return [ 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)(26,61)(27,51)(29,35)(30,65)(33,38)(34,58)(37,55)(40,46)(41,69)(42,56)(44,50)(45,73)(48,54)
        (49,77)(52,59)(53,81)(57,66)(60,64)(62,68)(63,82)(67,72)(70,76)(71,83)(74,80)(75,79)(78,84),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60)(61,62,63,64)
        (65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(23,52)(24,45)(26,32)(27,31)(30,49)(34,40)(35,73)(36,60)(38,44)(39,70)(42,48)(43,74)(46,64)(47,78)
        (50,56)(51,65)(54,59)(55,81)(58,63)(61,68)(62,82)(66,84)(67,79)(69,72)(71,77)(75,80)(76,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73)(74,75,76,77)(78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,25)( 4, 9)( 6,12)( 7,37)( 8,17)(10,21)(11,41)(14,20)(15,51)(16,29)(18,33)(19,55)
        (22,28)(23,43)(24,46)(26,32)(27,39)(30,47)(31,35)(34,40)(36,59)(38,44)(42,45)(48,54)(49,67)(50,60)(52,58)
        (53,71)(56,62)(57,75)(61,63)(64,70)(65,78)(66,76)(68,74)(69,84)(72,77)(73,81)(79,83)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,25)( 4, 9)( 6,12)( 7,37)( 8,17)(10,21)(11,41)(14,20)(15,36)(16,29)(18,34)(19,33)
        (22,28)(23,52)(24,45)(26,32)(27,56)(30,39)(31,60)(35,40)(38,44)(42,48)(43,61)(46,49)(47,64)(50,55)(51,68)
        (53,59)(54,73)(57,63)(58,76)(62,67)(65,71)(66,77)(69,72)(70,80)(74,79)(75,84)(78,82)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), 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)(22,47)
        (23,43)(25,31)(26,63)(27,48)(29,35)(30,64)(33,51)(34,67)(37,42)(38,77)(39,52)(41,46)(44,55)(45,78)(49,59)
        (50,56)(53,75)(54,71)(57,81)(58,73)(60,66)(61,83)(62,82)(65,70)(68,74)(69,84)(72,79)(76,80),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76)(77,78,79,80)(81,82,83,84) ), 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)(18,52)
        (22,35)(25,47)(26,43)(28,34)(29,67)(30,55)(32,38)(33,71)(36,42)(37,75)(40,46)(41,79)(44,59)(45,84)(48,54)
        (49,57)(50,60)(53,58)(56,63)(61,66)(62,81)(64,70)(65,77)(68,74)(69,73)(72,78)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(29,71)(30,59)(32,38)(33,72)(36,42)(37,75)(40,46)(41,79)(44,63)(45,84)(48,54)
        (49,61)(50,64)(52,58)(53,57)(56,62)(60,67)(65,70)(66,81)(68,74)(69,77)(73,78)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(34,69)(37,43)(38,81)(39,65)(41,47)(42,78)(45,51)(46,82)
        (49,55)(50,74)(53,59)(54,71)(57,63)(58,62)(61,68)(66,76)(67,72)(70,75)(73,83)(77,80)(79,84),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81)(82,83,84) ), 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)(42,84)(45,67)(46,81)
        (49,55)(50,62)(51,68)(53,59)(54,58)(57,63)(61,71)(66,75)(69,74)(70,77)(73,78)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(30,74)(31,60)(33,39)(34,76)(37,64)(38,71)(41,47)(42,84)(43,65)(45,51)
        (46,82)(49,68)(50,67)(54,59)(55,69)(57,63)(58,78)(61,73)(62,72)(66,80)(70,77)(75,79)(81,83),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), 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)(30,54)(31,64)(33,39)(34,74)(37,68)(38,75)(41,47)(42,84)(43,69)(45,51)
        (46,81)(49,72)(50,71)(53,59)(55,73)(57,63)(58,65)(61,67)(62,77)(66,76)(70,78)(79,83)(80,82),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77)(78,79,80,81)(82,83,84) ), 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)(38,74)(41,46)(42,68)(44,50)(45,84)
        (48,71)(49,70)(52,58)(53,81)(54,72)(56,62)(57,78)(60,66)(61,65)(64,75)(69,83)(73,80)(77,82),
      nbP := 84,
      next := ( 1, 2, 3)( 4, 5, 6, 7)( 8, 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(34,71)(37,51)(38,75)(41,46)(42,52)(44,50)(45,53)(48,55)
