 52, 73)( 53, 97)( 56, 61)( 57, 77)
        ( 59, 65)( 60,106)( 63, 68)( 64,109)( 67, 81)( 71, 93)( 72, 89)( 75, 80)( 76,101)( 78,105)( 79,118)( 83, 88)
        ( 84,110)( 86, 92)( 87,123)( 90,113)( 91,120)( 95,100)( 96,114)( 98,104)( 99,115)(102,117)(103,116)(107,112)
        (108,121)(111,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68)
        ( 69, 70, 71, 72)( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 73)( 33, 60)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 65)( 41, 47)( 42, 91)( 45, 68)( 46, 94)( 49, 55)( 50,106)( 51, 69)( 53, 59)( 54,107)
        ( 57, 72)( 58,110)( 62, 67)( 63, 80)( 66, 84)( 70,102)( 71, 98)( 74, 79)( 75,113)( 77, 83)( 78,118)( 81, 86)
        ( 82,121)( 85, 90)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,120)(103,109)(104,115)(108,112)
        (111,116)(114,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 73)( 33, 60)( 34, 76)
        ( 37, 43)( 38, 87)( 39, 65)( 41, 47)( 42, 91)( 45, 68)( 46, 94)( 49, 55)( 50,106)( 51, 69)( 53, 59)( 54,109)
        ( 57, 72)( 58,110)( 62, 67)( 63, 80)( 66, 84)( 70,102)( 71, 98)( 74, 79)( 75,113)( 77, 83)( 78,118)( 81, 86)
        ( 82,121)( 85, 90)( 88, 93)( 89,122)( 92, 97)( 95,101)( 96,123)( 99,105)(100,120)(103,108)(104,115)(107,112)
        (111,116)(114,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 32)( 18, 36)( 19, 64)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 88)( 39, 67)( 41, 47)( 42, 91)( 45, 71)( 46, 94)( 49, 55)( 50,106)( 51, 72)( 53, 59)( 54,109)
        ( 57, 75)( 58,110)( 62, 66)( 63, 83)( 65, 70)( 68, 87)( 69, 84)( 73,102)( 74, 98)( 77, 82)( 78,113)( 80, 86)
        ( 81,122)( 85,120)( 89, 93)( 90,117)( 92, 97)( 95,101)( 96,118)( 99,105)(100,124)(103,108)(104,115)(107,112)
        (111,116)(114,121)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 76)( 34, 40)( 35, 86)
        ( 36, 67)( 38, 44)( 39, 87)( 42, 71)( 43, 90)( 46, 52)( 47, 99)( 48, 72)( 50, 56)( 51,102)( 54, 75)( 55,103)
        ( 58, 63)( 59, 79)( 61, 66)( 62,111)( 65, 70)( 68, 83)( 69,112)( 73, 98)( 74, 94)( 77, 82)( 78,106)( 80,110)
        ( 81,122)( 84, 89)( 85,114)( 88, 93)( 91, 97)( 92,115)( 95,118)( 96,124)(100,105)(101,119)(104,109)(107,121)
        (108,120)(113,117)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 47)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 67)( 24, 51)( 26, 32)( 27, 71)( 30, 55)( 31, 75)( 34, 39)( 35, 83)
        ( 36, 56)( 38, 43)( 41, 59)( 42, 84)( 45, 50)( 46, 60)( 48, 54)( 49, 92)( 52, 63)( 53, 95)( 57, 79)( 58, 76)
        ( 61, 91)( 62, 87)( 64, 70)( 65,115)( 66, 99)( 68, 74)( 69,119)( 72, 78)( 73,122)( 77,103)( 80, 86)( 81,113)
        ( 82,104)( 85, 90)( 88,107)( 89,114)( 93, 98)( 94,108)( 96,102)( 97,109)(100,111)(101,110)(105,117)(106,123)
        (112,118)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 68)( 24, 52)( 26, 32)( 27, 72)( 30, 56)( 31, 75)( 34, 39)( 35, 86)
        ( 36, 57)( 38, 43)( 41, 60)( 42, 87)( 45, 51)( 46, 98)( 47, 61)( 49, 55)( 50, 99)( 53, 64)( 54,102)( 58, 82)
        ( 59, 79)( 62, 94)( 63, 90)( 65, 71)( 66,117)( 67,105)( 69, 74)( 70,121)( 73, 78)( 76, 81)( 77,122)( 80,109)
        ( 83, 89)( 84,115)( 85,110)( 88, 93)( 91, 97)( 92,116)( 95,101)( 96,107)(100,104)(103,108)(106,113)(111,119)
        (112,123)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 68)( 24, 52)( 26, 32)( 27, 72)( 30, 56)( 31, 75)( 34, 39)( 35, 87)
        ( 36, 57)( 38, 43)( 41, 60)( 42, 88)( 45, 51)( 46, 99)( 47, 61)( 49, 55)( 50,102)( 53, 64)( 54,103)( 58, 83)
        ( 59, 79)( 62, 95)( 63, 91)( 65, 71)( 66,117)( 67,106)( 69, 74)( 70,121)( 73, 78)( 76, 82)( 77,122)( 80,110)
        ( 81,123)( 84, 90)( 85,115)( 86,111)( 89, 94)( 92, 98)( 93,116)( 96,101)( 97,108)(100,105)(104,109)(107,113)
        (112,119)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 68)( 24, 52)( 26, 32)( 27, 72)( 30, 56)( 31, 76)( 34, 39)( 35, 87)
        ( 36, 57)( 38, 43)( 41, 60)( 42, 88)( 45, 51)( 46, 96)( 47, 61)( 49, 55)( 50, 99)( 53, 64)( 54,100)( 58, 83)
        ( 59, 79)( 62, 95)( 63, 91)( 65, 71)( 66,117)( 67,103)( 69, 75)( 70,121)( 73, 78)( 74,122)( 77, 82)( 80,107)
        ( 81,123)( 84, 90)( 85,115)( 86,108)( 89, 94)( 92,110)( 93,116)( 97,102)( 98,111)(101,106)(104,113)(105,112)
        (109,119)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 74)( 27, 55)( 29, 35)( 30, 78)( 33, 59)( 34, 82)
        ( 37, 42)( 38, 64)( 40, 46)( 41, 91)( 44, 67)( 45, 93)( 48, 54)( 49,101)( 50, 68)( 52, 58)( 53,105)( 56, 70)
        ( 57,109)( 60, 66)( 61, 95)( 62, 86)( 65, 90)( 69, 97)( 71, 77)( 72,117)( 73,110)( 75, 81)( 76,118)( 79, 85)
        ( 80,119)( 83, 89)( 84,115)( 87, 99)( 88,121)( 92, 96)( 94,100)( 98,104)(102,108)(103,122)(106,112)(107,123)
        (111,113)(114,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 75)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 91)( 39, 64)( 41, 46)( 44, 67)( 45, 92)( 48, 54)( 49,102)( 50, 68)( 52, 58)( 53,106)( 56, 71)
        ( 57,107)( 60, 66)( 61, 90)( 62, 83)( 65, 87)( 69, 98)( 70, 95)( 72, 78)( 73,122)( 74,110)( 77, 82)( 80, 86)
        ( 81,123)( 84,114)( 85,120)( 88, 94)( 89,115)( 93, 97)( 96,116)( 99,105)(100,121)(101,117)(103,109)(104,112)
        (108,113)(111,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 33)( 18, 37)( 19, 63)( 23, 45)( 24, 41)( 26, 32)( 27, 75)( 28, 52)( 30, 36)( 31, 78)( 34, 56)
        ( 35, 82)( 39, 44)( 40, 67)( 42, 70)( 43, 90)( 46, 51)( 47,101)( 48, 71)( 50, 55)( 53, 74)( 54,102)( 57, 62)
        ( 58,113)( 59, 85)( 61, 66)( 64, 69)( 65,114)( 68, 89)( 72, 97)( 73, 93)( 76, 81)( 77,105)( 79, 84)( 80,122)
        ( 83, 88)( 86,109)( 87,123)( 91, 96)( 92,115)( 94,117)( 95,111)( 98,104)( 99,107)(100,118)(103,108)(106,121)
        (110,116)(112,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 88)( 45, 51)( 46, 98)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,103)( 57, 63)
        ( 58,114)( 59, 83)( 61, 66)( 62,118)( 65, 70)( 68, 87)( 69,119)( 73, 94)( 74, 91)( 77, 82)( 78,106)( 80, 86)
        ( 81,122)( 84,110)( 85,123)( 89, 93)( 90,116)( 92,112)( 95,101)( 96,124)( 97,113)( 99,105)(100,108)(104,109)
        (107,121)(111,117)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 19)(  6, 31)(  7, 16)(  9, 23)( 10, 43)( 11, 20)( 13, 18)( 14, 55)
        ( 15, 24)( 17, 27)( 21, 39)( 22, 35)( 25, 51)( 26, 47)( 28, 34)( 29, 71)( 30, 56)( 32, 38)( 33, 75)( 36, 59)
        ( 37, 79)( 40, 46)( 41, 89)( 42, 60)( 44, 50)( 45, 93)( 48, 63)( 49, 94)( 52, 58)( 53,105)( 54, 64)( 57, 67)
        ( 61, 85)( 62, 82)( 65,101)( 66, 97)( 68, 74)( 69,118)( 70,106)( 72, 78)( 73,121)( 76, 81)( 77,112)( 80, 84)
        ( 83,109)( 86, 92)( 87,116)( 88,110)( 90, 96)( 91, 99)( 95,100)( 98,113)(102,108)(103,120)(104,114)(107,117)
        (111,122)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 74)( 27, 54)( 29, 34)( 32, 58)( 33, 75)( 36, 42)
        ( 37, 85)( 38, 63)( 40, 46)( 41, 89)( 44, 66)( 45, 90)( 48, 53)( 49,101)( 50, 67)( 52, 57)( 55, 70)( 56,102)
        ( 59, 65)( 60,113)( 61, 78)( 64, 82)( 68, 97)( 69, 93)( 71, 77)( 72, 80)( 73,105)( 76, 81)( 79,109)( 83, 88)
        ( 84,114)( 86, 92)( 87,122)( 91, 96)( 94,117)( 95,123)( 98,104)( 99,107)(100,118)(103,108)(106,112)(110,116)
        (111,119)(115,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 84)( 38, 43)( 39, 71)( 41, 47)( 42, 92)( 45, 75)( 46, 94)( 49, 55)( 50,105)( 51, 76)( 53, 59)( 54,109)
        ( 57, 79)( 58,110)( 61, 67)( 62,117)( 63, 87)( 65, 70)( 66,121)( 69, 74)( 72, 91)( 73,122)( 77,101)( 78, 98)
        ( 81, 86)( 82,113)( 85, 90)( 88,103)( 89,114)( 93, 97)( 95,100)( 96,123)( 99,119)(102,108)(104,120)(106,112)
        (107,115)(111,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 75)( 33, 56)( 34, 78)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 83)( 45, 51)( 46, 90)( 47, 72)( 49, 55)( 50, 94)( 53, 74)( 54, 95)( 57, 63)
        ( 58,106)( 59, 79)( 61, 66)( 62,110)( 65, 70)( 68, 82)( 69,111)( 73, 86)( 76, 81)( 77, 98)( 80,102)( 84, 89)
        ( 85,114)( 87, 93)( 88,118)( 91, 97)( 92,121)( 96,101)( 99,105)(100,122)(103,109)(104,123)(107,113)(108,120)
        (112,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 64)( 23, 44)( 24, 40)( 27, 32)( 28, 52)( 30, 56)( 31, 75)( 34, 39)( 35, 85)
        ( 36, 67)( 38, 43)( 41, 71)( 42, 86)( 45, 51)( 46, 93)( 47, 72)( 49, 55)( 50, 97)( 53, 74)( 54, 98)( 57, 63)
        ( 58,109)( 59, 78)( 61, 66)( 62,113)( 65, 70)( 68, 81)( 69,114)( 73, 89)( 76, 80)( 77,101)( 79,105)( 82, 88)
        ( 83,117)( 84,115)( 87, 92)( 90, 96)( 91,118)( 94,100)( 95,121)( 99,104)(102,108)(103,122)(106,112)(107,123)
        (110,116)(111,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 19)(  6, 31)(  7, 16)(  9, 23)( 10, 43)( 11, 20)( 13, 18)( 14, 55)
        ( 15, 24)( 17, 27)( 21, 39)( 22, 35)( 25, 51)( 26, 47)( 28, 34)( 29, 71)( 30, 56)( 32, 38)( 33, 74)( 36, 59)
        ( 37, 78)( 40, 46)( 41, 89)( 42, 60)( 44, 50)( 45, 93)( 48, 63)( 49, 94)( 52, 58)( 53,105)( 54, 64)( 57, 67)
        ( 61, 85)( 62, 82)( 65,101)( 66, 97)( 68, 73)( 69,118)( 70,106)( 72, 77)( 75, 81)( 76,119)( 79, 84)( 80,121)
        ( 83,109)( 86, 92)( 87,116)( 88,110)( 90, 96)( 91, 99)( 95,100)( 98,113)(102,108)(103,123)(104,114)(107,117)
        (111,115)(112,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 45)( 24, 41)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 65)( 42, 68)( 43, 92)( 46, 52)( 47, 95)( 48, 69)( 50, 56)( 51, 99)( 54, 72)( 55,103)
        ( 58, 64)( 59, 94)( 60, 87)( 63, 67)( 66, 91)( 70, 88)( 71, 93)( 73, 78)( 74,106)( 76, 82)( 77,111)( 80, 86)
        ( 81,114)( 84, 90)( 85,117)( 89, 98)( 96,102)( 97,118)(100,105)(101,121)(104,109)(107,110)(108,122)(112,116)
        (113,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 75)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 65)( 42, 68)( 43, 92)( 46, 52)( 47, 95)( 48, 69)( 50, 56)( 51, 99)( 54, 72)( 55,103)
        ( 58, 63)( 59, 94)( 60, 87)( 62, 67)( 66, 91)( 70, 88)( 71, 93)( 73, 78)( 74,107)( 76, 82)( 77,111)( 80, 86)
