return [ 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, 89)( 38, 44)( 39, 97)( 40, 73)( 42, 48)( 43,101)( 46, 77)( 47,105)( 50, 56)( 51,113)( 52, 78)( 54, 60)
        ( 55,117)( 58, 74)( 59,100)( 62, 68)( 63,126)( 64, 93)( 66, 72)( 67,123)( 70, 76)( 71,127)( 75, 84)( 79,110)
        ( 80,109)( 82, 88)( 83,128)( 86, 92)( 87,131)( 90, 96)( 91,136)( 94,121)( 95,133)( 98,104)( 99,118)(102,108)
        (103,137)(106,112)(107,141)(111,116)(114,120)(115,142)(119,140)(122,125)(124,130)(129,134)(132,135)(138,144)
        (139,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124)(125,126)(127,128,129,130)(131,132,133,134)(135,136)(137,138,139,140)(141,142,143,144) ), 
  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, 89)( 38, 44)( 39, 95)( 40, 73)( 42, 48)( 43, 99)( 46, 77)( 47,103)( 50, 56)( 51,111)( 52, 78)( 54, 60)
        ( 55,115)( 58, 74)( 59, 98)( 62, 68)( 63,120)( 64, 94)( 66, 72)( 67,123)( 70, 76)( 71,127)( 75, 84)( 79,108)
        ( 80,107)( 82, 88)( 83,128)( 86, 92)( 87,131)( 90, 93)( 91,119)( 96,102)( 97,116)(100,106)(101,135)(104,110)
        (105,139)(109,114)(112,118)(113,140)(117,138)(121,126)(122,132)(124,130)(125,144)(129,134)(133,143)(136,142)
        (137,141),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), 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, 66)( 16, 33)( 18, 37)( 19, 63)( 23, 49)( 24, 45)( 26, 32)( 27, 79)( 28, 57)( 30, 36)( 31, 83)( 34, 61)
        ( 35, 87)( 38, 44)( 39, 95)( 40, 67)( 42, 48)( 43, 99)( 46, 71)( 47,103)( 50, 56)( 51,116)( 52, 72)( 54, 60)
        ( 55,113)( 58, 75)( 59,117)( 62, 65)( 64, 70)( 68, 91)( 69, 88)( 73,111)( 74,107)( 76, 82)( 77,133)( 78,121)
        ( 80, 86)( 81,137)( 84, 90)( 85,141)( 89,128)( 92, 98)( 93,126)( 94,125)( 96,102)( 97,143)(100,106)(101,139)
        (104,110)(105,135)(108,119)(109,132)(112,115)(114,120)(118,124)(122,130)(123,129)(127,142)(131,136)(134,140)
        (138,144),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116)
        (117,118,119,120)(121,122,123,124)(125,126,127,128)(129,130,131,132)(133,134,135,136)(137,138,139,140)
        (141,142,143,144) ), 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, 38)( 19, 37)( 23, 49)( 24, 45)( 26, 32)( 27, 77)( 28, 57)( 30, 36)( 31, 81)( 34, 61)
        ( 35, 85)( 39, 44)( 40, 66)( 42, 48)( 43, 94)( 46, 69)( 47, 98)( 50, 56)( 51, 90)( 52, 70)( 54, 60)( 55, 99)
        ( 58, 73)( 59,103)( 62, 68)( 63, 71)( 64, 89)( 67, 93)( 72, 96)( 74, 80)( 75,113)( 76,107)( 78, 84)( 79,117)
        ( 82, 88)( 83,121)( 86, 92)( 87,125)( 91,102)( 95, 97)(100,106)(101,126)(104,110)(105,129)(108,111)(109,133)
        (112,116)(114,120)(115,134)(118,124)(119,138)(122,128)(123,141)(127,132)(130,136)(131,142)(135,137)(139,144)
        (140,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124)(125,126,127,128)(129,130,131,132)(133,134,135,136)(137,138,139,140)(141,142,143,144) ), 
  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, 38)( 19, 37)( 23, 49)( 24, 45)( 26, 32)( 27, 58)( 28, 57)( 30, 36)( 31, 74)( 34, 61)
        ( 35, 77)( 39, 44)( 40, 66)( 42, 48)( 43, 86)( 46, 69)( 47, 89)( 50, 56)( 51,101)( 52, 70)( 54, 60)( 55,105)
        ( 59, 73)( 62, 68)( 63,113)( 64, 81)( 67, 85)( 71, 97)( 72, 93)( 75, 80)( 76,106)( 78, 84)( 79,122)( 82,109)
        ( 83,125)( 87, 92)( 88,114)( 90, 96)( 91,134)( 94,117)( 95,138)( 98,104)( 99,130)(100,118)(102,108)(103,139)
        (107,121)(110,116)(111,119)(112,129)(115,133)(120,136)(123,128)(124,140)(126,132)(127,144)(131,142)(135,137)