        (49,80)(54,79)(56,62)(57,77)(58,84)(60,66)(61,73)(64,70)(65,69)(68,74)(72,78)(76,82)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(34,74)(35,57)(37,43)(38,70)(41,60)(42,67)(45,51)(46,82)
        (47,61)(49,55)(50,79)(53,64)(54,63)(58,83)(59,72)(62,76)(66,71)(69,75)(73,84)(77,81)(78,80),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), 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)(23,68)(24,53)(26,32)(27,72)(30,57)(31,76)(34,40)(35,74)(36,58)(38,44)(39,70)(42,61)(43,67)(46,52)
        (47,84)(48,62)(50,56)(51,82)(54,65)(55,64)(59,78)(60,77)(63,80)(66,71)(69,75)(73,79)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,25)( 4, 9)( 6,17)( 7,36)( 8,14)(10,21)(11,46)(12,18)(15,33)(16,29)(19,44)(20,40)
        (22,28)(23,61)(24,50)(26,32)(27,65)(30,53)(31,69)(34,39)(35,54)(37,43)(38,78)(41,48)(42,60)(45,49)(47,52)
        (51,57)(55,77)(56,73)(58,64)(59,79)(62,68)(63,83)(66,72)(67,84)(70,76)(71,75)(74,81)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35)(36,37,38,39)(40,41,42,43)(44,45)(46,47,48,49)(50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,12)( 3,24)( 4, 9)( 6,16)( 7,36)( 8,13)(10,20)(11,17)(14,32)(15,28)(18,41)(19,40)(21,27)
        (22,48)(23,42)(25,31)(26,52)(29,44)(30,56)(33,39)(34,67)(35,45)(37,43)(38,51)(46,64)(47,60)(49,55)(50,68)
        (53,59)(54,75)(57,63)(58,79)(61,71)(62,84)(65,70)(66,72)(69,78)(73,77)(74,81)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,25)( 4, 9)( 6,17)( 7,37)( 8,14)(10,21)(11,19)(12,18)(15,33)(16,29)(20,41)(22,28)
        (23,48)(24,42)(26,32)(27,52)(30,44)(31,56)(34,40)(35,67)(36,45)(38,43)(39,51)(46,64)(47,60)(49,55)(50,68)
        (53,59)(54,75)(57,63)(58,79)(61,71)(62,80)(65,70)(66,72)(69,78)(73,77)(74,84)(76,82)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(42,67)(45,51)(46,50)
        (49,64)(53,59)(54,74)(55,69)(57,63)(58,84)(62,72)(65,71)(66,81)(70,78)(73,79)(75,83)(77,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,20)( 7,39)( 8,17)(10,23)(11,47)(12,21)(14,19)(15,38)(16,31)(18,35)
        (22,43)(24,30)(25,63)(26,51)(28,34)(29,67)(32,55)(33,71)(36,42)(37,56)(40,46)(41,75)(44,50)(45,62)(48,54)
        (49,53)(52,59)(57,78)(58,72)(60,66)(61,76)(64,70)(65,81)(68,74)(69,84)(73,79)(77,80)(82,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(29,68)(32,55)(33,71)(36,42)(37,77)(38,60)(40,46)(41,81)(44,50)(45,66)
        (48,54)(49,53)(52,63)(56,62)(57,79)(58,72)(61,75)(64,70)(65,82)(69,74)(73,83)(76,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76)(77,78,79,80)(81,82,83,84) ), 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)(26,52)(27,51)(29,35)(30,68)(33,55)(34,71)(37,43)(38,77)(39,64)(41,47)(42,73)(45,50)
        (46,70)(49,54)(53,67)(56,62)(57,84)(58,75)(60,66)(61,82)(65,79)(69,74)(72,78)(76,80)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(29,68)(32,55)(33,71)(36,42)(37,77)(38,64)(40,46)(41,73)(44,50)(45,70)
        (48,54)(49,53)(52,67)(56,62)(57,81)(58,75)(60,66)(61,84)(65,79)(69,74)(72,78)(76,80)(82,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(26,68)(27,52)(29,35)(30,71)(33,56)(34,75)(37,43)(38,77)(39,64)(41,47)(42,73)(45,51)
        (46,70)(49,55)(50,54)(53,67)(58,63)(59,79)(61,66)(62,84)(65,81)(69,74)(72,78)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)
        (19,60)(23,40)(25,31)(26,55)(27,48)(29,35)(30,34)(33,52)(38,43)(39,64)(41,47)(42,72)(45,51)(46,75)(49,67)
        (50,80)(53,59)(54,68)(57,63)(58,81)(61,66)(62,82)(65,71)(69,84)(70,77)(73,78)(74,83)(76,79),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80)(81,82,83,84) ), 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)(18,57)
        (22,44)(23,40)(26,31)(27,45)(29,48)(30,63)(33,39)(34,70)(35,54)(37,43)(38,73)(41,58)(42,77)(46,62)(47,59)