        ( 81,114)( 84, 90)( 85,117)( 89, 98)( 96,102)( 97,118)(100,106)(101,121)(104,109)(105,122)(108,110)(112,116)
        (113,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 64)( 23, 45)( 24, 41)( 26, 32)( 27, 72)( 28, 53)( 30, 36)( 31, 75)( 34, 57)
        ( 35, 79)( 39, 44)( 40, 65)( 42, 48)( 43, 88)( 46, 52)( 47, 91)( 50, 56)( 51, 95)( 54, 68)( 55, 99)( 58, 63)
        ( 59, 90)( 60, 83)( 62, 67)( 66, 87)( 69, 74)( 70,109)( 71,103)( 73, 78)( 76, 82)( 77,110)( 80, 86)( 81,113)
        ( 84, 93)( 85,117)( 89, 94)( 92, 98)( 96,102)( 97,118)(100,105)(101,121)(104,106)(107,112)(108,122)(111,116)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 53)( 29, 35)( 30, 75)( 33, 56)( 34, 78)
        ( 37, 43)( 38, 87)( 39, 61)( 41, 47)( 42, 90)( 45, 64)( 46, 91)( 49, 55)( 50,102)( 51, 65)( 54, 68)( 57, 63)
        ( 58,109)( 59, 82)( 62, 86)( 66, 98)( 67, 94)( 69, 74)( 70,103)( 72, 77)( 73,118)( 76, 81)( 79, 85)( 80,119)
        ( 83,106)( 84,121)( 88, 93)( 89,110)( 92, 97)( 95,113)( 96,111)( 99,105)(100,123)(101,114)(104,117)(107,112)
        (108,116)(115,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 47)( 24, 43)( 26, 31)( 27, 51)( 29, 35)( 30, 72)( 33, 55)( 34, 75)
        ( 37, 42)( 38, 86)( 39, 64)( 41, 46)( 44, 67)( 45, 87)( 49, 54)( 50, 68)( 52, 71)( 53, 95)( 56, 62)( 57,106)
        ( 58, 78)( 60, 66)( 61,110)( 65, 82)( 69, 94)( 70, 90)( 73, 77)( 74, 98)( 76, 81)( 79,102)( 80, 99)( 83, 89)
        ( 84,119)( 85,111)( 88, 93)( 91,114)( 92,120)( 96,101)( 97,115)(100,105)(103,109)(104,116)(107,113)(108,123)
        (112,118)(117,122)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 32)( 18, 36)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 74)( 28, 48)( 30, 35)( 33, 52)( 34, 75)
        ( 38, 43)( 39, 64)( 41, 67)( 42, 83)( 46, 51)( 47, 68)( 49, 71)( 50, 91)( 53, 59)( 54,102)( 55, 78)( 57, 63)
        ( 58,106)( 61, 66)( 62,110)( 65, 82)( 69, 90)( 70, 86)( 72, 77)( 73, 94)( 76, 81)( 79, 98)( 80, 95)( 84, 89)
        ( 85,111)( 87,114)( 88,119)( 92, 97)( 93,115)( 96,101)( 99,105)(100,116)(103,109)(104,123)(107,113)(108,121)
        (112,118)(117,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 29)( 18, 33)( 19, 60)( 23, 44)( 24, 40)( 27, 32)( 28, 51)( 30, 55)( 31, 72)( 34, 39)( 35, 83)
        ( 36, 63)( 38, 43)( 41, 67)( 42, 84)( 45, 50)( 46, 68)( 48, 54)( 49, 92)( 52, 71)( 53, 95)( 56, 62)( 57,106)
        ( 58, 75)( 61, 66)( 64, 79)( 65,107)( 69, 91)( 70, 87)( 73, 78)( 74, 98)( 76,102)( 77,115)( 80, 86)( 81,118)
        ( 82,108)( 85, 90)( 88,110)( 89,119)( 93, 97)( 94,111)( 96,101)( 99,114)(100,112)(103,109)(104,121)(105,116)
        (113,122)(117,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 29)( 18, 33)( 19, 63)( 23, 44)( 24, 40)( 27, 32)( 28, 51)( 30, 55)( 31, 72)( 34, 39)( 35, 83)
        ( 36, 64)( 38, 43)( 41, 67)( 42, 84)( 45, 50)( 46, 94)( 47, 68)( 49, 54)( 52, 71)( 53, 95)( 56, 62)( 57,106)
        ( 58, 75)( 60, 66)( 61,107)( 65, 79)( 69, 91)( 70, 87)( 73, 78)( 74, 98)( 76,102)( 77,115)( 80, 86)( 81,118)
        ( 82,108)( 85, 90)( 88,110)( 89,119)( 92, 97)( 93,111)( 96,101)( 99,114)(100,112)(103,109)(104,121)(105,116)
        (113,122)(117,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 29)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 27, 32)( 28, 48)( 30, 52)( 31, 73)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 80)( 42, 47)( 43, 69)( 45, 51)( 46, 88)( 49, 72)( 50, 91)( 53, 59)( 54,102)( 55, 76)( 57, 63)
        ( 58,106)( 61, 67)( 62,107)( 65, 79)( 66,110)( 70, 87)( 71, 83)( 74, 78)( 75, 94)( 77, 98)( 81, 86)( 82,111)
        ( 84,114)( 85,119)( 89, 93)( 90,115)( 92, 97)( 95,101)( 96,116)( 99,105)(100,123)(103,109)(104,121)(108,113)
        (112,118)(117,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 26, 32)( 27, 75)( 28, 48)( 31, 52)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 80)( 42, 47)( 43, 90)( 44, 69)( 46, 51)( 49, 72)( 50, 91)( 53, 59)( 54,102)( 55, 76)( 57, 63)
        ( 58,106)( 61, 67)( 62,107)( 65, 79)( 66,110)( 70, 87)( 71, 83)( 73, 78)( 74, 94)( 77, 98)( 81, 86)( 82,111)
        ( 84,114)( 85,119)( 88, 93)( 89,115)( 92, 97)( 95,101)( 96,116)( 99,105)(100,123)(103,109)(104,121)(108,113)
        (112,118)(117,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 60)( 33, 64)( 34, 72)( 37, 43)
        ( 38, 79)( 39, 65)( 41, 47)( 42, 83)( 45, 67)( 46, 86)( 49, 55)( 50, 94)( 51, 68)( 53, 59)( 54, 97)( 57, 63)
        ( 58,101)( 61, 71)( 62,102)( 66, 75)( 69, 93)( 70, 90)( 73, 78)( 74,105)( 76, 82)( 77,114)( 80, 85)( 81,117)
        ( 84, 89)( 87, 92)( 88,118)( 91,109)( 95,100)( 96,110)( 98,104)( 99,122)(103,108)(106,113)(107,123)(111,121)
        (112,119)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 39)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 36)( 23, 32)( 26, 47)( 27, 43)( 30, 35)( 31, 59)( 33, 63)( 34, 72)( 37, 42)
        ( 38, 64)( 40, 46)( 41, 80)( 44, 67)( 45, 83)( 48, 54)( 49, 91)( 50, 68)( 52, 58)( 53, 94)( 56, 62)( 57, 98)
        ( 60, 71)( 61,102)( 65, 79)( 66, 75)( 69, 90)( 70, 87)( 73, 78)( 74,103)( 76,106)( 77,114)( 81, 86)( 82,107)
        ( 84, 89)( 85,118)( 88,109)( 92, 97)( 93,110)( 95,101)( 96,122)( 99,105)(100,123)(104,113)(108,117)(111,121)
        (112,119)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 90)( 39, 72)( 41, 47)( 42, 94)( 45, 75)( 46, 98)( 49, 55)( 50,110)( 51, 76)( 53, 59)( 54,114)
        ( 57, 79)( 58,118)( 61, 67)( 62, 96)( 63, 84)( 65, 71)( 66, 92)( 69, 74)( 70, 89)( 73, 87)( 77,106)( 78,102)
        ( 81, 86)( 82,104)( 85,100)( 88, 93)( 91, 97)( 95,101)( 99,105)(103,119)(107,113)(108,122)(109,120)(111,117)
        (112,123)(115,121)(116,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 56)( 30, 35)( 31, 83)( 34, 60)
        ( 37, 43)( 38, 90)( 39, 72)( 41, 47)( 42, 94)( 45, 75)( 46, 98)( 49, 55)( 50,110)( 51, 76)( 53, 59)( 54,114)
        ( 57, 79)( 58,118)( 61, 67)( 62, 96)( 63, 84)( 65, 71)( 66, 92)( 69, 74)( 70, 89)( 73, 87)( 77,106)( 78,102)
        ( 81, 86)( 82,104)( 85,100)( 88, 93)( 91, 97)( 95,101)( 99,105)(103,119)(107,113)(108,122)(109,120)(111,117)
        (112,123)(115,121)(116,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 79)( 35, 64)
        ( 37, 43)( 38, 83)( 41, 68)( 42, 87)( 45, 51)( 46, 99)( 47, 69)( 49, 55)( 50,103)( 53, 72)( 54,107)( 57, 63)
        ( 58, 73)( 61, 67)( 62,111)( 65, 76)( 66,115)( 70, 95)( 71, 91)( 74,114)( 75, 93)( 77, 82)( 78,119)( 80, 86)
        ( 81,120)( 84, 90)( 85,117)( 88, 94)( 89,113)( 92,108)( 96,102)( 97,122)( 98,109)(100,106)(101,123)(104,110)
        (105,124)(112,118)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 49)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 45)( 20, 41)( 22, 28)( 23, 69)( 24, 53)( 26, 32)( 27, 73)( 30, 57)( 31, 77)( 34, 40)( 35, 88)
        ( 36, 58)( 38, 44)( 39, 92)( 42, 61)( 43, 96)( 46, 52)( 47,107)( 48, 62)( 50, 56)( 51,111)( 54, 65)( 55,115)
        ( 59, 84)( 60, 81)( 63,103)( 64, 99)( 66, 72)( 67, 94)( 68,101)( 70, 76)( 71, 90)( 74, 80)( 75, 86)( 78, 83)
        ( 79,121)( 82,119)( 85, 91)( 87,120)( 89, 95)( 93, 98)( 97,102)(100,116)(104,110)(105,122)(106,117)(108,114)
        (109,123)(112,118)(113,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 87)( 45, 51)( 46, 98)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,105)( 57, 62)
        ( 58,117)( 59, 83)( 61, 66)( 64, 70)( 65,118)( 68, 86)( 69,119)( 73, 94)( 74, 90)( 77, 82)( 78,109)( 80, 85)
        ( 81,122)( 84,113)( 88, 93)( 89,115)( 91, 97)( 92,124)( 95,101)( 96,111)( 99,104)(100,107)(103,108)(106,112)
        (110,121)(114,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 87)( 45, 51)( 46, 98)( 47, 72)( 49, 55)( 50,102)( 53, 75)( 54,105)( 57, 63)
        ( 58,117)( 59, 83)( 61, 66)( 62,118)( 65, 70)( 68, 86)( 69,119)( 73, 94)( 74, 90)( 77, 82)( 78,109)( 80, 85)
        ( 81,122)( 84,113)( 88, 93)( 89,115)( 91, 97)( 92,124)( 95,101)( 96,111)( 99,104)(100,107)(103,108)(106,112)
        (110,121)(114,120)(116,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 52)( 30, 56)( 33, 39)( 34, 80)( 35, 61)
        ( 37, 43)( 38, 83)( 41, 64)( 42, 87)( 45, 51)( 46, 99)( 47, 65)( 49, 55)( 50,100)( 53, 68)( 54,103)( 57, 63)
        ( 58, 79)( 59, 73)( 62, 76)( 66, 95)( 67, 91)( 69, 75)( 70,121)( 71,107)( 74,111)( 77, 82)( 78,112)( 81, 86)
        ( 84, 90)( 85,113)( 88, 94)( 89,123)( 92,115)( 93,120)( 96,102)( 97,105)( 98,116)(101,106)(104,110)(108,118)
        (109,117)(114,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 52)( 30, 56)( 33, 39)( 34, 80)( 35, 61)
        ( 37, 43)( 38, 83)( 41, 64)( 42, 87)( 45, 51)( 46, 98)( 47, 65)( 49, 55)( 50, 99)( 53, 68)( 54,102)( 57, 63)
        ( 58, 79)( 59, 73)( 62, 76)( 66, 95)( 67, 91)( 69, 75)( 70,121)( 71,106)( 74,110)( 77, 82)( 78,111)( 81, 86)
        ( 84, 90)( 85,112)( 88, 94)( 89,123)( 92,114)( 93,120)( 96,101)( 97,115)(100,105)(103,109)(104,116)(107,118)
        (108,117)(113,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 64)( 23, 44)( 24, 40)( 26, 31)( 27, 79)( 28, 52)( 30, 35)( 33, 56)( 34, 80)
        ( 38, 43)( 39, 67)( 41, 71)( 42, 88)( 45, 51)( 46, 99)( 47, 72)( 49, 55)( 50,100)( 53, 75)( 54,103)( 57, 63)
        ( 58,115)( 59, 83)( 61, 66)( 62,119)( 65, 70)( 68, 87)( 69,120)( 73, 95)( 74, 91)( 76, 82)( 77, 85)( 78,107)
        ( 81, 86)( 84,111)( 89, 94)( 90,117)( 92,122)( 93,113)( 96,102)( 97,105)( 98,123)(101,106)(104,110)(108,114)
        (109,124)(112,118)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 75)( 27, 55)( 29, 34)( 32, 59)( 33, 76)( 36, 42)
        ( 37, 84)( 38, 64)( 40, 46)( 41, 87)( 44, 67)( 45, 90)( 48, 54)( 49, 99)( 50, 68)( 52, 58)( 53,102)( 56, 71)
        ( 57,105)( 60, 66)( 61,117)( 62, 79)( 65, 83)( 69, 98)( 70, 94)( 72, 78)( 73, 81)( 74,109)( 77, 82)( 80,113)
        ( 85, 89)( 86,118)( 88, 93)( 91, 97)( 92,119)( 95,121)( 96,115)(100,104)(101,122)(103,108)(106,112)(107,123)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 75)( 27, 55)( 29, 34)( 32, 59)( 33, 76)( 36, 42)
