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