        (49,55)(50,72)(51,66)(53,56)(60,82)(61,81)(64,69)(65,83)(67,75)(68,79)(71,76)(74,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11)(12,13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(34,78)(35,60)(37,43)(38,74)(41,64)(42,71)(45,51)(46,84)
        (47,65)(49,55)(50,82)(53,68)(54,67)(58,63)(59,72)(61,77)(62,76)(66,80)(70,75)(73,79)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15)(16,17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), 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)(38,73)(41,63)(42,70)(45,50)(46,64)
        (48,54)(49,84)(52,67)(53,66)(56,62)(57,78)(58,71)(61,75)(65,83)(69,74)(72,80)(76,82)(77,81),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(31,72)(34,40)(35,81)(36,65)(38,44)(39,77)(42,68)(43,74)(46,52)
        (47,51)(48,69)(50,56)(54,71)(55,70)(58,63)(59,75)(61,67)(62,83)(66,79)(73,78)(76,82)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70)(71,72,73,74)(75,76,77,78)(79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,26)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,47)(12,22)(14,20)(15,54)(16,29)(18,33)
        (19,58)(23,45)(24,41)(27,32)(28,43)(30,50)(31,39)(34,40)(35,53)(36,62)(38,44)(42,48)(46,49)(51,57)(52,67)
        (55,61)(56,70)(59,65)(60,73)(63,66)(64,77)(68,72)(69,81)(71,76)(74,80)(75,82)(78,84)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46)(47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,26)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,47)(12,22)(14,20)(15,58)(16,29)(18,33)
        (19,62)(23,45)(24,41)(27,32)(28,51)(30,54)(31,71)(34,40)(35,82)(36,66)(38,44)(39,76)(42,49)(43,73)(46,50)
        (48,53)(52,70)(55,61)(56,80)(57,74)(59,65)(60,81)(63,69)(64,68)(67,78)(72,77)(75,83)(79,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46)(47,48,49,50)(51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), 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)(35,39)(36,68)(38,44)(42,72)(43,69)(46,52)(47,77)
        (48,73)(50,56)(51,84)(55,79)(58,64)(59,74)(60,76)(62,67)(63,81)(66,71)(70,82)(75,80)(78,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,26)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,49)(12,22)(14,20)(15,59)(16,29)(18,33)
        (19,63)(23,45)(24,41)(27,32)(28,52)(30,56)(31,74)(34,40)(35,82)(36,68)(38,44)(39,79)(42,69)(43,76)(46,51)
        (47,71)(48,70)(50,55)(53,73)(54,72)(57,62)(58,77)(60,66)(61,84)(64,67)(65,81)(75,80)(78,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51)(52,53,54,55)(56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(18,32)
        (19,61)(23,42)(24,38)(27,31)(28,49)(30,53)(33,37)(35,41)(36,62)(39,65)(40,70)(43,48)(44,66)(46,52)(47,78)
        (50,56)(51,81)(54,60)(55,75)(58,64)(59,72)(63,69)(67,77)(68,73)(71,76)(74,82)(79,84)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33)(34,35,36,37)(38,39,40,41)(42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)
        (65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,33)( 8,17)(10,25)(11,44)(12,22)(14,20)(15,51)(16,30)(18,32)
        (19,55)(23,40)(24,36)(26,31)(27,54)(28,48)(34,39)(35,59)(37,63)(38,72)(41,47)(42,65)(43,64)(45,50)(46,76)
        (49,67)(52,58)(53,68)(56,62)(57,79)(60,71)(61,84)(66,75)(69,82)(70,77)(73,78)(74,81)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,34)( 8,17)(10,25)(11,45)(12,22)(14,20)(15,57)(16,29)(18,32)
        (19,61)(23,42)(24,38)(26,31)(27,49)(30,53)(33,37)(35,41)(36,62)(39,65)(40,70)(43,48)(44,66)(46,52)(47,78)
        (50,56)(51,81)(54,60)(55,75)(58,64)(59,72)(63,69)(67,77)(68,73)(71,76)(74,82)(79,84)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33)(34,35,36,37)(38,39,40,41)(42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)
