return [ 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, 37)( 19, 67)( 23, 47)( 24, 43)( 26, 32)( 27, 79)( 28, 55)( 30, 36)( 31, 83)( 34, 59)
        ( 35, 87)( 38, 42)( 40, 46)( 41, 68)( 44, 71)( 45, 96)( 48, 54)( 49, 92)( 50, 72)( 52, 58)( 53,103)( 56, 75)
        ( 57,107)( 60, 66)( 61, 73)( 62, 91)( 64, 70)( 65,100)( 69, 95)( 74, 99)( 76, 82)( 77, 81)( 78,111)( 80, 86)
        ( 84, 90)( 85,112)( 88, 94)( 89,115)( 93,106)( 97,102)( 98,101)(104,110)(105,116)(108,114)(109,120)(113,118)
        (117,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 25)( 11, 23)( 12, 22)( 14, 20)
        ( 15, 53)( 16, 33)( 18, 37)( 19, 57)( 24, 45)( 26, 32)( 27, 47)( 28, 46)( 30, 36)( 31, 43)( 34, 49)( 35, 39)
        ( 38, 44)( 40, 61)( 42, 48)( 50, 56)( 51, 69)( 52, 62)( 54, 60)( 55, 73)( 58, 64)( 59, 77)( 63, 65)( 66, 72)
        ( 67, 85)( 68, 78)( 70, 76)( 71, 89)( 74, 80)( 75, 93)( 79, 81)( 82, 88)( 83,101)( 84, 94)( 86, 92)( 87,105)
        ( 90, 96)( 91,109)( 95, 97)( 98,104)( 99,118)(100,110)(102,108)(103,115)(106,112)(107,120)(111,113)(114,117)
        (116,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118)(119,120) ), 
  rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 42)(  8, 17)( 10, 25)( 11, 34)( 12, 22)( 14, 20)
        ( 15, 23)( 16, 33)( 18, 38)( 19, 37)( 24, 40)( 26, 32)( 27, 51)( 28, 43)( 30, 36)( 31, 55)( 35, 46)( 39, 41)
        ( 44, 47)( 45, 56)( 48, 54)( 49, 67)( 50, 59)( 52, 58)( 53, 71)( 57, 62)( 60, 63)( 61, 72)( 64, 70)( 65, 83)
        ( 66, 75)( 68, 74)( 69, 87)( 73, 78)( 76, 79)( 77, 88)( 80, 86)( 81, 99)( 82, 91)( 84, 90)( 85,103)( 89, 94)
        ( 92, 95)( 93,104)( 96,102)( 97,113)( 98,107)(100,106)(101,117)(105,110)(108,111)(109,118)(112,116)(114,120)
        (115,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112)(113,114,115,116)
        (117,118,119,120) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 51)( 12, 22)( 14, 20)
        ( 15, 59)( 16, 31)( 18, 36)( 19, 35)( 23, 47)( 24, 43)( 26, 30)( 28, 34)( 29, 52)( 32, 55)( 33, 68)( 37, 42)
        ( 38, 60)( 40, 46)( 41, 76)( 44, 63)( 45, 79)( 48, 54)( 49, 91)( 50, 64)( 53, 67)( 56, 62)( 57, 99)( 58, 71)
        ( 61, 75)( 65, 87)( 66, 83)( 69, 74)( 70, 92)( 72, 95)( 73,108)( 77, 82)( 78,100)( 80, 86)( 81,116)( 84,103)
        ( 85,120)( 88, 94)( 89,112)( 90,104)( 93,107)( 96,102)( 97,105)( 98,111)(101,115)(106,118)(109,114)(110,113)
        (117,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), 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, 19)( 16, 33)( 18, 37)( 23, 49)( 24, 45)( 26, 32)( 27, 69)( 28, 57)( 30, 36)( 31, 73)( 34, 40)( 35, 77)
        ( 38, 44)( 39, 81)( 42, 48)( 43, 85)( 46, 61)( 47, 89)( 50, 56)( 51, 99)( 52, 62)( 54, 60)( 55,103)( 58, 66)
        ( 59, 65)( 63, 97)( 64, 93)( 67, 72)( 68,104)( 70, 76)( 71,108)( 74, 80)( 75,111)( 78, 84)( 79,115)( 82, 88)
        ( 83,120)( 86, 92)( 87,117)( 90, 96)( 91,113)( 94,101)( 95,110)( 98,102)(100,106)(105,107)(109,114)(112,118)
        (116,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)(119,120) ), 
  rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 25)( 11, 47)( 12, 22)( 14, 20)
        ( 15, 56)( 16, 34)( 18, 35)( 19, 59)( 23, 44)( 24, 43)( 26, 32)( 27, 71)( 28, 51)( 30, 33)( 31, 55)( 36, 42)
        ( 37, 79)( 38, 63)( 40, 46)( 41, 83)( 45, 50)( 48, 54)( 49, 84)( 52, 67)( 53, 87)( 57, 62)( 58, 72)( 60, 66)
        ( 61, 96)( 64, 75)( 65, 99)( 68, 74)( 69,107)( 70, 91)( 73, 95)( 76, 82)( 77,111)( 78,103)( 80, 86)( 81,115)
        ( 85, 90)( 88, 94)( 89,116)( 92,104)( 93,114)( 97,102)( 98,108)(100,106)(101,120)(105,110)(109,119)(112,118)
        (113,117),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 19)(  7, 35)(  8, 15)( 10, 23)( 11, 47)( 12, 20)( 14, 18)
        ( 16, 31)( 17, 28)( 21, 43)( 22, 39)( 24, 30)( 25, 67)( 26, 51)( 29, 55)( 32, 38)( 33, 75)( 34, 56)( 36, 42)
        ( 37, 79)( 40, 60)( 41, 59)( 44, 50)( 45, 83)( 46, 61)( 48, 54)( 49, 87)( 52, 63)( 53, 91)( 57, 71)( 58, 68)
        ( 62, 80)( 64, 70)( 65,107)( 66, 95)( 69, 99)( 72, 78)( 73,113)( 74,100)( 76, 82)( 77,117)( 81, 86)( 84, 90)
        ( 85,118)( 88, 94)( 89,106)( 92, 98)( 93, 97)( 96,103)(101,111)(102,108)(104,110)(105,119)(109,115)(112,116)
        (114,120),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112)(113,114,115,116)
        (117,118,119,120) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 26)( 11, 25)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 49)( 24, 45)( 27, 32)( 28, 50)( 30, 36)( 31, 74)( 34, 53)( 35, 77)
        ( 38, 44)( 39, 89)( 40, 65)( 42, 48)( 43, 93)( 46, 69)( 47, 97)( 51, 73)( 52, 70)( 54, 60)( 55,109)( 56, 81)
        ( 58, 64)( 59,113)( 62, 68)( 63,118)( 66, 85)( 67,115)( 71,102)( 72,101)( 75, 80)( 76,103)( 78, 84)( 79, 99)
        ( 82,105)( 83, 95)( 86, 92)( 87,120)( 88,111)( 90, 96)( 91,108)( 94,100)( 98,104)(106,112)(107,119)(110,116)
        (114,117),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118)(119,120) ), 
  rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 26)( 11, 25)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 49)( 24, 45)( 27, 32)( 28, 50)( 30, 36)( 31, 74)( 34, 53)( 35, 77)
        ( 38, 44)( 39, 66)( 40, 65)( 42, 48)( 43, 86)( 46, 69)( 47, 89)( 51, 73)( 52, 70)( 54, 60)( 55,106)( 56, 81)
        ( 58, 64)( 59,103)( 62, 68)( 63,107)( 67, 85)( 71, 97)( 72, 93)( 75, 80)( 76, 98)( 78, 84)( 79,114)( 82,101)
        ( 83,117)( 87, 92)( 88,108)( 90, 96)( 91,119)( 94,111)( 95,116)( 99,113)(100,112)(102,105)(104,110)(109,118)
        (115,120),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106)(107,108,109,110)(111,112)(113,114,115,116)(117,118,119,120) ), 
  rec(
      invers := (  1,  5)(  2, 13)(  3, 29)(  4,  9)(  6, 21)(  7, 41)(  8, 17)( 10, 26)( 11, 25)( 12, 22)( 14, 20)
        ( 15, 57)( 16, 33)( 18, 37)( 19, 61)( 23, 49)( 24, 45)( 27, 32)( 28, 50)( 30, 36)( 31, 72)( 34, 53)( 35, 75)
        ( 38, 44)( 39, 81)( 40, 65)( 42, 48)( 43, 77)( 46, 69)( 47, 74)( 51, 71)( 52, 70)( 54, 60)( 55, 87)( 56, 79)
