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