        (65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,20)( 7,38)( 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)(37,41)(43,49)(44,59)(47,50)(48,62)(51,57)(52,74)
        (53,66)(55,61)(56,77)(60,65)(63,69)(64,78)(67,70)(68,81)(71,76)(72,83)(73,82)(75,80)(79,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37)(38,39,40,41)(42,43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(27,56)(29,35)(30,71)(33,60)(34,75)(37,43)(38,61)(41,47)(42,46)(45,62)(49,55)
        (50,76)(51,63)(53,59)(54,79)(57,64)(58,84)(65,70)(66,73)(67,81)(69,74)(72,78)(77,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,20)( 7,40)( 8,17)(10,24)(11,48)(12,21)(14,19)(15,46)(16,32)(18,36)
        (22,44)(23,41)(25,31)(26,60)(27,52)(29,35)(30,64)(33,50)(34,68)(37,43)(38,42)(39,47)(45,51)(49,55)(53,56)
        (54,69)(57,63)(58,78)(59,72)(61,67)(62,79)(65,71)(66,82)(70,75)(73,76)(74,83)(77,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77)(78,79,80,81)(82,83,84) ), 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)(30,74)(33,60)(34,77)(37,43)(38,42)(39,65)(41,47)(45,68)(46,66)
        (49,55)(50,82)(51,69)(53,59)(54,83)(57,71)(58,79)(61,67)(62,70)(63,81)(72,76)(75,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70)(71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(30,76)(33,59)(34,79)(37,43)(38,61)(39,68)(41,47)(42,81)(45,71)
        (46,78)(49,54)(50,72)(52,58)(53,84)(56,75)(57,74)(60,66)(62,80)(64,70)(65,69)(73,83)(77,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,40)( 8,17)(10,25)(11,51)(12,22)(14,20)(15,60)(16,32)(18,36)
        (19,63)(23,47)(24,44)(26,31)(27,55)(29,35)(30,76)(33,59)(34,57)(37,43)(38,78)(39,67)(41,46)(42,81)(45,71)
        (48,54)(49,65)(50,72)(52,58)(53,62)(56,75)(61,66)(64,70)(68,77)(69,73)(74,82)(79,84)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76)(77,78,79,80)(81,82,83,84) ), 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)(27,76)(28,55)(30,35)(31,79)(34,59)(37,43)(38,61)(39,68)(41,47)(42,81)(45,71)
        (46,78)(49,54)(50,72)(52,58)(53,84)(56,75)(57,74)(60,66)(62,80)(64,70)(65,69)(73,83)(77,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(31,84)(34,59)(35,81)(38,43)(39,67)(41,46)(42,68)(45,71)
        (48,54)(49,78)(50,72)(52,58)(53,57)(56,75)(60,66)(61,73)(62,77)(65,70)(69,74)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,41)( 8,17)(10,25)(11,51)(12,22)(14,20)(15,62)(16,33)(18,37)
        (19,63)(23,49)(24,45)(26,32)(27,74)(28,55)(30,36)(31,78)(34,58)(35,79)(38,44)(39,67)(40,66)(42,48)(43,82)
        (46,53)(47,73)(50,54)(52,57)(56,70)(59,65)(60,84)(61,76)(64,69)(68,81)(71,77)(72,83)(75,80),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50)(51,52,53,54)(55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,41)( 8,17)(10,25)(11,51)(12,22)(14,20)(15,62)(16,33)(18,37)
        (19,66)(23,49)(24,45)(26,32)(27,56)(28,55)(30,36)(31,71)(34,59)(35,74)(38,44)(39,80)(40,67)(42,48)(43,76)
        (46,53)(47,73)(50,54)(52,58)(57,70)(60,65)(61,78)(63,69)(64,84)(68,82)(72,77)(75,81)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50)(51,52,53,54)(55,56,57,58)(59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), 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)
        (19,64)(23,48)(24,44)(26,31)(27,34)(28,55)(30,35)(33,59)(37,43)(38,42)(39,67)(41,47)(45,71)(46,68)(49,54)
        (50,81)(51,72)(53,58)(56,62)(57,82)(60,66)(61,77)(65,70)(69,78)(73,79)(74,75)(76,83)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80)(81,82,83,84) ), 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)(38,70)(39,73)(41,47)(42,66)(45,74)(46,62)