        ( 58, 64)( 59, 91)( 62, 68)( 63, 95)( 66, 83)( 67, 99)( 73, 78)( 76, 82)( 80, 84)( 85, 90)( 86,103)( 88, 94)
        ( 89,108)( 92, 98)( 93,111)( 96,102)( 97,115)(100,106)(101,120)(104,107)(105,117)(109,114)(110,113)(112,118)
        (116,119),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  5)(  2, 14)(  3, 13)(  4,  9)(  6, 21)(  7, 31)(  8, 17)( 10, 23)( 11, 32)( 12, 22)( 15, 20)
        ( 16, 24)( 18, 27)( 19, 40)( 25, 39)( 26, 35)( 28, 34)( 29, 55)( 30, 43)( 33, 38)( 36, 47)( 37, 56)( 41, 46)
        ( 42, 48)( 44, 51)( 45, 64)( 49, 63)( 50, 59)( 52, 58)( 53, 79)( 54, 67)( 57, 62)( 60, 71)( 61, 80)( 65, 70)
        ( 66, 72)( 68, 75)( 69, 88)( 73, 87)( 74, 83)( 76, 82)( 77,103)( 78, 91)( 81, 86)( 84, 95)( 85,104)( 89, 94)
        ( 90, 96)( 92, 99)( 93,112)( 97,111)( 98,107)(100,106)(101,120)(102,115)(105,110)(108,116)(109,119)(113,118)
        (114,117),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  5)(  2, 15)(  3,120)(  4, 10)(  6, 14)(  7, 27)(  8, 19)(  9, 11)( 12,119)( 13, 18)( 16, 22)
        ( 17, 28)( 20, 23)( 21, 31)( 24, 30)( 25, 43)( 26, 35)( 29, 34)( 32, 38)( 33, 44)( 36, 39)( 37, 47)( 40, 46)
        ( 41, 59)( 42, 51)( 45, 50)( 48, 54)( 49, 60)( 52, 55)( 53, 63)( 56, 62)( 57, 75)( 58, 67)( 61, 66)( 64, 70)
        ( 65, 76)( 68, 71)( 69, 79)( 72, 78)( 73, 91)( 74, 83)( 77, 82)( 80, 86)( 81, 92)( 84, 87)( 85, 95)( 88, 94)
        ( 89,107)( 90, 99)( 93, 98)( 96,102)( 97,108)(100,103)(101,111)(104,110)(105,118)(106,117)(109,114)(112,116)
        (113,115),
      nbP := 120,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  3)(  2, 12)(  4, 10)(  5, 31)(  6, 16)(  7, 11)(  8, 19)(  9, 35)( 13, 15)( 14, 23)( 17, 28)
        ( 18, 27)( 20, 26)( 21, 47)( 22, 39)( 24, 30)( 25, 51)( 29, 34)( 32, 38)( 33, 52)( 36, 42)( 37, 55)( 40, 43)
        ( 41, 59)( 44, 50)( 45, 71)( 46, 63)( 48, 54)( 49, 75)( 53, 58)( 56, 62)( 57, 76)( 60, 66)( 61, 79)( 64, 67)
        ( 65, 83)( 68, 74)( 69, 95)( 70, 87)( 72, 78)( 73, 99)( 77, 82)( 80, 86)( 81,100)( 84, 90)( 85,103)( 88, 91)
        ( 89,107)( 92, 98)( 93,112)( 94,111)( 96,102)( 97,116)(101,106)(104,110)(105,117)(108,114)(109,120)(113,115)
        (118,119),
      nbP := 120,
      next := (  1,  2)(  3,  4,  5,  6)(  7,  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ), rec(
      invers := (  1,  3)(  2,  4)(  5, 10)(  6,  7)(  8, 11)(  9, 12)( 13, 18)( 14, 15)( 16, 19)( 17, 20)( 21, 26)
        ( 22, 23)( 24, 27)( 25, 28)( 29, 34)( 30, 31)( 32, 35)( 33, 36)( 37, 42)( 38, 39)( 40, 43)( 41, 44)( 45, 50)
        ( 46, 47)( 48, 51)( 49, 52)( 53, 58)( 54, 55)( 56, 59)( 57, 60)( 61, 66)( 62, 63)( 64, 67)( 65, 68)( 69, 74)
        ( 70, 71)( 72, 75)( 73, 76)( 77, 82)( 78, 79)( 80, 83)( 81, 84)( 85, 90)( 86, 87)( 88, 91)( 89, 92)( 93, 98)
        ( 94, 95)( 96, 99)( 97,100)(101,106)(102,103)(104,107)(105,108)(109,114)(110,111)(112,115)(113,116)(117,120)
        (118,119),
      nbP := 120,
      next := (  1,  2)(  3,  4,  5,  6)(  7,  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120) ) ];