        ( 37, 86)( 38, 64)( 40, 46)( 41, 87)( 44, 67)( 45, 90)( 48, 54)( 49,101)( 50, 68)( 52, 58)( 53,102)( 56, 71)
        ( 57,105)( 60, 66)( 61,117)( 62, 79)( 65, 83)( 69, 98)( 70, 94)( 72, 78)( 73, 81)( 74,109)( 77, 82)( 80,113)
        ( 84, 89)( 85,118)( 88, 93)( 91, 97)( 92,119)( 95,121)( 96,115)( 99,104)(100,122)(103,108)(106,112)(107,123)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 66)( 23, 47)( 24, 43)( 26, 31)( 27, 82)( 28, 55)( 30, 35)( 33, 59)( 34, 83)
        ( 37, 42)( 38, 70)( 40, 46)( 41, 71)( 44, 74)( 45, 90)( 48, 54)( 49,101)( 50, 75)( 52, 58)( 53,105)( 56, 78)
        ( 57,106)( 60, 65)( 61,117)( 62, 86)( 64, 69)( 67, 73)( 68,118)( 72, 93)( 76, 98)( 77, 94)( 79, 85)( 80, 88)
        ( 81,109)( 84, 89)( 87,113)( 91, 97)( 92,119)( 95,121)( 96,115)( 99,104)(100,122)(102,108)(103,123)(107,112)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 63)( 33, 39)( 34, 83)
        ( 37, 67)( 38, 84)( 41, 47)( 42, 95)( 43, 68)( 45, 51)( 46, 99)( 49, 71)( 50,102)( 53, 58)( 54,114)( 55, 72)
        ( 57, 62)( 60, 66)( 61,115)( 64, 75)( 65,118)( 69, 91)( 70, 87)( 73,110)( 74,106)( 76, 82)( 77,112)( 78,119)
        ( 80, 86)( 81,123)( 85, 90)( 88, 94)( 89,124)( 92, 98)( 93,108)( 96,101)( 97,104)(100,105)(103,109)(107,121)
        (111,117)(113,122)(116,120),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 64)( 33, 39)( 34, 83)
        ( 37, 67)( 38, 84)( 41, 47)( 42, 95)( 43, 68)( 45, 51)( 46, 96)( 49, 71)( 50, 99)( 53, 59)( 54,111)( 55, 72)
        ( 57, 63)( 58,112)( 61, 66)( 62,115)( 65, 75)( 69, 91)( 70, 87)( 73,107)( 74,103)( 76, 82)( 77,109)( 78,116)
        ( 80, 86)( 81,123)( 85, 90)( 88,118)( 89,124)( 92, 98)( 93,101)( 94,119)( 97,102)(100,106)(104,121)(105,120)
        (108,114)(110,122)(113,117),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 63)( 33, 39)( 34, 83)
        ( 37, 67)( 38, 84)( 41, 47)( 42, 92)( 43, 68)( 45, 51)( 46, 95)( 49, 71)( 50, 98)( 53, 59)( 54,110)( 55, 72)
        ( 57, 62)( 58,113)( 61, 66)( 64, 75)( 65,114)( 69, 91)( 70, 87)( 73,106)( 74,102)( 76, 82)( 77,108)( 78,115)
        ( 80, 86)( 81,123)( 85, 90)( 88,117)( 89,124)( 93, 97)( 94,118)( 96,101)( 99,105)(100,119)(103,121)(104,120)
        (107,112)(109,122)(111,116),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 64)( 33, 39)( 34, 83)
        ( 37, 67)( 38, 84)( 41, 47)( 42, 94)( 43, 68)( 45, 51)( 46, 95)( 49, 71)( 50, 98)( 53, 59)( 54,110)( 55, 72)
        ( 57, 63)( 58,113)( 61, 66)( 62,114)( 65, 75)( 69, 91)( 70, 87)( 73,106)( 74,102)( 76, 82)( 77,108)( 78,115)
        ( 80, 86)( 81,123)( 85, 90)( 88,117)( 89,124)( 92, 97)( 93,118)( 96,101)( 99,105)(100,119)(103,121)(104,120)
        (107,112)(109,122)(111,116),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 63)( 33, 39)( 34, 83)
        ( 37, 67)( 38, 84)( 41, 47)( 42, 92)( 43, 68)( 45, 51)( 46, 95)( 49, 71)( 50, 99)( 53, 59)( 54,110)( 55, 72)
        ( 57, 62)( 58,114)( 61, 66)( 64, 75)( 65,115)( 69, 91)( 70, 87)( 73,106)( 74,102)( 76, 82)( 77,108)( 78,112)
        ( 80, 86)( 81,123)( 85, 90)( 88,117)( 89,124)( 93, 98)( 94,118)( 96,101)( 97,119)(100,105)(103,121)(104,120)
        (107,113)(109,122)(111,116),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 60)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 79)( 31, 64)( 33, 39)( 34, 83)
        ( 37, 68)( 38, 84)( 41, 47)( 42, 94)( 43, 69)( 45, 51)( 46, 98)( 49, 72)( 50, 99)( 53, 59)( 54,110)( 55, 73)
        ( 57, 63)( 58,114)( 61, 67)( 62,115)( 65, 76)( 66,112)( 70, 91)( 71, 87)( 74,106)( 75,102)( 77, 82)( 78,108)
        ( 80, 86)( 81,123)( 85, 90)( 88,117)( 89,124)( 92, 97)( 93,118)( 95,101)( 96,119)(100,105)(103,121)(104,120)
        (107,113)(109,122)(111,116),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 63)( 23, 47)( 24, 43)( 26, 31)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 67)( 40, 46)( 41, 88)( 44, 71)( 45, 90)( 48, 54)( 49,102)( 50, 72)( 52, 58)( 53,106)( 56, 75)
        ( 57,109)( 61, 66)( 62, 83)( 64, 70)( 65, 84)( 68, 87)( 69,117)( 73, 98)( 74, 94)( 77, 82)( 78,113)( 80, 86)
        ( 81,122)( 85,120)( 89, 93)( 91, 97)( 92,118)( 95,101)( 96,124)( 99,105)(100,115)(103,108)(104,111)(107,112)
        (110,116)(114,121)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 19)(  7, 39)(  8, 16)( 10, 23)( 11, 51)( 12, 20)( 14, 18)
        ( 15, 31)( 17, 35)( 21, 47)( 22, 43)( 24, 30)( 25, 66)( 26, 55)( 28, 34)( 29, 70)( 32, 38)( 33, 74)( 36, 42)
        ( 37, 78)( 40, 46)( 41, 82)( 44, 59)( 45, 86)( 48, 54)( 49, 95)( 50, 60)( 52, 58)( 53, 98)( 56, 63)( 57,101)
        ( 61, 94)( 62, 90)( 64, 69)( 65,105)( 67, 73)( 68,114)( 71, 77)( 72,117)( 75, 81)( 76,121)( 79, 85)( 80,122)
        ( 83, 89)( 84,123)( 87, 93)( 88,119)( 91,109)( 92,116)( 96,100)( 97,110)( 99,104)(102,108)(103,111)(106,113)
        (107,112)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 33)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 56)( 29, 35)( 30, 75)( 34, 63)( 37, 43)
        ( 38, 83)( 39, 60)( 41, 47)( 42, 86)( 45, 64)( 46, 90)( 49, 55)( 50, 99)( 51, 65)( 53, 59)( 54,102)( 57, 68)
        ( 58,105)( 61, 79)( 62, 76)( 66, 98)( 67, 94)( 69, 74)( 70,109)( 72, 78)( 73,122)( 77,116)( 80, 85)( 81, 88)
        ( 82,113)( 84, 89)( 87, 93)( 91, 97)( 92,114)( 95,117)( 96,124)(100,104)(101,118)(103,108)(106,112)(107,119)
        (110,121)(111,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 19)(  7, 39)(  8, 16)( 10, 23)( 11, 51)( 12, 20)( 14, 18)
        ( 15, 31)( 17, 35)( 21, 47)( 22, 43)( 24, 30)( 25, 66)( 26, 55)( 28, 34)( 29, 70)( 32, 38)( 33, 74)( 36, 42)
        ( 37, 78)( 40, 46)( 41, 82)( 44, 59)( 45, 86)( 48, 54)( 49, 95)( 50, 60)( 52, 58)( 53, 98)( 56, 63)( 57,102)
        ( 61, 94)( 62, 90)( 64, 69)( 65,105)( 67, 73)( 68,114)( 71, 77)( 72,117)( 75, 81)( 76,121)( 79, 85)( 80,122)
        ( 83, 89)( 84,123)( 87, 93)( 88,119)( 91,109)( 92,116)( 96,101)( 97,110)( 99,104)(100,111)(103,108)(106,113)
        (107,112)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 16)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 32)( 17, 36)( 18, 33)( 22, 48)( 23, 44)( 25, 31)( 26, 71)( 27, 56)( 29, 35)( 30, 75)( 34, 63)( 37, 43)
        ( 38, 83)( 39, 60)( 41, 47)( 42, 86)( 45, 64)( 46, 90)( 49, 55)( 50, 99)( 51, 65)( 53, 59)( 54,102)( 57, 68)
        ( 58,106)( 61, 79)( 62, 76)( 66, 98)( 67, 94)( 69, 74)( 70,109)( 72, 78)( 73,122)( 77,116)( 80, 85)( 81, 88)
        ( 82,113)( 84, 89)( 87, 93)( 91, 97)( 92,114)( 95,117)( 96,124)(100,105)(101,118)(103,108)(104,119)(107,112)
        (110,121)(111,120)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 77)( 35, 64)
        ( 37, 43)( 38, 79)( 41, 68)( 42, 83)( 45, 51)( 46, 95)( 47, 69)( 49, 55)( 50, 99)( 53, 72)( 54,102)( 57, 63)
        ( 58, 73)( 61, 67)( 62,110)( 65, 76)( 66,114)( 70, 91)( 71, 87)( 74,113)( 75,106)( 78, 82)( 80, 86)( 81,115)
        ( 84, 90)( 85,122)( 88, 94)( 89,121)( 92, 98)( 93,108)( 96,101)( 97,104)(100,105)(103,109)(107,118)(111,117)
        (112,119)(116,124)(120,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 79)( 35, 64)
        ( 37, 43)( 38, 82)( 41, 67)( 42, 86)( 45, 51)( 46, 98)( 47, 68)( 49, 55)( 50, 99)( 53, 71)( 54,102)( 57, 63)
        ( 58, 72)( 61, 66)( 62,110)( 65, 75)( 69, 94)( 70, 90)( 73,113)( 74,106)( 76, 81)( 77,121)( 78,111)( 80, 85)
        ( 83, 89)( 84,122)( 87, 93)( 88,123)( 91,114)( 92,120)( 95,101)( 96,104)( 97,115)(100,105)(103,109)(107,117)
        (108,116)(112,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 77)( 35, 64)
        ( 37, 43)( 38, 80)( 41, 68)( 42, 83)( 45, 51)( 46, 92)( 47, 69)( 49, 55)( 50, 95)( 53, 72)( 54, 98)( 57, 63)
        ( 58, 73)( 61, 67)( 62,106)( 65, 76)( 66,110)( 70, 91)( 71, 87)( 74,109)( 75,102)( 78, 82)( 79,113)( 81, 86)
        ( 84, 90)( 85,114)( 88,117)( 89,124)( 93, 97)( 94,118)( 96,101)( 99,105)(100,119)(103,121)(104,120)(107,112)
        (108,122)(111,116)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 79)( 35, 64)
        ( 37, 43)( 38, 83)( 41, 67)( 42, 86)( 45, 51)( 46, 97)( 47, 68)( 49, 55)( 50, 98)( 53, 71)( 54,101)( 57, 63)
        ( 58, 72)( 61, 66)( 62,109)( 65, 75)( 69, 94)( 70, 90)( 73,112)( 74,105)( 76, 82)( 77,121)( 78,110)( 80, 85)
        ( 81,122)( 84, 89)( 87, 93)( 88,123)( 91,113)( 92,120)( 95,100)( 96,114)( 99,104)(102,108)(103,115)(106,117)
        (107,116)(111,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 32)( 19, 60)( 23, 44)( 24, 40)( 26, 31)( 27, 59)( 28, 52)( 33, 39)( 34, 79)( 35, 64)
        ( 37, 43)( 38, 80)( 41, 68)( 42, 83)( 45, 51)( 46, 92)( 47, 69)( 49, 55)( 50, 95)( 53, 72)( 54, 99)( 57, 63)
        ( 58, 73)( 61, 67)( 62,106)( 65, 76)( 66,110)( 70, 91)( 71, 87)( 74,109)( 75,102)( 77, 82)( 78,113)( 81, 86)
        ( 84, 90)( 85,114)( 88,117)( 89,124)( 93, 98)( 94,118)( 96,101)( 97,119)(100,105)(103,121)(104,120)(107,112)
        (108,122)(111,116)(115,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 68)( 24, 52)( 26, 32)( 27, 72)( 30, 56)( 31, 76)( 34, 39)( 35, 57)
        ( 37, 43)( 38, 84)( 41, 60)( 42, 87)( 45, 51)( 46, 99)( 47, 61)( 49, 55)( 50,103)( 53, 64)( 54,106)( 58, 83)
        ( 59, 79)( 62, 95)( 63, 91)( 65, 71)( 66,121)( 67,110)( 69, 75)( 70,117)( 73, 78)( 74, 81)( 77, 82)( 80,114)
        ( 85, 90)( 86,115)( 88, 94)( 89,123)( 92, 98)( 93,120)( 96,102)( 97,112)(100,105)(101,108)(104,109)(107,113)
        (111,118)(116,122)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 65)( 42, 68)( 43, 92)( 46, 52)( 47,103)( 48, 69)( 50, 56)( 51,106)( 54, 72)( 55,110)
        ( 58, 64)( 59, 94)( 60, 87)( 63, 67)( 66, 91)( 70, 99)( 71, 95)( 73, 78)( 74,118)( 75,111)( 77, 82)( 80, 86)
        ( 81,119)( 84, 90)( 85,116)( 88, 97)( 89,121)( 93, 98)( 96,102)(100,105)(101,122)(104,109)(107,113)(108,123)
        (112,114)(115,120)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 62)( 23, 45)( 24, 41)( 26, 32)( 27, 76)( 28, 53)( 30, 36)( 31, 79)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 65)( 42, 68)( 43, 92)( 46, 52)( 47,100)( 48, 69)( 50, 56)( 51,103)( 54, 72)( 55,107)