        (49,55)(50,84)(51,75)(53,59)(54,81)(57,63)(58,77)(61,67)(65,71)(69,72)(76,78)(79,83)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), 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)(23,47)(24,44)(26,31)(27,55)(29,35)(30,74)(33,59)(34,77)(37,43)(38,61)(39,68)(41,46)(42,82)(45,69)
        (48,54)(49,76)(50,70)(52,58)(53,57)(56,73)(60,66)(62,81)(65,67)(71,79)(72,83)(75,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)
        (19,65)(23,48)(24,44)(26,31)(27,77)(28,56)(30,35)(33,60)(34,78)(37,43)(38,62)(39,69)(41,47)(42,82)(45,70)
        (46,76)(49,55)(50,54)(51,71)(53,59)(57,73)(58,72)(61,67)(63,81)(66,68)(74,80)(75,83)(79,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69)(70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,49)(12,22)(14,20)(15,61)(16,31)(18,35)
        (19,65)(23,45)(24,41)(26,30)(27,53)(29,34)(32,57)(33,54)(36,40)(38,44)(39,66)(42,69)(43,78)(46,52)(47,74)
        (48,70)(50,56)(51,75)(55,76)(58,64)(59,71)(60,73)(62,68)(63,82)(67,77)(72,81)(79,84)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30)
        (31,32,33,34)(35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,50)(12,22)(14,20)(15,58)(16,33)(18,37)
        (19,62)(23,46)(24,43)(26,32)(27,66)(28,54)(30,36)(31,69)(34,48)(35,73)(38,42)(40,45)(41,63)(44,60)(47,53)
        (49,61)(51,57)(52,74)(55,65)(56,77)(59,64)(67,72)(68,81)(70,76)(71,82)(75,80)(78,84)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38)(39,40,41,42)(43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)
        (19,68)(23,48)(24,44)(26,31)(27,77)(28,55)(30,35)(33,59)(34,78)(37,43)(38,61)(39,65)(41,47)(42,82)(45,69)
        (46,76)(49,54)(50,71)(51,70)(53,58)(56,73)(57,72)(60,66)(62,81)(64,67)(74,80)(75,83)(79,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)
        (19,68)(23,48)(24,45)(26,32)(27,56)(28,55)(30,36)(31,74)(34,59)(35,77)(38,44)(39,61)(40,65)(42,47)(43,82)
        (46,69)(49,54)(50,76)(51,70)(53,58)(57,73)(60,66)(62,81)(64,67)(71,79)(72,83)(75,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47)(48,49,50,51)(52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(27,31)(28,52)(30,36)(34,56)(35,53)(39,43)(41,68)(42,65)(45,51)(46,80)(47,69)
        (49,55)(50,81)(54,75)(57,63)(58,77)(59,72)(61,67)(62,84)(66,79)(70,73)(71,76)(74,82)(78,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,50)(12,22)(14,20)(15,62)(16,33)(18,37)
        (19,66)(23,47)(24,43)(26,32)(27,31)(28,54)(30,36)(34,58)(35,55)(38,42)(40,46)(41,67)(44,70)(45,79)(48,53)
        (49,71)(51,57)(52,76)(56,77)(59,65)(60,82)(61,74)(63,69)(64,83)(68,78)(72,75)(73,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38)(39,40,41,42)(43,44,45,46)(47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80)(81,82,83,84) ), 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)(27,31)(28,55)(30,36)(34,59)(35,56)(38,42)(40,46)(41,68)(44,71)(45,80)(48,54)
        (49,76)(50,72)(52,58)(53,77)(57,78)(60,66)(61,73)(62,75)(64,70)(65,83)(69,79)(74,82)(81,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,48)(12,22)(14,20)(15,58)(16,32)(18,36)
        (19,62)(23,44)(24,40)(26,31)(27,75)(28,53)(30,35)(33,54)(34,76)(38,43)(39,66)(41,70)(42,82)(45,51)(46,79)
        (47,71)(49,52)(50,74)(55,61)(56,72)(57,78)(59,65)(60,84)(63,69)(64,68)(67,81)(73,83)(77,80),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,50)(12,22)(14,20)(15,58)(16,31)(18,35)
        (19,62)(23,47)(24,43)(26,30)(28,34)(29,51)(32,54)(33,70)(36,42)(37,81)(38,65)(40,46)(41,75)(44,49)(45,72)
        (48,53)(52,69)(55,61)(56,80)(57,73)(59,64)(60,67)(63,68)(66,77)(71,76)(74,82)(78,84)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,21)( 7,38)( 8,17)(10,25)(11,49)(12,22)(14,20)(15,57)(16,31)(18,35)
        (19,61)(23,45)(24,42)(26,30)(28,34)(29,50)(32,53)(33,74)(36,41)(37,65)(39,44)(40,82)(43,69)(46,52)(47,76)