        (141,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124)(125,126,127,128)(129,130,131,132)(133,134,135,136)(137,138)(139,140,141,142)(143,144) ), 
  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)( 97,115)( 98,107)(100,106)(101,119)(105,110)(108,111)(109,120)(112,118)(113,131)
        (114,123)(116,122)(117,135)(121,126)(124,127)(125,136)(128,134)(129,140)(130,139)(132,138)(133,144)(137,142)
        (141,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), 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, 59)( 41, 83)( 44, 50)( 45, 95)( 46, 60)( 48, 54)( 49, 99)( 52, 63)( 53,103)( 57, 71)( 58, 68)
        ( 61, 91)( 62, 87)( 64, 70)( 65,123)( 66,107)( 69,111)( 72, 78)( 73,131)( 74,112)( 76, 82)( 77,136)( 80, 86)
        ( 81,133)( 84, 90)( 85,129)( 88,115)( 89,137)( 92, 98)( 93,105)( 94,116)( 96,102)( 97,101)(100,106)(104,110)
        (108,119)(109,117)(113,127)(114,124)(118,141)(120,126)(121,143)(122,142)(125,139)(128,134)(130,140)(132,135)
        (138,144),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136)(137,138,139,140)
        (141,142,143,144) ), 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, 59)( 41, 83)( 44, 50)( 45, 95)( 46, 60)( 48, 54)( 49, 99)( 52, 63)( 53,103)( 57, 71)( 58, 68)
        ( 61, 91)( 62, 87)( 64, 70)( 65,123)( 66,107)( 69,111)( 72, 78)( 73,131)( 74,112)( 76, 82)( 77,136)( 80, 86)
        ( 81,133)( 84, 90)( 85,129)( 88,115)( 89,137)( 92, 98)( 93, 97)( 94,116)( 96,102)(100,106)(101,117)(104,110)
        (105,142)(108,120)(109,119)(113,127)(114,124)(118,141)(121,126)(122,143)(125,139)(128,134)(130,140)(132,135)
        (138,144),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136)(137,138,139,140)
        (141,142,143,144) ), 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)( 55,113)( 56, 81)
        ( 58, 64)( 59,117)( 62, 68)( 63,122)( 66, 85)( 67,119)( 71,105)( 72,101)( 75, 80)( 76,106)( 78, 84)( 79,126)
        ( 82,109)( 83,129)( 86, 92)( 87,137)( 88,115)( 90, 96)( 91,141)( 94,100)( 95,135)( 98,104)( 99,131)(102,123)
        (103,128)(107,125)(108,124)(110,116)(111,140)(112,133)(114,120)(118,121)(127,132)(130,136)(134,142)(138,144)
        (139,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122)(123,124)(125,126,127,128)(129,130,131,132)(133,134,135,136)(137,138,139,140)(141,142,143,144) ), 
  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)( 63,117)( 66, 85)( 67,121)( 71,102)( 72,101)( 75, 80)( 76,103)( 78, 84)( 79, 99)
        ( 82,105)( 83, 95)( 86, 92)( 87,131)( 88,125)( 90, 96)( 91,108)( 94,100)( 98,104)(106,112)(107,132)(110,116)
        (111,135)(114,120)(115,139)(118,124)(119,144)(122,128)(123,141)(126,129)(127,137)(130,134)(133,138)(136,142)
        (140,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70, 71, 72)
        ( 73, 74, 75, 76)( 77, 78, 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)( 93, 94, 95, 96)
        ( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)
        (121,122,123,124)(125,126,127,128)(129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)(143,144) ), 
  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)(101,119)(104,107)(105,123)(109,114)(110,127)(112,118)
        (113,132)(116,122)(117,135)(120,126)(121,139)(124,130)(125,144)(128,131)(129,141)(133,138)(134,137)(136,142)
        (140,143),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22, 23, 24)