        ( 58, 64)( 59, 94)( 60, 87)( 63, 67)( 66, 91)( 70, 99)( 71, 95)( 73, 78)( 74,118)( 75,108)( 77, 82)( 80, 86)
        ( 81,119)( 84, 90)( 85,116)( 88, 97)( 89,121)( 93, 98)( 96,111)(101,106)(102,112)(104,110)(105,123)(109,114)
        (113,122)(115,120)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 38)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 55)( 28, 34)( 29, 68)( 32, 59)( 33, 71)( 36, 42)
        ( 37, 60)( 40, 46)( 41, 79)( 44, 63)( 45, 83)( 48, 54)( 49, 95)( 50, 64)( 52, 58)( 53, 96)( 56, 67)( 57, 99)
        ( 61, 82)( 62, 75)( 65, 91)( 66, 87)( 69, 74)( 70,103)( 72, 78)( 73,111)( 76,106)( 77,114)( 80, 86)( 81,107)
        ( 84, 90)( 85,108)( 88, 94)( 89,118)( 92, 98)( 93,121)( 97,102)(100,105)(101,122)(104,110)(109,117)(112,116)
        (113,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 77)( 28, 53)( 30, 36)( 31, 80)( 34, 57)
        ( 35, 83)( 39, 44)( 40, 66)( 42, 69)( 43, 92)( 46, 52)( 47,103)( 48, 70)( 50, 56)( 51,106)( 54, 73)( 55,107)
        ( 58, 64)( 59,118)( 60, 87)( 62, 68)( 63,122)( 67, 91)( 71, 99)( 72, 95)( 74, 79)( 75, 85)( 76,110)( 78, 82)
        ( 81, 86)( 84, 90)( 88,114)( 89,111)( 93, 98)( 94,123)( 96,116)( 97,120)(100,105)(101,112)(102,117)(104,109)
        (108,113)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 32)( 18, 36)( 19, 63)( 23, 44)( 24, 40)( 26, 31)( 27, 78)( 28, 52)( 30, 35)( 33, 56)( 34, 79)
        ( 38, 43)( 39, 67)( 41, 70)( 42, 87)( 45, 51)( 46, 98)( 47, 71)( 49, 55)( 50,101)( 53, 74)( 54,102)( 57, 62)
        ( 58,113)( 59, 82)( 61, 66)( 64, 69)( 65,114)( 68, 86)( 72, 94)( 73, 90)( 75, 81)( 76,122)( 77,105)( 80, 85)
        ( 83,109)( 84,123)( 88, 93)( 89,115)( 91,117)( 92,111)( 95,100)( 96,107)( 97,118)( 99,104)(103,108)(106,121)
        (110,116)(112,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 60)( 33, 64)( 34, 73)( 37, 43)
        ( 38, 84)( 39, 65)( 41, 47)( 42, 85)( 45, 68)( 46, 88)( 49, 55)( 50, 99)( 51, 69)( 53, 59)( 54,102)( 57, 63)
        ( 58,105)( 61, 72)( 62,109)( 66, 80)( 67, 76)( 70, 95)( 71, 91)( 74, 79)( 75,113)( 77,117)( 78,114)( 81, 87)
        ( 82, 93)( 83,118)( 86, 90)( 89, 94)( 92,121)( 96,101)( 97,107)( 98,122)(100,104)(103,108)(106,112)(110,116)
        (111,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 29)( 18, 33)( 19, 61)( 23, 41)( 24, 37)( 27, 32)( 28, 49)( 30, 53)( 31, 73)( 35, 40)( 36, 65)
        ( 38, 68)( 39, 80)( 42, 48)( 43, 91)( 44, 69)( 46, 52)( 47, 94)( 50, 72)( 51, 98)( 54, 60)( 55,106)( 56, 76)
        ( 58, 64)( 59,110)( 62, 67)( 63,113)( 66, 79)( 70, 87)( 71, 83)( 74, 78)( 75, 99)( 77,102)( 81, 86)( 82,114)
        ( 84, 90)( 85,118)( 88, 93)( 89,121)( 92, 97)( 95,101)( 96,122)(100,105)(103,109)(104,123)(107,112)(108,120)
        (111,116)(115,117)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 29)( 18, 33)( 19, 61)( 23, 41)( 24, 37)( 27, 32)( 28, 49)( 30, 53)( 31, 73)( 35, 40)( 36, 64)
        ( 38, 68)( 39, 80)( 42, 48)( 43, 88)( 44, 69)( 46, 52)( 47, 91)( 50, 72)( 51, 95)( 54, 60)( 55,103)( 56, 76)
        ( 58, 63)( 59,107)( 62, 67)( 65, 79)( 66,108)( 70, 87)( 71, 83)( 74, 78)( 75, 96)( 77, 99)( 81, 86)( 82,111)
        ( 84,114)( 85,118)( 89, 94)( 90,115)( 92, 98)( 93,122)( 97,102)(100,106)(101,123)(104,110)(105,120)(109,113)
        (112,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 29)( 18, 33)( 19, 61)( 23, 41)( 24, 37)( 27, 32)( 28, 49)( 30, 53)( 31, 73)( 35, 40)( 36, 65)
        ( 38, 68)( 39, 80)( 42, 48)( 43, 88)( 44, 69)( 46, 52)( 47, 91)( 50, 72)( 51, 95)( 54, 60)( 55,103)( 56, 76)
        ( 58, 64)( 59,107)( 62, 67)( 63,110)( 66, 79)( 70, 87)( 71, 83)( 74, 78)( 75, 96)( 77, 99)( 81, 86)( 82,111)
        ( 84,114)( 85,118)( 89, 94)( 90,115)( 92, 98)( 93,122)( 97,102)(100,106)(101,123)(104,109)(105,120)(108,113)
        (112,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 52)( 29, 56)( 30, 69)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 80)( 41, 64)( 42, 83)( 45, 51)( 46, 92)( 47, 65)( 49, 55)( 50, 95)( 53, 68)( 54, 99)( 57, 63)
        ( 58,107)( 59, 72)( 62, 75)( 66, 91)( 67, 87)( 70, 74)( 71,100)( 73,103)( 76, 82)( 77,118)( 78,108)( 81, 86)
        ( 84, 90)( 85,119)( 88,111)( 89,116)( 93, 98)( 94,112)( 96,102)( 97,122)(101,106)(104,110)(105,123)(109,114)
        (113,121)(115,120)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 60)( 33, 64)( 34, 73)( 37, 43)
        ( 38, 84)( 39, 65)( 41, 47)( 42, 85)( 45, 68)( 46, 88)( 49, 55)( 50, 99)( 51, 69)( 53, 59)( 54,103)( 57, 63)
        ( 58,106)( 61, 72)( 62,107)( 66, 80)( 67, 76)( 70, 95)( 71, 91)( 74, 79)( 75,110)( 77,114)( 78,122)( 81, 87)
        ( 82, 93)( 83,115)( 86, 90)( 89, 94)( 92,118)( 96,102)( 97,124)( 98,119)(100,105)(101,112)(104,109)(108,113)
        (111,121)(116,120)(117,123),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 75)( 31, 60)( 33, 39)( 34, 76)
        ( 37, 64)( 38, 79)( 41, 47)( 42, 91)( 43, 65)( 45, 51)( 46, 94)( 49, 68)( 50, 95)( 53, 59)( 54,106)( 55, 69)
        ( 58, 63)( 61, 72)( 62,107)( 66, 87)( 67, 83)( 70,102)( 71, 98)( 73, 78)( 74,110)( 77, 82)( 80, 86)( 81,111)
        ( 84,114)( 85,121)( 88, 93)( 89,100)( 90,115)( 92, 97)( 96,101)( 99,118)(103,109)(104,123)(105,119)(108,113)
        (112,124)(116,120)(117,122),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 76)( 31, 63)( 33, 39)( 34, 77)
        ( 37, 67)( 38, 79)( 41, 47)( 42, 88)( 43, 68)( 45, 51)( 46, 91)( 49, 71)( 50, 92)( 53, 58)( 54,103)( 55, 72)
        ( 57, 62)( 60, 66)( 61,104)( 64, 75)( 65,107)( 69, 87)( 70, 83)( 73, 99)( 74, 95)( 78, 82)( 80, 86)( 81,108)
        ( 84,111)( 85,118)( 89, 94)( 90,112)( 93, 98)( 96,115)( 97,113)(100,106)(101,120)(102,116)(105,110)(109,121)
        (114,122)(117,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 52)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 60)( 33, 64)( 34, 73)( 37, 43)
        ( 38, 81)( 39, 65)( 41, 47)( 42, 84)( 45, 68)( 46, 88)( 49, 55)( 50, 96)( 51, 69)( 53, 59)( 54,100)( 57, 63)
        ( 58,103)( 61, 72)( 62,104)( 66, 80)( 67, 76)( 70, 92)( 71, 89)( 74, 79)( 75,107)( 77,111)( 78,118)( 82, 87)
        ( 83,112)( 85, 91)( 86,122)( 90,114)( 93, 99)( 94,120)( 95,115)( 97,102)( 98,109)(101,106)(105,110)(108,117)
        (113,121)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 29)(  7, 16)(  9, 24)( 10, 40)( 11, 21)( 13, 19)( 14, 51)
        ( 15, 25)( 17, 28)( 18, 55)( 22, 36)( 23, 32)( 26, 48)( 27, 44)( 30, 35)( 31, 59)( 33, 63)( 34, 72)( 37, 43)
        ( 38, 83)( 39, 64)( 41, 47)( 42, 86)( 45, 67)( 46, 90)( 49, 54)( 50, 68)( 52, 58)( 53, 95)( 56, 62)( 57, 98)
        ( 60, 71)( 61,102)( 65, 79)( 66, 75)( 69, 94)( 70, 91)( 73, 78)( 74,105)( 76, 82)( 77,114)( 80, 85)( 81,117)
        ( 84, 89)( 87, 93)( 88,118)( 92,109)( 96,101)( 97,110)( 99,104)(100,122)(103,108)(106,113)(107,123)(111,121)
        (112,119)(115,120)(116,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 16)(  7, 32)(  8, 14)( 10, 20)( 11, 43)( 12, 17)( 15, 28)
        ( 18, 40)( 19, 36)( 21, 27)( 22, 59)( 23, 47)( 25, 31)( 26, 63)( 29, 35)( 30, 67)( 33, 39)( 34, 70)( 37, 51)
        ( 38, 74)( 41, 46)( 42, 52)( 44, 50)( 45, 83)( 48, 55)( 49, 86)( 53, 82)( 54, 78)( 56, 62)( 57,101)( 58, 90)
        ( 60, 66)( 61,105)( 64, 69)( 65,109)( 68, 73)( 71, 77)( 72,110)( 75, 81)( 76,113)( 79, 94)( 80,117)( 84, 89)
        ( 85, 95)( 87, 93)( 88, 96)( 91, 98)( 92,122)( 97,121)( 99,104)(100,123)(102,108)(103,119)(106,112)(107,115)
        (111,116)(114,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 32)
        ( 16, 28)( 19, 44)( 20, 40)( 22, 27)( 23, 68)( 24, 52)( 26, 31)( 29, 56)( 30, 69)( 33, 39)( 34, 77)( 35, 57)
        ( 37, 43)( 38, 80)( 41, 60)( 42, 83)( 45, 51)( 46, 95)( 47, 61)( 49, 55)( 50, 98)( 53, 64)( 54,102)( 58, 76)
        ( 59, 72)( 62, 91)( 63, 87)( 65, 71)( 66,113)( 67,103)( 70, 75)( 73,106)( 74,114)( 78, 82)( 79,107)( 81, 86)
        ( 84, 90)( 85,108)( 88, 94)( 89,118)( 92, 97)( 93,121)( 96,101)( 99,105)(100,122)(104,110)(109,117)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 76)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 84)
        ( 37, 43)( 38, 96)( 39, 65)( 41, 47)( 42, 97)( 45, 68)( 46, 94)( 49, 55)( 50, 89)( 51, 69)( 53, 59)( 54, 99)
        ( 57, 72)( 58,103)( 61, 67)( 62, 70)( 63, 88)( 66, 92)( 71, 95)( 73, 79)( 74,115)( 75,107)( 77, 83)( 78,116)
        ( 81, 87)( 82,113)( 85, 91)( 86,118)( 90,102)( 93, 98)(100,106)(101,119)(104,110)(105,122)(108,111)(109,123)
        (112,117)(114,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 75)( 28, 56)( 30, 36)( 31, 79)( 34, 60)
        ( 35, 83)( 38, 43)( 39, 91)( 40, 69)( 42, 47)( 45, 51)( 46, 92)( 49, 55)( 50, 95)( 53, 59)( 54, 99)( 57, 71)
        ( 58,103)( 61, 67)( 62, 97)( 63, 87)( 65, 70)( 66, 94)( 72, 78)( 73,115)( 74,107)( 76, 82)( 77,116)( 80, 86)
        ( 81,113)( 84, 90)( 85,118)( 88,101)( 89,122)( 93, 98)( 96,102)(100,106)(104,110)(105,123)(108,111)(109,120)
        (112,117)(114,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 79)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 43)( 39, 95)( 40, 69)( 42, 47)( 45, 71)( 46, 96)( 49, 55)( 50,102)( 51, 72)( 53, 59)( 54,106)
        ( 57, 75)( 58,107)( 61, 67)( 62,100)( 63, 91)( 65, 70)( 66, 98)( 73, 92)( 74, 99)( 76, 82)( 77,118)( 78,110)
        ( 80, 86)( 81,119)( 84, 90)( 85,116)( 88, 94)( 89,121)( 93,105)( 97,101)(103,109)(104,122)(108,113)(111,114)
        (112,123)(115,120)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 48)( 24, 44)( 26, 32)( 27, 78)( 28, 55)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 43)( 39, 94)( 40, 68)( 42, 47)( 45, 70)( 46, 95)( 49, 54)( 50,106)( 51, 71)( 53, 58)( 56, 74)
        ( 57,107)( 60, 66)( 61,100)( 62, 90)( 64, 69)( 65, 97)( 72,102)( 73, 98)( 75, 81)( 76,118)( 77,110)( 79, 85)
        ( 80,119)( 83, 89)( 84,116)( 87, 93)( 88,121)( 91, 99)( 92,105)( 96,101)(103,109)(104,122)(108,113)(111,114)
        (112,123)(115,120)(117,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 72)( 27, 55)( 29, 35)( 30, 75)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 90)( 39, 64)( 41, 46)( 44, 67)( 45, 91)( 48, 54)( 49,101)( 50, 68)( 52, 58)( 53,105)( 56, 71)