        (48,70)(51,73)(54,60)(55,67)(56,77)(58,64)(59,63)(62,68)(66,81)(71,79)(72,83)(75,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37)(38,39,40,41)(42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,40)( 8,17)(10,25)(11,23)(12,22)(14,20)(15,51)(16,32)(18,36)
        (19,55)(24,44)(26,31)(27,45)(29,35)(30,42)(33,47)(34,38)(37,43)(39,59)(41,46)(48,54)(49,67)(50,60)(52,58)
        (53,71)(56,62)(57,75)(61,63)(64,70)(65,81)(66,76)(68,74)(69,82)(72,78)(73,83)(77,79)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,40)( 8,17)(10,25)(11,23)(12,22)(14,20)(15,51)(16,32)(18,36)
        (19,55)(24,44)(26,31)(27,45)(29,35)(30,42)(33,47)(34,38)(37,43)(39,59)(41,46)(48,54)(49,67)(50,60)(52,58)
        (53,71)(56,62)(57,75)(61,63)(64,70)(65,84)(66,76)(68,74)(69,81)(72,78)(73,82)(77,79)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,20)( 7,41)( 8,17)(10,24)(11,42)(12,21)(14,19)(15,39)(16,32)(18,36)
        (22,33)(23,38)(25,31)(26,54)(27,46)(29,35)(30,58)(34,45)(37,40)(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)(72,76)(73,83)(75,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41)(42,43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,20)( 7,41)( 8,17)(10,24)(11,46)(12,21)(14,19)(15,54)(16,32)(18,36)
        (22,42)(23,38)(25,31)(26,61)(27,50)(29,35)(30,65)(33,44)(34,69)(37,40)(39,55)(43,49)(45,56)(47,53)(48,70)
        (51,57)(52,73)(58,64)(59,78)(60,77)(62,68)(63,82)(66,72)(67,83)(71,76)(74,80)(75,84)(79,81),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19)(20,21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41)(42,43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56)(57,58,59,60)(61,62,63,64)
        (65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,38)( 8,17)(10,24)(11,44)(12,22)(14,20)(15,42)(16,32)(18,83)
        (19,36)(23,40)(25,31)(26,56)(27,48)(29,35)(30,60)(33,46)(34,64)(37,84)(39,43)(41,47)(45,51)(49,52)(50,65)
        (53,59)(54,75)(55,68)(57,63)(58,79)(61,67)(62,80)(66,71)(69,72)(70,81)(73,78)(74,77)(76,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66,67)(68,69,70,71)(72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,44)(12,22)(14,20)(15,42)(16,33)(18,83)
        (19,37)(23,34)(24,41)(26,32)(27,56)(28,48)(30,36)(31,60)(35,47)(38,84)(40,43)(45,51)(46,61)(49,52)(50,64)
        (53,59)(54,75)(55,68)(57,63)(58,79)(62,67)(65,71)(66,80)(69,72)(70,81)(73,78)(74,77)(76,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,38)( 8,17)(10,25)(11,48)(12,22)(14,20)(15,42)(16,33)(18,83)
        (19,36)(23,44)(24,40)(26,32)(27,64)(28,52)(30,35)(31,68)(34,56)(37,84)(39,43)(41,57)(45,51)(46,72)(47,58)
        (49,55)(50,73)(53,60)(54,76)(59,69)(61,67)(62,82)(63,81)(65,71)(66,78)(70,75)(74,79)(77,80),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81,82)(83,84) ), 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)(18,33)
        (19,32)(23,40)(25,31)(26,64)(27,48)(30,52)(34,39)(35,57)(37,43)(38,68)(41,47)(42,71)(45,51)(46,75)(49,60)
        (50,80)(53,59)(54,81)(55,65)(58,67)(61,66)(62,84)(63,77)(69,74)(70,82)(72,78)(73,83)(76,79),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)(60,61,62,63)
        (64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,34)(12,22)(14,20)(15,23)(16,33)(18,38)
        (19,37)(24,40)(26,32)(27,49)(28,41)(30,36)(31,53)(35,44)(42,45)(43,54)(46,52)(47,65)(48,57)(50,56)(51,69)
        (55,60)(58,61)(59,70)(62,68)(63,79)(64,73)(66,72)(67,82)(71,76)(74,77)(75,83)(78,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78)(79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,41)( 8,17)(10,25)(11,48)(12,22)(14,20)(15,46)(16,33)(18,38)
        (19,37)(23,44)(24,42)(26,32)(27,60)(28,52)(30,36)(31,64)(34,50)(35,68)(39,43)(40,47)(45,51)(49,55)(53,56)