        ( 25, 26, 27, 28)( 29, 30, 31, 32)( 33, 34, 35, 36)( 37, 38, 39, 40)( 41, 42, 43, 44)( 45, 46, 47, 48)
        ( 49, 50, 51, 52)( 53, 54, 55, 56)( 57, 58, 59, 60)( 61, 62, 63, 64)( 65, 66, 67, 68)( 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), rec(
      invers := (  1,  5)(  2, 13)(  3, 27)(  4,  9)(  6, 21)(  7, 39)(  8, 17)( 10, 23)( 11, 40)( 12, 22)( 14, 20)
        ( 15, 51)( 16, 31)( 18, 35)( 19, 55)( 24, 30)( 25, 67)( 26, 43)( 28, 34)( 29, 71)( 32, 47)( 33, 75)( 36, 42)
        ( 37, 85)( 38, 59)( 41, 46)( 44, 63)( 45, 86)( 48, 54)( 49, 94)( 50, 80)( 52, 58)( 53, 97)( 56, 62)( 57,101)
        ( 60, 81)( 61,105)( 64, 70)( 65,117)( 66, 89)( 68, 74)( 69,121)( 72, 78)( 73,125)( 76, 79)( 77, 93)( 82, 88)
        ( 83,133)( 84,109)( 87, 92)( 90,113)( 91,134)( 95,100)( 96,126)( 98,104)( 99,142)(102,108)(103,132)(106,112)
        (107,111)(110,129)(114,120)(115,119)(116,137)(118,124)(122,128)(123,138)(127,141)(130,136)(131,143)(135,140)
        (139,144),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80)( 81, 82, 83, 84)( 85, 86, 87, 88)( 89, 90, 91, 92)
        ( 93, 94, 95, 96)( 97, 98, 99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)
        (117,118,119,120)(121,122,123,124)(125,126,127,128)(129,130,131,132)(133,134,135,136)(137,138,139,140)
        (141,142,143,144) ), 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)(101,127)(102,115)(105,110)(108,119)(109,128)(113,118)
        (114,120)(116,123)(117,136)(121,135)(122,131)(124,130)(125,144)(126,139)(129,134)(132,140)(133,143)(137,142)
        (138,141),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10, 11, 12)( 13, 14, 15, 16)( 17, 18, 19, 20)( 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), rec(
      invers := (  1,  5)(  2, 15)(  3,144)(  4, 10)(  6, 14)(  7, 27)(  8, 19)(  9, 11)( 12,143)( 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)(105,123)(106,115)(109,114)(112,118)
        (113,124)(116,119)(117,127)(120,126)(121,139)(122,131)(125,130)(128,134)(129,140)(132,136)(133,135)(137,142)
        (138,141),
      nbP := 144,
      next := (  1,  2,  3,  4)(  5,  6,  7,  8)(  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), 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)( 93,119)( 94,111)( 96,102)( 97,123)(101,106)(104,110)(105,124)(108,114)(109,127)(112,115)
        (113,131)(116,122)(117,136)(118,135)(120,126)(121,140)(125,130)(128,134)(129,141)(132,138)(133,144)(137,139)
        (142,143),
      nbP := 144,
      next := (  1,  2)(  3,  4,  5,  6)(  7,  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ), 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)(117,122)
        (118,119)(120,123)(121,124)(125,130)(126,127)(128,131)(129,132)(133,138)(134,135)(136,139)(137,140)(141,144)
        (142,143),
      nbP := 144,
      next := (  1,  2)(  3,  4,  5,  6)(  7,  8,  9, 10)( 11, 12, 13, 14)( 15, 16, 17, 18)( 19, 20, 21, 22)
        ( 23, 24, 25, 26)( 27, 28, 29, 30)( 31, 32, 33, 34)( 35, 36, 37, 38)( 39, 40, 41, 42)( 43, 44, 45, 46)
        ( 47, 48, 49, 50)( 51, 52, 53, 54)( 55, 56, 57, 58)( 59, 60, 61, 62)( 63, 64, 65, 66)( 67, 68, 69, 70)
        ( 71, 72, 73, 74)( 75, 76, 77, 78)( 79, 80, 81, 82)( 83, 84, 85, 86)( 87, 88, 89, 90)( 91, 92, 93, 94)
        ( 95, 96, 97, 98)( 99,100,101,102)(103,104,105,106)(107,108,109,110)(111,112,113,114)(115,116,117,118)
        (119,120,121,122)(123,124,125,126)(127,128,129,130)(131,132,133,134)(135,136,137,138)(139,140,141,142)
        (143,144) ) ];