        ( 57,106)( 60, 66)( 61,113)( 62, 83)( 65, 87)( 69, 97)( 70, 94)( 73, 78)( 74,109)( 76, 82)( 77,118)( 80, 86)
        ( 81,119)( 84, 99)( 85,121)( 88, 93)( 89,114)( 92, 96)( 95,115)( 98,104)(100,116)(102,108)(103,122)(107,112)
        (110,117)(111,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 62)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 71)( 27, 54)( 29, 35)( 30, 74)( 33, 58)( 34, 78)
        ( 37, 42)( 38, 89)( 39, 63)( 41, 46)( 44, 66)( 45, 90)( 48, 53)( 49,101)( 50, 67)( 52, 57)( 55, 70)( 56,102)
        ( 59, 65)( 60,113)( 61, 82)( 64, 86)( 68, 97)( 69, 93)( 72, 77)( 73,105)( 75, 81)( 76,118)( 79, 85)( 80,119)
        ( 83,109)( 84,121)( 87, 92)( 88,114)( 91, 96)( 94,111)( 95,115)( 98,104)( 99,122)(100,112)(103,108)(106,117)
        (107,123)(110,116)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 66)( 23, 47)( 24, 43)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 42)( 39, 70)( 41, 46)( 44, 74)( 45, 71)( 48, 54)( 49,101)( 50, 75)( 52, 58)( 53,105)( 56, 78)
        ( 57,109)( 60, 65)( 61,113)( 62, 90)( 64, 69)( 67, 73)( 68,114)( 72, 96)( 76, 97)( 77, 94)( 80, 85)( 81,110)
        ( 83, 89)( 84,118)( 87, 93)( 88,119)( 91, 99)( 92,121)( 95,115)( 98,104)(100,116)(102,108)(103,122)(106,112)
        (107,123)(111,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 68)( 27, 52)( 29, 35)( 30, 71)( 33, 55)( 34, 75)
        ( 37, 42)( 38, 60)( 40, 46)( 41, 84)( 44, 63)( 45, 87)( 48, 54)( 49, 98)( 50, 64)( 53, 67)( 56, 62)( 57,106)
        ( 58, 79)( 61, 83)( 65, 94)( 66, 90)( 69, 74)( 70, 99)( 72, 78)( 73,115)( 76, 82)( 77,116)( 80,102)( 81,118)
        ( 85, 89)( 86,107)( 88, 93)( 91,110)( 92,108)( 95,101)( 96,120)( 97,111)(100,114)(103,109)(104,113)(105,122)
        (112,123)(117,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 32)( 18, 36)( 22, 47)( 23, 43)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 72)( 33, 55)( 34, 75)
        ( 37, 42)( 38, 86)( 39, 60)( 41, 46)( 44, 63)( 45, 87)( 48, 54)( 49, 98)( 50, 64)( 53, 67)( 56, 62)( 57,106)
        ( 58, 79)( 61, 83)( 65, 94)( 66, 90)( 68, 74)( 69,115)( 70, 99)( 73, 78)( 76, 82)( 77,116)( 80,102)( 81,118)
        ( 84, 89)( 85,107)( 88, 93)( 91,110)( 92,108)( 95,101)( 96,120)( 97,111)(100,114)(103,109)(104,113)(105,122)
        (112,123)(117,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 43)( 39, 69)( 41, 47)( 42, 96)( 45, 72)( 46, 98)( 49, 55)( 50, 92)( 51, 73)( 53, 59)( 54,102)
        ( 57, 76)( 58,106)( 61, 67)( 62, 74)( 63, 91)( 65, 71)( 66,100)( 70, 95)( 75, 99)( 77, 82)( 78,115)( 79,110)
        ( 81, 86)( 84, 90)( 85,116)( 88, 94)( 89,118)( 93,105)( 97,101)(103,109)(104,119)(107,113)(108,122)(111,114)
        (112,123)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 83)( 34, 60)
        ( 35, 87)( 38, 43)( 39, 69)( 41, 47)( 42, 96)( 45, 72)( 46, 99)( 49, 55)( 50,106)( 51, 73)( 53, 59)( 54,110)
        ( 57, 76)( 58,114)( 61, 67)( 62,108)( 63, 91)( 65, 71)( 66,104)( 70, 95)( 74,102)( 75,100)( 77, 82)( 78, 85)
        ( 79,118)( 81, 86)( 84, 90)( 88, 94)( 89,119)( 92,112)( 93,122)( 97,101)( 98,105)(103,109)(107,113)(111,117)
        (115,121)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 51)( 28, 34)( 29, 68)( 32, 55)( 33, 71)( 36, 42)
        ( 37, 82)( 38, 60)( 40, 46)( 41, 83)( 44, 63)( 45, 86)( 49, 54)( 50, 64)( 52, 67)( 53, 95)( 56, 62)( 57,106)
        ( 58, 74)( 61, 78)( 65, 94)( 66, 90)( 69, 73)( 70, 98)( 72, 77)( 75,102)( 76, 99)( 79, 85)( 80,121)( 81,107)
        ( 84, 89)( 87, 93)( 88,122)( 91,110)( 92,123)( 96,101)( 97,111)(100,116)(103,109)(104,120)(105,114)(108,117)
        (112,115)(113,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 70)( 27, 51)( 29, 34)( 32, 55)( 33, 71)( 36, 42)
        ( 37, 82)( 38, 60)( 40, 46)( 41, 86)( 44, 63)( 45, 87)( 49, 54)( 50, 64)( 52, 67)( 53, 95)( 56, 62)( 57,106)
        ( 58, 74)( 61, 78)( 65, 94)( 66, 90)( 68, 73)( 69, 98)( 72, 77)( 75,102)( 76, 99)( 79, 85)( 80,121)( 81,107)
        ( 83, 89)( 84,122)( 88, 93)( 91,110)( 92,123)( 96,101)( 97,111)(100,116)(103,109)(104,120)(105,114)(108,117)
        (112,115)(113,119)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 80)( 33, 60)( 34, 82)
        ( 37, 43)( 38, 91)( 39, 72)( 41, 47)( 42, 94)( 45, 76)( 46, 98)( 49, 55)( 50,106)( 51, 77)( 53, 59)( 54, 88)
        ( 57, 79)( 58, 84)( 61, 67)( 62,110)( 63, 86)( 65, 71)( 66,111)( 69, 75)( 70,114)( 73, 90)( 74,118)( 78,102)
        ( 81, 85)( 83, 89)( 87,107)( 92, 97)( 93,122)( 95,101)( 96,123)( 99,105)(100,120)(103,109)(104,116)(108,113)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 44)( 20, 40)( 22, 28)( 23, 67)( 24, 52)( 26, 32)( 27, 68)( 30, 55)( 31, 71)( 34, 39)( 35, 56)
        ( 37, 43)( 38, 80)( 41, 59)( 42, 83)( 45, 51)( 46, 94)( 47, 60)( 49, 54)( 50, 98)( 53, 63)( 57, 79)( 58, 75)
        ( 61, 90)( 62, 86)( 64, 70)( 65,113)( 66, 99)( 69, 74)( 72, 78)( 73,114)( 76,102)( 77,117)( 81, 85)( 82,103)
        ( 84, 89)( 87,106)( 88,104)( 91, 97)( 92,121)( 93,107)( 95,101)( 96,122)(100,110)(105,109)(108,118)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 35)(  8, 14)( 10, 21)( 11, 47)( 12, 18)( 15, 32)
        ( 16, 28)( 19, 43)( 20, 39)( 22, 27)( 23, 63)( 24, 48)( 26, 31)( 29, 51)( 30, 64)( 33, 38)( 34, 52)( 36, 42)
        ( 37, 72)( 40, 55)( 41, 75)( 44, 50)( 45, 87)( 46, 56)( 49, 59)( 53, 71)( 54, 67)( 57, 83)( 58, 79)( 60, 66)
        ( 61,102)( 62, 88)( 65, 70)( 68, 91)( 69,103)( 73, 78)( 74, 92)( 76, 82)( 77,111)( 80, 95)( 81,112)( 84, 90)
        ( 85,121)( 86, 96)( 89, 99)( 93,110)( 94,106)( 97,118)( 98,114)(100,105)(101,122)(104,109)(107,116)(108,123)
        (113,117)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 40)(  8, 17)( 10, 24)( 11, 52)( 12, 21)( 14, 19)
        ( 15, 64)( 16, 32)( 18, 36)( 22, 48)( 23, 44)( 25, 31)( 26, 75)( 27, 56)( 29, 35)( 30, 79)( 33, 60)( 34, 83)
        ( 37, 43)( 38, 95)( 39, 65)( 41, 47)( 42, 96)( 45, 68)( 46, 93)( 49, 55)( 50, 88)( 51, 69)( 53, 59)( 54, 98)
        ( 57, 72)( 58,102)( 61, 67)( 62, 70)( 63, 87)( 66, 91)( 71, 94)( 73, 78)( 74,106)( 76, 82)( 77,110)( 80, 86)
        ( 81,113)( 84, 90)( 85,117)( 89,101)( 92, 97)( 99,105)(100,118)(103,108)(104,121)(107,109)(111,116)(112,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 55)( 16, 31)( 18, 35)( 22, 43)( 23, 39)( 25, 30)( 26, 48)( 28, 34)( 29, 64)( 32, 51)( 33, 67)( 37, 42)
        ( 38, 56)( 40, 59)( 41, 76)( 44, 50)( 45, 87)( 46, 60)( 49, 63)( 52, 58)( 53, 95)( 54, 71)( 57, 75)( 61, 83)
        ( 62, 79)( 65, 70)( 66, 88)( 68, 74)( 69,104)( 72, 91)( 73,107)( 77, 82)( 78, 96)( 80, 99)( 81,116)( 84, 90)
        ( 85,121)( 86,100)( 89,103)( 92, 98)( 93,119)( 94,111)( 97,115)(101,112)(102,118)(105,110)(106,122)(108,114)
        (109,123)(113,124)(117,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 37)( 19, 62)( 23, 43)( 24, 40)( 26, 32)( 27, 70)( 28, 51)( 30, 36)( 31, 74)( 34, 55)
        ( 35, 78)( 39, 42)( 41, 63)( 44, 50)( 45, 57)( 46, 64)( 48, 54)( 49, 83)( 52, 66)( 53, 86)( 56, 61)( 58, 82)
        ( 60, 65)( 67, 73)( 68, 95)( 69, 90)( 71, 77)( 72, 98)( 75, 81)( 76,102)( 79, 85)( 80,106)( 84, 89)( 87, 93)
        ( 88,107)( 91, 94)( 92,110)( 96,101)( 97,114)( 99,105)(100,119)(103,109)(104,121)(108,113)(111,117)(112,122)
        (115,118)(116,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 45)( 26, 32)( 27, 80)( 28, 56)( 30, 36)( 31, 84)( 34, 60)
        ( 35, 88)( 38, 44)( 39, 96)( 40, 69)( 42, 47)( 43, 97)( 46, 72)( 49, 55)( 50, 66)( 51, 73)( 53, 59)( 54, 62)
        ( 57, 76)( 58, 93)( 61, 67)( 63, 92)( 65, 71)( 70, 74)( 75, 98)( 77, 83)( 78,106)( 79, 99)( 81, 87)( 82,109)
        ( 85, 91)( 86,113)( 89, 95)( 90,117)( 94,102)(100,103)(101,118)(104,108)(105,121)(107,112)(110,116)(111,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 67)( 23, 47)( 24, 44)( 26, 32)( 27, 82)( 28, 55)( 30, 36)( 31, 86)( 34, 59)
        ( 35, 90)( 38, 43)( 39, 71)( 41, 46)( 42, 99)( 45, 74)( 48, 54)( 49, 65)( 50, 75)( 52, 58)( 53, 61)( 56, 78)
        ( 57, 95)( 60, 66)( 62, 94)( 64, 70)( 68, 73)( 69, 76)( 72, 98)( 77,100)( 79, 85)( 80,106)( 81,101)( 83, 89)
        ( 84,109)( 87, 93)( 88,113)( 91, 97)( 92,117)( 96,104)(102,105)(103,118)(107,112)(108,121)(110,116)(111,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 36)( 19, 63)( 23, 43)( 25, 31)( 26, 72)( 27, 51)( 29, 35)( 30, 75)( 33, 55)( 34, 79)
        ( 37, 42)( 38, 86)( 39, 67)( 41, 46)( 44, 50)( 45, 87)( 48, 54)( 49, 90)( 52, 71)( 53, 94)( 56, 62)( 57,106)
        ( 58, 80)( 60, 66)( 61,107)( 64, 70)( 65,110)( 68, 83)( 69,114)( 73, 78)( 74, 98)( 76, 82)( 77, 99)( 81,102)
        ( 84, 89)( 85,117)( 88, 93)( 91, 97)( 92,118)( 95,101)( 96,121)(100,105)(103,109)(104,122)(108,113)(111,116)
        (112,123)(115,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 53)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 73)( 31, 60)( 33, 39)( 34, 76)
        ( 37, 64)( 38, 80)( 41, 47)( 42, 92)( 43, 65)( 45, 51)( 46, 95)( 49, 68)( 50, 98)( 54, 59)( 55, 69)( 57, 63)
        ( 58,107)( 61, 72)( 62,110)( 66, 88)( 67, 84)( 70,106)( 71,102)( 74, 79)( 75,111)( 77, 83)( 78,122)( 81, 87)
        ( 82,123)( 85,114)( 86,120)( 89, 94)( 90,100)( 91,115)( 93, 97)( 96,101)( 99,105)(103,117)(104,116)(108,113)
        (109,118)(112,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 53)
        ( 15, 25)( 17, 28)( 18, 56)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 77)
        ( 37, 64)( 38, 80)( 41, 47)( 42, 91)( 43, 65)( 45, 51)( 46, 94)( 49, 68)( 50, 98)( 54, 59)( 55, 69)( 57, 63)
        ( 58,106)( 61, 72)( 62,109)( 66, 88)( 67, 84)( 70,105)( 71,101)( 73, 79)( 74,122)( 75,110)( 78, 83)( 81, 87)
        ( 82,123)( 85,113)( 86,120)( 89, 93)( 90,114)( 92, 97)( 95,100)( 96,115)( 99,104)(102,117)(103,116)(107,112)
        (108,118)(111,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 16)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 28)( 17, 32)( 18, 57)( 22, 44)( 23, 40)( 26, 31)( 27, 52)( 29, 56)( 30, 69)( 33, 39)( 34, 80)( 35, 60)