        (54,69)(57,63)(58,81)(59,72)(61,67)(62,78)(65,71)(66,82)(70,75)(73,76)(74,83)(77,80)(79,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77,78,79)(80,81)(82,83,84) ), 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)(18,38)
        (19,37)(23,49)(24,45)(26,32)(27,72)(28,53)(30,36)(31,77)(34,56)(35,74)(39,44)(40,61)(42,48)(43,79)(46,64)
        (47,81)(50,55)(51,65)(54,68)(57,63)(58,83)(59,70)(62,78)(66,71)(67,82)(69,75)(73,76)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70,71)(72,73,74,75)(76,77)(78,79,80)(81,82,83,84) ), 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)(18,37)
        (19,36)(23,48)(24,44)(26,31)(27,55)(29,35)(30,72)(33,59)(34,73)(38,43)(39,64)(41,47)(42,80)(45,67)(46,84)
        (49,54)(50,76)(51,68)(53,58)(56,71)(57,77)(60,66)(61,69)(62,75)(65,79)(70,82)(74,78)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27)(28,29,30,31)
        (32,33,34,35)(36,37,38,39)(40,41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(18,38)
        (19,37)(23,48)(24,45)(26,32)(27,71)(28,56)(30,36)(31,72)(34,60)(35,75)(39,44)(40,65)(42,47)(43,66)(46,62)
        (49,55)(50,76)(51,63)(53,59)(54,79)(57,68)(58,84)(61,67)(69,74)(70,81)(73,78)(77,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(18,38)
        (19,37)(23,48)(24,44)(26,32)(27,76)(28,56)(30,36)(31,73)(34,60)(35,77)(39,43)(40,65)(42,47)(45,68)(46,66)
        (49,55)(50,82)(51,69)(53,59)(54,83)(57,71)(58,79)(61,67)(62,70)(63,81)(72,75)(74,80)(78,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43)(44,45,46,47)(48,49,50,51)(52,53,54,55)(56,57,58,59)
        (60,61,62,63)(64,65,66,67)(68,69,70)(71,72,73,74)(75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,49)(12,22)(14,20)(15,43)(16,33)(18,38)
        (19,37)(23,45)(24,41)(26,32)(27,63)(28,53)(30,36)(31,67)(34,57)(35,71)(40,44)(42,58)(46,52)(47,72)(48,59)
        (50,56)(51,75)(54,60)(55,79)(61,66)(62,84)(64,70)(65,81)(68,74)(69,77)(73,78)(76,82)(80,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59)
        (60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(65,80)(66,75)(68,74)(69,82)(73,78)(76,79)(77,83)(81,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,19)( 7,35)( 8,15)(10,23)(11,46)(12,20)(14,18)(16,31)(17,28)(21,43)
        (22,39)(24,30)(25,65)(26,49)(29,53)(32,38)(33,70)(34,54)(36,42)(37,73)(40,57)(41,77)(44,48)(45,58)(47,52)
        (50,61)(51,59)(55,69)(56,66)(60,81)(62,68)(63,75)(64,82)(67,72)(71,76)(74,80)(78,84)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45)(46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(33,72)(34,56)(36,42)(37,75)(40,59)(41,79)(44,50)(45,49)(46,60)
        (48,54)(52,63)(53,61)(57,71)(58,68)(62,82)(64,70)(65,77)(66,83)(69,74)(73,78)(76,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,30)( 4, 9)( 6,21)( 7,35)( 8,17)(10,25)(11,47)(12,22)(14,20)(15,55)(16,27)(18,31)
        (19,59)(23,43)(24,39)(26,29)(28,51)(32,38)(33,37)(34,63)(36,42)(40,67)(41,64)(44,50)(45,74)(46,68)(48,54)
        (49,75)(52,58)(53,78)(56,62)(57,79)(60,66)(61,82)(65,73)(69,70)(71,77)(72,83)(76,81)(80,84),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), 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)(31,68)(34,53)(35,71)(38,44)(39,77)(40,64)(42,48)(43,73)(46,52)
        (47,70)(51,67)(54,60)(55,84)(56,75)(58,63)(59,82)(62,66)(65,79)(69,74)(72,78)(76,80)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63)(64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), 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)(31,70)(34,53)(35,73)(38,44)(39,79)(40,64)(42,48)(43,75)(46,67)
        (47,72)(51,69)(52,68)(54,60)(55,83)(56,77)(58,63)(59,84)(62,66)(65,81)(71,76)(74,80)(78,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63)(64,65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), 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)(31,71)(34,53)(35,74)(38,44)(39,80)(40,64)(42,48)(43,76)(46,68)
        (47,73)(51,70)(52,69)(54,60)(55,84)(56,78)(58,63)(59,66)(62,67)(65,82)(72,77)(75,81)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63)(64,65,66,67)(68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,27)( 8,17)(10,24)(11,23)(12,22)(14,20)(15,43)(16,31)(18,35)
        (19,47)(25,30)(26,36)(29,34)(32,39)(33,37)(38,51)(40,46)(41,59)(42,52)(44,50)(45,63)(48,54)(49,67)(53,55)
        (56,62)(57,75)(58,68)(60,66)(61,79)(64,70)(65,74)(69,71)(72,78)(73,80)(76,82)(77,84)(81,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23)(24,25,26,27)(28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81,82)(83,84) ), rec(
      invers := ( 1, 5)( 2,12)( 3,25)( 4, 9)( 6,19)( 7,24)( 8,15)(10,21)(11,20)(13,18)(14,29)(16,33)(17,38)(22,28)
        (23,34)(26,32)(27,45)(30,37)(31,49)(35,48)(36,41)(39,44)(40,53)(42,57)(43,62)(46,52)(47,58)(50,56)(51,69)
        (54,61)(55,73)(59,72)(60,65)(63,68)(64,77)(66,71)(67,83)(70,76)(74,80)(75,84)(78,82)(79,81),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11)(12,13,14)(15,16,17,18)(19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 5)( 2,15)( 3,12)( 4,10)( 6,14)( 7,27)( 8,19)( 9,11)(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)(73,84)(74,83)(77,81)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,15)( 3,12)( 4,10)( 6,14)( 7,27)( 8,19)( 9,11)(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)(57,74)(58,67)(61,66)(64,70)(65,75)(68,71)(69,78)(72,77)(73,84)(76,81)(79,83)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,15)( 3,12)( 4,10)( 6,14)( 7,26)( 8,19)( 9,11)(13,23)(16,22)(17,31)(18,24)(20,27)(21,35)
        (25,28)(29,34)(30,39)(32,38)(33,44)(36,42)(37,47)(40,43)(41,51)(45,50)(46,55)(48,54)(49,60)(52,58)(53,63)
        (56,59)(57,67)(61,66)(62,71)(64,70)(65,76)(68,74)(69,78)(72,75)(73,84)(77,81)(79,83)(80,82),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 5)( 2,15)( 3,24)( 4,10)( 6,14)( 7,34)( 8,19)( 9,11)(12,23)(13,38)(16,22)(17,50)(18,27)(20,31)
        (21,51)(25,30)(26,42)(28,46)(29,59)(32,37)(33,54)(35,41)(36,67)(39,45)(40,70)(43,58)(44,74)(47,53)(48,81)
        (49,62)(52,57)(55,66)(56,82)(60,65)(61,75)(63,77)(64,72)(68,73)(69,80)(71,76)(78,84)(79,83),
      nbP := 84,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33)(34,35,36,37)(38,39,40,41)(42,43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76)(77,78,79,80)(81,82,83,84) ), rec(
      invers := ( 1, 3)( 2,12)( 4,10)( 5,30)( 6,16)( 7,11)( 8,18)( 9,34)(13,15)(14,22)(17,26)(19,25)(20,46)(21,38)
        (23,29)(24,50)(27,33)(28,54)(31,37)(32,58)(35,41)(36,62)(39,42)(40,66)(43,49)(44,71)(45,70)(47,53)(48,75)
        (51,57)(52,78)(55,61)(56,82)(59,65)(60,83)(63,69)(64,80)(67,73)(68,77)(72,74)(76,81)(79,84),
      nbP := 84,
      next := ( 1, 2)( 3, 4, 5, 6)( 7, 8, 9,10)(11,12,13,14)(15,16,17)(18,19,20,21)(22,23,24,25)(26,27,28,29)
        (30,31,32,33)(34,35,36,37)(38,39,40,41)(42,43,44,45)(46,47,48,49)(50,51,52,53)(54,55,56,57)(58,59,60,61)
        (62,63,64,65)(66,67,68,69)(70,71,72,73)(74,75,76,77)(78,79,80,81)(82,83,84) ), rec(
      invers := ( 1, 3)( 2,83)( 4,79)( 5,84)( 6,10)( 7,12)( 8,17)( 9,14)(11,13)(15,21)(16,18)(19,25)(20,22)(23,29)
        (24,26)(27,33)(28,30)(31,37)(32,34)(35,41)(36,38)(39,45)(40,42)(43,49)(44,46)(47,53)(48,50)(51,57)(52,54)
        (55,61)(56,58)(59,65)(60,62)(63,69)(64,66)(67,73)(68,70)(71,77)(72,74)(75,81)(76,78)(80,82),
      nbP := 84,
      next := ( 1, 2)( 3, 4, 5)( 6, 7, 8, 9)(10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84) ) ];