        ( 37, 43)( 38, 81)( 41, 64)( 42, 84)( 45, 51)( 46, 95)( 47, 65)( 49, 55)( 50, 98)( 53, 68)( 54,102)( 58, 63)
        ( 59, 72)( 61, 76)( 62,110)( 66, 92)( 67, 88)( 70, 75)( 71,105)( 73,109)( 74,118)( 77, 83)( 78,122)( 79,111)
        ( 82, 87)( 85, 91)( 86,123)( 89,113)( 90,120)( 93, 97)( 94,114)( 96,101)( 99,104)(100,115)(103,108)(106,117)
        (107,116)(112,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 49)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 45)( 20, 41)( 22, 28)( 23, 64)( 24, 53)( 26, 32)( 27, 68)( 30, 36)( 31, 72)( 34, 40)( 35, 76)
        ( 38, 44)( 39, 80)( 42, 57)( 43, 84)( 46, 52)( 47, 95)( 48, 58)( 50, 56)( 51, 98)( 54, 61)( 55,102)( 59, 92)
        ( 60, 88)( 62, 67)( 63,105)( 65, 71)( 66,114)( 69, 75)( 70,117)( 73, 79)( 74,121)( 77, 83)( 78,122)( 81, 87)
        ( 82,123)( 85, 91)( 86,119)( 89,109)( 90,116)( 93, 97)( 94,110)( 96,101)( 99,104)(100,111)(103,108)(106,113)
        (107,112)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 29)( 18, 33)( 19, 65)( 23, 45)( 24, 41)( 27, 32)( 28, 53)( 30, 57)( 31, 73)( 34, 40)( 35, 79)
        ( 36, 66)( 38, 44)( 39, 83)( 42, 68)( 43, 86)( 46, 52)( 47, 95)( 48, 69)( 50, 56)( 51, 98)( 54, 72)( 55,102)
        ( 58, 64)( 59,114)( 60, 76)( 62, 67)( 63, 82)( 70, 94)( 71, 90)( 74, 78)( 75,106)( 77,110)( 80, 85)( 81,115)
        ( 84, 89)( 87, 93)( 88,116)( 91,118)( 92,112)( 96,101)( 97,119)( 99,105)(100,123)(103,109)(104,124)(107,113)
        (108,121)(111,117)(120,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 30)( 18, 33)( 19, 64)( 23, 44)( 24, 40)( 26, 32)( 27, 75)( 28, 52)( 31, 56)( 34, 39)( 35, 65)
        ( 37, 43)( 38, 80)( 41, 68)( 42, 83)( 45, 51)( 46, 95)( 47, 69)( 49, 55)( 50, 96)( 53, 72)( 54, 99)( 57, 63)
        ( 58,111)( 59, 76)( 61, 67)( 62,115)( 66, 79)( 70, 91)( 71, 87)( 73, 78)( 74,103)( 77,107)( 81, 86)( 82,116)
        ( 84, 90)( 85,113)( 88,118)( 89,109)( 92, 98)( 93,123)( 94,119)( 97,102)(100,106)(101,124)(104,110)(105,121)
        (108,114)(112,117)(120,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 28)( 18, 32)( 22, 44)( 23, 40)( 26, 31)( 27, 52)( 29, 56)( 30, 69)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 82)( 41, 64)( 42, 86)( 45, 51)( 46, 98)( 47, 65)( 49, 55)( 50,101)( 53, 68)( 54,105)( 57, 63)
        ( 58,117)( 59, 72)( 62, 75)( 66, 94)( 67, 90)( 70, 74)( 71,109)( 73,113)( 76, 81)( 77, 84)( 78,118)( 80, 85)
        ( 83, 89)( 87, 93)( 88,119)( 91,121)( 92,115)( 95,100)( 96,103)( 97,122)( 99,104)(102,108)(106,112)(107,123)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 29)( 18, 32)( 22, 44)( 23, 40)( 25, 31)( 26, 71)( 27, 52)( 30, 56)( 33, 39)( 34, 79)( 35, 61)
        ( 37, 43)( 38, 82)( 41, 64)( 42, 86)( 45, 51)( 46, 98)( 47, 65)( 49, 55)( 50,101)( 53, 68)( 54,105)( 57, 63)
        ( 58,117)( 59, 72)( 62, 75)( 66, 94)( 67, 90)( 69, 74)( 70,109)( 73,113)( 76, 81)( 77, 84)( 78,118)( 80, 85)
        ( 83, 89)( 87, 93)( 88,119)( 91,121)( 92,115)( 95,100)( 96,103)( 97,122)( 99,104)(102,108)(106,112)(107,123)
        (110,116)(111,124)(114,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 31)(  7, 16)(  9, 24)( 10, 43)( 11, 21)( 13, 19)( 14, 55)
        ( 15, 25)( 17, 28)( 18, 59)( 22, 39)( 23, 35)( 26, 51)( 27, 47)( 29, 34)( 30, 63)( 32, 38)( 33, 76)( 36, 67)
        ( 37, 79)( 40, 46)( 41, 88)( 42, 68)( 44, 50)( 45, 91)( 48, 71)( 49, 95)( 52, 58)( 53,107)( 54, 72)( 56, 62)
        ( 57,111)( 60, 66)( 61,112)( 64, 75)( 65,109)( 69, 87)( 70, 83)( 73,103)( 74, 99)( 77, 82)( 78,105)( 80, 86)
        ( 81,120)( 84,114)( 85,121)( 89, 94)( 90,115)( 92, 98)( 93,123)( 96,102)( 97,124)(100,118)(101,117)(104,110)
        (106,119)(108,113)(116,122),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 25)(  4,  9)(  6, 17)(  7, 37)(  8, 14)( 10, 21)( 11, 49)( 12, 18)( 15, 33)
        ( 16, 29)( 19, 45)( 20, 41)( 22, 28)( 23, 64)( 24, 53)( 26, 32)( 27, 68)( 30, 36)( 31, 72)( 34, 40)( 35, 76)
        ( 38, 44)( 39, 79)( 42, 57)( 43, 83)( 46, 52)( 47, 92)( 48, 58)( 50, 56)( 51, 95)( 54, 61)( 55, 99)( 59, 91)
        ( 60, 87)( 62, 67)( 63,103)( 65, 71)( 66,112)( 69, 75)( 70,115)( 73, 78)( 74,119)( 77, 82)( 80, 86)( 81,120)
        ( 84, 90)( 85,117)( 88,107)( 89,114)( 93, 98)( 94,108)( 96,102)( 97,123)(100,106)(101,124)(104,111)(105,110)
        (109,122)(113,118)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 17)(  7, 36)(  8, 14)( 10, 21)( 11, 48)( 12, 18)( 15, 32)
        ( 16, 28)( 19, 44)( 20, 40)( 22, 27)( 23, 52)( 25, 31)( 26, 65)( 29, 56)( 30, 68)( 33, 39)( 34, 79)( 35, 57)
        ( 37, 43)( 38, 83)( 41, 60)( 42, 86)( 45, 51)( 46, 98)( 47, 61)( 49, 55)( 50,101)( 53, 64)( 54,105)( 58, 76)
        ( 59, 72)( 62, 94)( 63, 90)( 66, 71)( 67,109)( 69, 75)( 70,118)( 73, 78)( 74,121)( 77, 82)( 80, 85)( 81,122)
        ( 84, 89)( 87, 93)( 88,123)( 91,113)( 92,120)( 95,100)( 96,103)( 97,114)( 99,104)(102,108)(106,112)(107,115)
        (110,117)(111,116)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 51)( 12, 21)( 14, 19)
        ( 15, 63)( 16, 31)( 18, 35)( 22, 47)( 23, 43)( 25, 30)( 26, 55)( 28, 34)( 29, 71)( 32, 59)( 33, 74)( 36, 42)
        ( 37, 82)( 38, 64)( 40, 46)( 41, 86)( 44, 66)( 45, 87)( 48, 54)( 49, 98)( 50, 67)( 52, 58)( 53, 99)( 56, 70)
        ( 57,102)( 60, 65)( 61, 85)( 62, 78)( 68, 94)( 69, 90)( 72, 77)( 73,106)( 75, 81)( 76,119)( 79,110)( 80,120)
        ( 83, 89)( 84,111)( 88, 93)( 91,114)( 92,112)( 95,101)( 96,104)( 97,115)(100,105)(103,109)(107,118)(108,116)
        (113,122)(117,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65)( 66, 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 20)(  7, 36)(  8, 17)( 10, 24)( 11, 47)( 12, 21)( 14, 19)
        ( 15, 59)( 16, 31)( 18, 35)( 22, 43)( 23, 39)( 25, 30)( 26, 51)( 28, 34)( 29, 68)( 32, 55)( 33, 71)( 37, 42)
        ( 38, 60)( 40, 63)( 41, 79)( 44, 50)( 45, 89)( 46, 64)( 48, 54)( 49, 93)( 52, 67)( 53, 97)( 56, 62)( 57,105)
        ( 58, 75)( 61, 78)( 65, 86)( 66, 82)( 69, 74)( 70, 98)( 72, 77)( 73,114)( 76,101)( 80, 85)( 81,106)( 83,109)
        ( 84,118)( 87, 92)( 88,110)( 90, 96)( 91,111)( 94,100)( 95,122)( 99,113)(102,108)(103,120)(104,115)(107,117)
        (112,121)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 32)( 18, 36)( 19, 68)( 23, 48)( 24, 44)( 26, 31)( 27, 56)( 29, 35)( 30, 76)( 33, 60)( 34, 79)
        ( 37, 43)( 38, 86)( 39, 69)( 41, 47)( 42, 90)( 45, 71)( 46, 91)( 49, 55)( 50,102)( 51, 72)( 53, 59)( 54,106)
        ( 57, 75)( 58,109)( 61, 67)( 62,121)( 63, 82)( 65, 70)( 66, 89)( 73, 98)( 74, 94)( 77, 81)( 78,113)( 80, 85)
        ( 83,117)( 84,114)( 87, 93)( 88,122)( 92, 97)( 95,119)( 96,123)( 99,105)(100,115)(101,120)(103,108)(104,111)
        (107,112)(110,116)(118,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 60)( 16, 29)( 18, 33)( 19, 61)( 23, 44)( 24, 40)( 27, 32)( 28, 52)( 30, 56)( 31, 73)( 34, 39)( 35, 82)
        ( 36, 64)( 38, 43)( 41, 68)( 42, 83)( 45, 51)( 46, 91)( 47, 69)( 49, 55)( 50, 94)( 53, 72)( 54, 98)( 57, 63)
        ( 58,109)( 59, 76)( 62, 67)( 65, 79)( 66,110)( 70, 90)( 71, 86)( 74, 78)( 75,102)( 77,105)( 80, 85)( 81,113)
        ( 84, 89)( 87,117)( 88,114)( 92, 97)( 93,118)( 95,101)( 96,119)( 99,104)(100,122)(103,108)(106,112)(107,123)
        (111,116)(115,124)(120,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 50)( 12, 22)( 14, 20)
        ( 15, 62)( 16, 32)( 18, 35)( 19, 66)( 23, 46)( 24, 42)( 26, 31)( 27, 54)( 29, 34)( 30, 75)( 33, 58)( 36, 41)
        ( 37, 82)( 38, 67)( 40, 45)( 43, 70)( 44, 83)( 47, 53)( 48, 91)( 49, 71)( 51, 57)( 52, 94)( 55, 74)( 56, 97)
        ( 59, 65)( 60,105)( 61, 76)( 63, 69)( 64,109)( 68, 78)( 72, 90)( 73, 86)( 77,101)( 79, 85)( 80,118)( 81,110)
        ( 84, 89)( 87,113)( 88,119)( 92, 96)( 93,114)( 95,100)( 98,104)( 99,115)(102,108)(103,122)(106,112)(107,123)
        (111,117)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41)( 42, 43, 44, 45)( 46, 47, 48, 49)
        ( 50, 51, 52, 53)( 54, 55, 56, 57)( 58, 59, 60, 61)( 62, 63, 64, 65)( 66, 67, 68, 69)( 70, 71, 72, 73)
        ( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)( 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 32)( 18, 35)( 19, 63)( 23, 43)( 24, 39)( 26, 31)( 27, 51)( 29, 34)( 30, 75)( 33, 55)( 37, 42)
        ( 38, 67)( 40, 70)( 41, 79)( 44, 50)( 45, 89)( 46, 71)( 48, 54)( 49, 90)( 52, 74)( 53, 93)( 56, 62)( 57,101)
        ( 58, 76)( 60, 66)( 61,105)( 64, 69)( 65,109)( 68, 78)( 72, 86)( 73, 82)( 77, 97)( 80, 85)( 81,110)( 83,113)
        ( 84,118)( 87, 92)( 88,114)( 91, 96)( 94,100)( 95,115)( 98,104)( 99,122)(102,108)(103,123)(106,112)(107,120)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69)
        ( 70, 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 19)(  6, 31)(  7, 16)(  9, 23)( 10, 43)( 11, 20)( 13, 18)( 14, 55)
        ( 15, 24)( 17, 27)( 21, 39)( 22, 35)( 25, 51)( 26, 47)( 28, 34)( 29, 71)( 30, 56)( 32, 38)( 33, 75)( 36, 59)
        ( 37, 78)( 40, 46)( 41, 90)( 42, 60)( 44, 50)( 45, 91)( 48, 63)( 49, 94)( 52, 58)( 53,106)( 54, 64)( 57, 67)
        ( 61, 86)( 62, 82)( 65,102)( 66, 98)( 68, 74)( 69,118)( 70,107)( 72, 77)( 73,119)( 76, 81)( 79, 85)( 80,120)
        ( 83,110)( 84,116)( 87, 93)( 88, 96)( 89,111)( 92, 97)( 95,101)( 99,105)(100,112)(103,109)(104,123)(108,114)
        (113,122)(115,121)(117,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 20)(  6, 32)(  7, 16)(  9, 24)( 10, 44)( 11, 21)( 13, 19)( 14, 56)
        ( 15, 25)( 17, 28)( 18, 57)( 22, 40)( 23, 36)( 26, 52)( 27, 48)( 29, 35)( 30, 76)( 31, 60)( 33, 39)( 34, 79)
        ( 37, 64)( 38, 82)( 41, 47)( 42, 93)( 43, 65)( 45, 51)( 46, 94)( 49, 68)( 50, 97)( 53, 59)( 54,109)( 55, 69)
        ( 58, 63)( 61, 72)( 62,110)( 66, 90)( 67, 86)( 70,105)( 71,101)( 73, 78)( 74, 84)( 75,113)( 77, 81)( 80, 85)
        ( 83, 89)( 87,117)( 88,114)( 91, 96)( 92,118)( 95,100)( 98,104)( 99,119)(102,108)(103,122)(106,112)(107,123)
        (111,116)(115,124)(120,121),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 32)( 18, 36)( 19, 64)( 23, 47)( 24, 43)( 26, 31)( 27, 55)( 29, 35)( 30, 76)( 33, 59)( 34, 79)
        ( 37, 42)( 38, 67)( 40, 46)( 41, 88)( 44, 71)( 45, 89)( 48, 54)( 49, 99)( 50, 72)( 52, 58)( 53,102)( 56, 75)
        ( 57,106)( 60, 66)( 61,114)( 62, 83)( 65, 70)( 68, 87)( 69,115)( 73, 95)( 74, 91)( 77, 82)( 78,107)( 80, 86)
        ( 81,119)( 84,110)( 85,121)( 90, 94)( 92,112)( 93,116)( 96,101)( 97,122)( 98,113)(100,105)(103,109)(104,123)
        (108,118)(111,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 37)(  8, 17)( 10, 24)( 11, 48)( 12, 21)( 14, 19)
        ( 15, 60)( 16, 32)( 18, 36)( 22, 44)( 23, 40)( 25, 31)( 26, 72)( 27, 52)( 29, 35)( 30, 76)( 33, 56)( 34, 80)
        ( 38, 43)( 39, 61)( 41, 64)( 42, 89)( 45, 51)( 46, 85)( 47, 65)( 49, 55)( 50, 91)( 53, 68)( 54, 95)( 57, 63)
        ( 58, 66)( 59, 84)( 62, 88)( 67, 90)( 69, 75)( 70,104)( 71, 99)( 73, 79)( 74,107)( 77, 83)( 78,110)( 81, 87)
        ( 82,114)( 86, 94)( 92, 98)( 93,115)( 96,102)( 97,118)(100,103)(101,119)(105,109)(106,122)(108,113)(111,117)
        (112,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 63)( 16, 33)( 18, 37)( 19, 64)( 23, 47)( 24, 43)( 26, 32)( 27, 78)( 28, 55)( 30, 36)( 31, 82)( 34, 59)
        ( 35, 86)( 38, 42)( 39, 67)( 41, 46)( 44, 71)( 45, 68)( 48, 54)( 49, 91)( 50, 72)( 52, 58)( 53, 94)( 56, 75)
        ( 57, 98)( 60, 66)( 61, 73)( 62, 90)( 65, 70)( 69, 74)( 76, 81)( 77,102)( 79, 85)( 80,107)( 83, 89)( 84,110)
        ( 87, 93)( 88,114)( 92, 97)( 95,101)( 96,115)( 99,105)(100,118)(103,106)(104,121)(108,113)(109,122)(111,117)
        (112,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 25)( 11, 52)( 12, 22)( 14, 20)
        ( 15, 64)( 16, 33)( 18, 37)( 19, 68)( 23, 48)( 24, 44)( 26, 32)( 27, 83)( 28, 56)( 30, 36)( 31, 87)( 34, 60)
        ( 35, 91)( 38, 43)( 39, 72)( 41, 47)( 42,100)( 45, 75)( 46,102)( 49, 55)( 50, 62)( 51, 76)( 53, 59)( 54, 96)
        ( 57, 79)( 58,106)( 61, 67)( 63, 95)( 65, 71)( 66, 77)( 69, 74)( 70,104)( 73, 99)( 78,103)( 80, 86)( 81,115)
        ( 82,110)( 84, 90)( 85,116)( 88, 94)( 89,118)( 92, 98)( 93,122)( 97,109)(101,105)(107,113)(108,123)(111,114)
        (112,120)(117,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 19)(  6, 28)(  7, 15)(  9, 23)( 10, 39)( 11, 20)( 13, 18)( 14, 24)
        ( 16, 27)( 17, 44)( 21, 35)( 22, 31)( 25, 43)( 26, 40)( 29, 34)( 30, 47)( 32, 51)( 33, 60)( 36, 42)( 37, 71)
        ( 38, 52)( 41, 55)( 45, 50)( 46, 56)( 48, 59)( 49, 76)( 53, 67)( 54, 63)( 57, 75)( 58, 72)( 61, 66)( 62, 79)
        ( 64, 83)( 65, 92)( 68, 74)( 69,102)( 70, 84)( 73, 87)( 77, 82)( 78, 88)( 80, 91)( 81,107)( 85, 99)( 86, 95)
        ( 89,106)( 90,103)( 93, 98)( 94,110)( 96,113)( 97,122)(100,105)(101,114)(104,117)(108,112)(109,118)(111,121)
        (115,120)(116,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 20)(  7, 39)(  8, 17)( 10, 24)( 11, 49)( 12, 21)( 14, 19)
        ( 15, 57)( 16, 32)( 18, 36)( 22, 45)( 23, 42)( 25, 31)( 26, 65)( 27, 53)( 29, 35)( 30, 69)( 33, 47)( 34, 73)
        ( 37, 41)( 38, 58)( 40, 44)( 43, 59)( 46, 52)( 48, 60)( 50, 56)( 51, 74)( 54, 61)( 55, 77)( 62, 68)( 63, 89)
        ( 64, 81)( 66, 72)( 67, 93)( 70, 76)( 71, 97)( 75, 80)( 78, 84)( 79, 98)( 82, 85)( 83,101)( 86, 92)( 87,110)
        ( 88,105)( 90, 96)( 91,113)( 94,100)( 95,117)( 99,104)(102,108)(103,118)(106,109)(107,121)(111,116)(112,122)
        (114,120)(115,123)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41)( 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 16)(  6, 28)(  7, 13)(  9, 20)( 10, 40)( 11, 17)( 14, 24)( 15, 21)
        ( 18, 36)( 19, 32)( 22, 48)( 23, 44)( 25, 31)( 26, 64)( 27, 49)( 29, 35)( 30, 68)( 33, 52)( 34, 72)( 37, 43)
        ( 38, 83)( 39, 53)( 41, 47)( 42, 87)( 45, 56)( 46, 90)( 50, 60)( 51, 57)( 54, 80)( 55, 76)( 58, 98)( 59, 94)
        ( 61, 67)( 62,111)( 63, 99)( 65, 71)( 66,114)( 69, 75)( 70,115)( 73, 79)( 74,118)( 77,102)( 78,109)( 81, 86)
        ( 82,103)( 84, 89)( 85,123)( 88, 93)( 91, 97)( 92,124)( 95,106)( 96,105)(100,110)(101,107)(104,122)(108,119)
        (112,117)(113,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 74)( 28, 53)( 30, 36)( 31, 77)( 34, 57)
        ( 35, 78)( 39, 44)( 40, 66)( 42, 69)( 43, 86)( 46, 52)( 47, 97)( 48, 70)( 50, 56)( 51,100)( 54, 73)( 55,103)
        ( 58, 64)( 59,114)( 60, 81)( 62, 68)( 63,118)( 67, 85)( 71, 93)( 72, 89)( 75, 80)( 76,107)( 79, 84)( 82,111)
        ( 83,108)( 87, 92)( 88,119)( 90,121)( 91,116)( 94, 99)( 95,105)( 96,122)( 98,102)(101,106)(104,110)(109,123)
        (112,117)(113,124)(115,120),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99)(100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)(118,119,120)
        (121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 49)( 12, 22)( 14, 20)
        ( 15, 61)( 16, 33)( 18, 37)( 19, 65)( 23, 45)( 24, 41)( 26, 32)( 27, 77)( 28, 53)( 30, 36)( 31, 78)( 34, 57)
        ( 35, 79)( 39, 44)( 40, 66)( 42, 69)( 43, 82)( 46, 52)( 47, 93)( 48, 70)( 50, 56)( 51, 96)( 54, 73)( 55, 99)
        ( 58, 64)( 59,107)( 60, 75)( 62, 68)( 63,111)( 67, 81)( 71, 89)( 72, 85)( 74, 80)( 76,103)( 83, 88)( 84,112)
        ( 86,115)( 87,120)( 90, 95)( 91,101)( 92,116)( 94, 98)( 97,102)(100,106)(104,110)(105,117)(108,114)(109,123)
        (113,119)(118,122)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95)
        ( 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 29)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 27, 32)( 28, 48)( 30, 52)( 31, 69)( 35, 40)( 36, 61)
        ( 38, 64)( 39, 76)( 42, 47)( 43, 65)( 45, 51)( 46, 84)( 49, 68)( 50, 87)( 53, 59)( 54, 99)( 55, 72)( 57, 63)
        ( 58,103)( 62, 75)( 66, 83)( 67, 79)( 70, 74)( 71, 91)( 73, 95)( 77, 82)( 78,104)( 80,107)( 81,112)( 85, 90)
        ( 86,108)( 88, 94)( 89,120)( 92, 98)( 93,122)( 96,102)( 97,117)(100,106)(101,114)(105,111)(109,119)(110,115)
        (113,118)(116,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 16)(  6, 28)(  7, 13)(  9, 20)( 10, 40)( 11, 17)( 14, 24)( 15, 21)
        ( 18, 36)( 19, 32)( 22, 48)( 23, 44)( 25, 31)( 26, 64)( 27, 49)( 29, 35)( 30, 68)( 33, 52)( 34, 72)( 37, 43)
        ( 38, 84)( 39, 53)( 41, 47)( 42, 87)( 45, 56)( 46, 90)( 50, 60)( 51, 57)( 54, 80)( 55, 76)( 58, 98)( 59, 94)
        ( 61, 67)( 62,114)( 63, 99)( 65, 71)( 66,115)( 69, 75)( 70,116)( 73, 79)( 74,112)( 77,102)( 78,118)( 81, 86)
        ( 82, 92)( 83,103)( 85, 89)( 88, 93)( 91, 97)( 95,106)( 96,104)(100,110)(101,107)(105,122)(108,120)(109,123)
        (111,117)(113,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 38)(  8, 17)( 10, 25)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 33)( 18, 37)( 19, 63)( 23, 44)( 24, 40)( 26, 32)( 27, 75)( 28, 51)( 30, 36)( 31, 76)( 34, 55)
        ( 35, 79)( 39, 43)( 41, 67)( 42, 64)( 45, 50)( 46, 95)( 47, 68)( 49, 54)( 52, 71)( 53, 96)( 56, 62)( 57,107)
        ( 58, 83)( 60, 66)( 61,108)( 65, 90)( 69, 91)( 70, 87)( 72, 78)( 73,115)( 74, 99)( 77, 82)( 80, 86)( 81,116)
        ( 84,103)( 85,118)( 88,111)( 89,109)( 92, 98)( 93,122)( 94,112)( 97,102)(100,114)(101,123)(104,110)(105,113)
        (106,121)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 30)( 18, 33)( 19, 60)( 23, 40)( 24, 36)( 26, 32)( 27, 71)( 28, 48)( 31, 52)( 35, 39)( 37, 64)
        ( 38, 61)( 41, 47)( 42, 79)( 43, 65)( 45, 51)( 46, 83)( 49, 67)( 50, 87)( 53, 59)( 54, 98)( 55, 72)( 57, 63)
        ( 58,102)( 62, 78)( 66, 75)( 68, 74)( 69,107)( 70, 90)( 73, 94)( 76, 82)( 77,103)( 80, 86)( 81,110)( 84, 89)
        ( 85,114)( 88, 93)( 91,106)( 92,115)( 95,101)( 96,121)( 97,108)( 99,105)(100,122)(104,113)(109,118)(111,117)
        (112,123)(116,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 26)(  4,  9)(  6, 21)(  7, 34)(  8, 17)( 10, 25)( 11, 45)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 29)( 18, 33)( 19, 60)( 23, 41)( 24, 37)( 27, 32)( 28, 48)( 30, 52)( 31, 72)( 35, 40)( 36, 63)
        ( 38, 67)( 39, 80)( 42, 47)( 43, 91)( 44, 68)( 46, 51)( 49, 71)( 50, 92)( 53, 59)( 54,103)( 55, 75)( 57, 62)
        ( 58,107)( 61, 66)( 64, 79)( 65,108)( 69, 87)( 70, 83)( 73, 78)( 74, 95)( 76, 99)( 77, 96)( 81, 86)( 82,111)
        ( 84,115)( 85,112)( 88, 94)( 89,120)( 90,116)( 93, 98)( 97,121)(100,106)(101,117)(102,119)(104,110)(105,123)
        (109,114)(113,124)(118,122),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 37)(  8, 17)( 10, 24)( 11, 43)( 12, 22)( 14, 20)
        ( 15, 55)( 16, 32)( 18, 36)( 19, 56)( 23, 39)( 25, 31)( 26, 63)( 27, 47)( 29, 35)( 30, 67)( 33, 51)( 34, 71)
        ( 38, 42)( 40, 46)( 41, 57)( 44, 50)( 45, 53)( 48, 59)( 49, 76)( 52, 58)( 54, 75)( 60, 66)( 61, 87)( 62, 79)
        ( 64, 70)( 65, 91)( 68, 74)( 69, 95)( 72, 78)( 73, 99)( 77, 82)( 80, 83)( 81,100)( 84, 90)( 85,108)( 86,103)
        ( 88, 94)( 89,111)( 92, 98)( 93,115)( 96,102)( 97,118)(101,106)(104,107)(105,119)(109,114)(110,122)(112,117)
        (113,123)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 40)(  8, 17)( 10, 24)( 11, 48)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 32)( 18, 36)( 19, 60)( 23, 44)( 25, 31)( 26, 71)( 27, 52)( 29, 35)( 30, 75)( 33, 56)( 34, 78)
        ( 37, 43)( 38, 90)( 39, 63)( 41, 47)( 42, 94)( 45, 51)( 46, 98)( 49, 55)( 50, 99)( 53, 67)( 54,102)( 58, 62)
        ( 59, 82)( 61, 66)( 64, 86)( 65, 83)( 68, 74)( 69,114)( 70,106)( 72, 77)( 73,115)( 76, 81)( 79, 85)( 80,116)
        ( 84,113)( 87, 93)( 88,118)( 89,110)( 91, 97)( 92,119)( 95,101)( 96,122)(100,105)(103,109)(104,123)(107,111)
        (108,121)(112,117)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 28)(  4,  9)(  6, 21)(  7, 36)(  8, 17)( 10, 24)( 11, 44)( 12, 22)( 14, 20)
        ( 15, 55)( 16, 29)( 18, 32)( 19, 59)( 23, 40)( 25, 31)( 26, 54)( 27, 47)( 30, 51)( 33, 39)( 34, 75)( 35, 63)
        ( 37, 43)( 38, 79)( 41, 46)( 42, 83)( 45, 50)( 48, 67)( 49, 84)( 52, 58)( 53, 68)( 56, 62)( 57, 91)( 60, 66)
        ( 61, 95)( 64, 71)( 65, 99)( 69, 94)( 70, 87)( 72, 78)( 73,114)( 74,102)( 76, 82)( 77,115)( 80, 86)( 81,118)
        ( 85, 90)( 88,106)( 89,119)( 92, 98)( 93,107)( 96,101)( 97,122)(100,105)(103,110)(104,123)(108,124)(109,113)
        (111,117)(112,120)(116,121),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 44)( 15, 21)
        ( 17, 24)( 18, 48)( 22, 40)( 23, 36)( 25, 31)( 26, 64)( 27, 52)( 29, 35)( 30, 68)( 33, 39)( 34, 72)( 37, 56)
        ( 38, 76)( 41, 47)( 42, 88)( 43, 57)( 45, 51)( 46, 92)( 49, 55)( 50, 95)( 53, 60)( 54, 99)( 58, 84)( 59, 80)
        ( 61, 67)( 62,114)( 63,103)( 65, 71)( 66,118)( 69, 75)( 70,122)( 73, 79)( 74,123)( 77, 83)( 78,120)( 81,107)
        ( 82,116)( 85, 91)( 86,101)( 87,108)( 89, 94)( 90, 97)( 93, 98)( 96,102)(100,106)(104,111)(105,109)(110,113)
        (112,117)(115,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74, 75)( 76, 77, 78, 79)( 80, 81, 82, 83)( 84, 85, 86, 87)( 88, 89, 90, 91)( 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 12)(  7, 36)(  8, 16)( 10, 20)( 11, 40)( 14, 19)( 15, 28)
        ( 17, 32)( 18, 49)( 21, 27)( 22, 57)( 23, 44)( 25, 31)( 26, 60)( 29, 48)( 30, 64)( 33, 39)( 34, 75)( 35, 52)
        ( 37, 43)( 38, 79)( 41, 47)( 42, 83)( 45, 56)( 46, 87)( 50, 55)( 51, 68)( 53, 72)( 54, 69)( 58, 63)( 59, 90)
        ( 61, 67)( 62, 99)( 65, 71)( 66,102)( 70, 97)( 73, 78)( 74, 94)( 76, 82)( 77,107)( 80, 86)( 81,110)( 84, 89)
        ( 85,114)( 88, 93)( 91, 98)( 92,115)( 95,106)( 96,103)(100,105)(101,118)(104,124)(108,113)(109,122)(111,117)
        (112,120)(116,121)(119,123),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66, 67)( 68, 69, 70, 71)
        ( 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 44)( 15, 21)
        ( 17, 24)( 18, 48)( 22, 40)( 23, 36)( 25, 31)( 26, 64)( 27, 52)( 29, 35)( 30, 67)( 33, 39)( 34, 71)( 37, 56)
        ( 38, 75)( 41, 47)( 42, 83)( 43, 57)( 45, 51)( 46, 86)( 49, 55)( 50, 90)( 53, 60)( 54, 91)( 58, 82)( 59, 78)
        ( 61, 66)( 62,106)( 63, 94)( 65, 70)( 68, 74)( 69,107)( 72, 77)( 73,110)( 76, 81)( 79, 98)( 80,111)( 84, 89)
        ( 85, 99)( 87, 93)( 88,119)( 92, 97)( 95,102)( 96,120)(100,118)(101,114)(103,109)(104,116)(105,122)(108,113)
        (112,117)(115,123)(121,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 44)( 15, 21)
        ( 17, 24)( 18, 48)( 22, 40)( 23, 36)( 25, 31)( 26, 63)( 27, 52)( 29, 35)( 30, 67)( 33, 39)( 34, 71)( 37, 56)
        ( 38, 75)( 41, 47)( 42, 79)( 43, 57)( 45, 51)( 46, 83)( 49, 55)( 50, 87)( 53, 59)( 54, 91)( 58, 76)( 60, 66)
        ( 61,103)( 62, 95)( 64, 70)( 65,106)( 68, 74)( 69,109)( 72, 78)( 73,113)( 77, 82)( 80, 86)( 81,114)( 84, 90)
        ( 85,117)( 88, 94)( 89,121)( 92, 98)( 93,122)( 96, 99)( 97,123)(100,105)(101,111)(102,119)(104,108)(107,112)
        (110,116)(115,120)(118,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 44)( 15, 21)
        ( 17, 24)( 18, 48)( 22, 40)( 23, 36)( 25, 31)( 26, 64)( 27, 52)( 29, 35)( 30, 67)( 33, 39)( 34, 71)( 37, 56)
        ( 38, 75)( 41, 47)( 42, 86)( 43, 57)( 45, 51)( 46, 90)( 49, 55)( 50, 94)( 53, 60)( 54, 95)( 58, 82)( 59, 79)
        ( 61, 66)( 62,106)( 63, 98)( 65, 70)( 68, 74)( 69,107)( 72, 78)( 73,110)( 76, 81)( 77,114)( 80, 85)( 83, 89)
        ( 84,115)( 87, 93)( 88,118)( 91, 97)( 92,122)( 96,101)( 99,102)(100,123)(103,109)(104,112)(105,120)(108,113)
        (111,117)(116,121)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46, 47)
        ( 48, 49, 50, 51)( 52, 53, 54, 55)( 56, 57, 58, 59)( 60, 61, 62, 63)( 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 43)( 15, 21)
        ( 17, 24)( 18, 47)( 22, 40)( 23, 36)( 25, 31)( 26, 63)( 27, 51)( 29, 35)( 30, 67)( 33, 39)( 34, 71)( 37, 55)
        ( 38, 72)( 41, 46)( 42, 56)( 44, 50)( 45, 80)( 48, 54)( 49, 83)( 52, 59)( 53, 87)( 57, 79)( 58, 75)( 60, 66)
        ( 61,102)( 62, 91)( 64, 70)( 65,106)( 68, 74)( 69,109)( 73, 78)( 76, 95)( 77,110)( 81, 86)( 82, 96)( 84, 90)
        ( 85,118)( 88, 94)( 89,119)( 92, 99)( 93,121)( 97,117)( 98,113)(100,105)(101,122)(103,108)(104,115)(107,112)
        (111,116)(114,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101)(102,103,104,105)(106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 21)(  4,  9)(  6, 12)(  7, 33)(  8, 14)( 10, 17)( 11, 37)( 15, 29)( 16, 25)
        ( 18, 24)( 19, 53)( 20, 41)( 22, 28)( 23, 54)( 26, 45)( 27, 57)( 30, 36)( 31, 69)( 32, 46)( 34, 40)( 35, 73)
        ( 38, 44)( 39, 74)( 42, 49)( 43, 77)( 47, 65)( 48, 61)( 50, 56)( 51, 93)( 52, 81)( 55, 60)( 58, 64)( 59, 94)
        ( 62, 85)( 63, 97)( 66, 72)( 67,108)( 68, 86)( 70, 76)( 71,111)( 75, 80)( 78, 84)( 79,112)( 82, 89)( 83,115)
        ( 87,104)( 88,100)( 90, 96)( 91,102)( 92,119)( 95, 99)( 98,103)(101,122)(105,110)(106,117)(107,123)(109,114)
        (113,118)(116,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99)(100,101,102,103)(104,105,106,107)(108,109,110)(111,112,113,114)(115,116,117,118)(119,120,121)
        (122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 43)( 15, 21)
        ( 17, 24)( 18, 47)( 22, 39)( 23, 36)( 25, 31)( 26, 59)( 27, 51)( 29, 35)( 30, 63)( 33, 38)( 34, 67)( 37, 42)
        ( 40, 46)( 41, 68)( 44, 50)( 45, 71)( 48, 54)( 49, 75)( 52, 55)( 53, 79)( 56, 62)( 57, 91)( 58, 83)( 60, 66)
        ( 61, 95)( 64, 70)( 65, 99)( 69, 74)( 72, 78)( 73,100)( 76, 82)( 77,103)( 80, 86)( 81,107)( 84, 87)( 85,111)
        ( 88, 94)( 89,122)( 90,114)( 92, 98)( 93,123)( 96,102)( 97,120)(101,106)(104,110)(105,121)(108,113)(109,116)
        (112,117)(115,118)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 40)( 15, 21)
        ( 17, 24)( 18, 43)( 22, 39)( 23, 35)( 25, 31)( 26, 59)( 27, 47)( 29, 34)( 30, 63)( 33, 38)( 36, 51)( 37, 64)
        ( 41, 46)( 42, 52)( 44, 50)( 45, 72)( 48, 55)( 49, 75)( 53, 71)( 54, 67)( 56, 62)( 57, 91)( 58, 79)( 60, 66)
        ( 61, 95)( 65, 70)( 68, 83)( 69, 96)( 73, 78)( 74, 84)( 76, 82)( 77,104)( 80, 87)( 81,107)( 85,103)( 86, 99)
        ( 88, 94)( 89,119)( 90,111)( 92, 98)( 93,122)( 97,102)(100,114)(101,123)(105,110)(106,115)(108,113)(109,116)
        (112,118)(117,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 40)( 15, 21)
        ( 17, 24)( 18, 43)( 22, 39)( 23, 35)( 25, 31)( 26, 59)( 27, 47)( 29, 34)( 30, 63)( 33, 38)( 36, 51)( 37, 64)
        ( 41, 46)( 42, 52)( 44, 50)( 45, 72)( 48, 55)( 49, 75)( 53, 71)( 54, 67)( 56, 62)( 57, 91)( 58, 79)( 60, 66)
        ( 61, 95)( 65, 70)( 68, 83)( 69, 96)( 73, 78)( 74, 84)( 76, 82)( 77,104)( 80, 87)( 81,107)( 85,103)( 86, 99)
        ( 88, 94)( 89,121)( 90,110)( 92, 98)( 93,122)( 97,102)(100,114)(101,123)(105,109)(106,115)(108,113)(111,118)
        (112,116)(117,120)(119,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120)(121,122,123,124) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 24)(  4,  9)(  6, 12)(  7, 36)(  8, 17)( 10, 20)( 11, 40)( 14, 19)( 15, 51)
        ( 16, 28)( 18, 32)( 21, 27)( 22, 59)( 23, 44)( 25, 31)( 26, 63)( 29, 47)( 30, 67)( 33, 39)( 34, 78)( 35, 52)
        ( 37, 43)( 38, 82)( 41, 46)( 42, 86)( 45, 55)( 48, 54)( 49, 77)( 50, 71)( 53, 74)( 56, 62)( 57, 95)( 58, 87)
        ( 60, 66)( 61, 98)( 64, 70)( 65,102)( 68, 73)( 69,106)( 72, 90)( 75, 81)( 76, 91)( 79, 85)( 80,110)( 83, 89)
        ( 84,114)( 88, 94)( 92,113)( 93,107)( 96,101)( 97,115)( 99,105)(100,123)(103,109)(104,121)(108,118)(111,117)
        (112,119)(116,122)(120,124),
      nbP := 124,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38, 39)( 40, 41, 42, 43)( 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73)( 74, 75, 76, 77)( 78, 79, 80, 81)( 82, 83, 84, 85)( 86, 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 28)(  7, 16)(  9, 20)( 10, 32)( 13, 19)( 14, 43)( 15, 21)
        ( 17, 24)( 18, 47)( 22, 39)( 23, 36)( 25, 31)( 26, 59)( 27, 51)( 29, 35)( 30, 63)( 33, 38)( 34, 67)( 37, 42)
        ( 40, 46)( 41, 68)( 44, 50)( 45, 71)( 48, 54)( 49, 75)( 52, 55)( 53, 79)( 56, 62)( 57, 90)( 58, 83)( 60, 66)
        ( 61, 94)( 64, 70)( 65, 98)( 69, 74)( 72, 78)( 73, 99)( 76, 82)( 77,102)( 80, 86)( 81,106)( 84, 87)( 85,110)
        ( 88, 93)( 89,111)( 91, 97)( 92,115)( 95,101)( 96,118)(100,105)(103,109)(104,119)(107,113)(108,122)(112,114)
        (116,121)(117,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14, 15)( 16, 17, 18, 19)( 20, 21, 22, 23)
        ( 24, 25, 26, 27)( 28, 29, 30, 31)( 32, 33, 34, 35)( 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89)( 90, 91, 92, 93)
        ( 94, 95, 96, 97)( 98, 99,100,101)(102,103,104,105)(106,107,108,109)(110,111,112,113)(114,115,116,117)
        (118,119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 12)(  3,  8)(  5, 11)(  6, 27)(  7, 15)(  9, 19)( 10, 28)( 13, 18)( 14, 20)( 16, 23)
        ( 17, 36)( 21, 35)( 22, 31)( 24, 30)( 25, 51)( 26, 39)( 29, 34)( 32, 43)( 33, 52)( 37, 42)( 38, 44)( 40, 47)
        ( 41, 60)( 45, 59)( 46, 55)( 48, 54)( 49, 75)( 50, 63)( 53, 58)( 56, 67)( 57, 76)( 61, 66)( 62, 68)( 64, 71)
        ( 65, 84)( 69, 83)( 70, 79)( 72, 78)( 73, 99)( 74, 87)( 77, 82)( 80, 91)( 81,100)( 85, 90)( 86, 92)( 88, 95)
        ( 89,108)( 93,107)( 94,103)( 96,102)( 97,122)( 98,111)(101,106)(104,115)(105,123)(109,114)(110,116)(112,119)
        (113,117)(118,121)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10, 11)( 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121)(122,123,124) ), rec(
      invers := (  1,  4)(  2, 11)(  3,  8)(  5, 10)(  6, 23)(  7, 15)(  9, 14)( 12, 18)( 13, 24)( 16, 19)( 17, 27)
        ( 20, 26)( 21, 39)( 22, 31)( 25, 30)( 28, 34)( 29, 40)( 32, 35)( 33, 43)( 36, 42)( 37, 55)( 38, 47)( 41, 46)
        ( 44, 50)( 45, 56)( 48, 51)( 49, 59)( 52, 58)( 53, 71)( 54, 63)( 57, 62)( 60, 66)( 61, 72)( 64, 67)( 65, 75)
        ( 68, 74)( 69, 87)( 70, 79)( 73, 78)( 76, 82)( 77, 88)( 80, 83)( 81, 91)( 84, 90)( 85,103)( 86, 95)( 89, 94)
        ( 92, 98)( 93,104)( 96, 99)( 97,107)(100,106)(101,118)(102,111)(105,110)(108,114)(109,119)(112,115)(113,122)
        (116,121)(117,123)(120,124),
      nbP := 124,
      next := (  1,  2,  3)(  4,  5,  6,  7)(  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117)
        (118,119,120,121)(122,123,124) ) ];
