# Singular

#### D.15.18.18 groupActionOnHashes

Procedure from library `gitfan.lib` (see gitfan_lib).

Usage:
groupActionOnHashes(Asigma,OCmov); Asigma: list, OCmov: list of list of cones

Purpose:
From the list of orbits of orbitcones, and the symmetry group represenation given by the matrices in Asigma, compute the corresponding permutation representation of the symmetry group on the orbit cones. The permutations are specified in a map representation of length the sum of the size of the orbits of OCmov.

Return:
list of permutations

Example:
 ```LIB "gitfan.lib"; ring R = 0,T(1..10),wp(1,1,1,1,1,1,1,1,1,1); ideal J = T(5)*T(10)-T(6)*T(9)+T(7)*T(8), T(1)*T(9)-T(2)*T(7)+T(4)*T(5), T(1)*T(8)-T(2)*T(6)+T(3)*T(5), T(1)*T(10)-T(3)*T(7)+T(4)*T(6), T(2)*T(10)-T(3)*T(9)+T(4)*T(8); intmat Q[5][10] = 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 1; list AF= afaces(J); list OC = orbitCones(AF,Q); list generatorsG = permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )), permutationFromIntvec(intvec( 5, 7, 1, 6, 9, 2, 8, 4, 10, 3 )); list Asigmagens = groupActionOnQImage(generatorsG,Q); groupActionOnHashes(Asigmagens,list(OC)); ==> [1]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \ 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 \ 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 5\ 4 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\ 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 \ 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 1\ 09 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 12\ 7 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145\ 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 \ 164 165 166 167 168 169 170 171 172| ==> | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 44 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 0 0 0 120 0 0 0 124 0\ 126 127 128 129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 86 0 0 0 90 0 92 93 \ 94 95 0 0 0 0 0 0 0 137 0 0 0 141 0 143 144 145 14\ 6 0 0 0 0 0 0 153 155 154 156 0 163 165 164 166 0 158 160\ 159 161 0 168 170 169 171 172| ==> ==> [2]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 \ 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 \ 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 5\ 4 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\ 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 \ 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 1\ 09 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 12\ 7 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145\ 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 \ 164 165 166 167 168 169 170 171 172| ==> | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 120 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 0 0 0 126 0 0 0 128 0\ 44 124 127 129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ 0 0 0 0 0 0 0 0 0 0 165 0 0 0 163 0 141 90 1\ 64 166 0 0 0 0 0 0 0 155 0 0 0 153 0 137 86 154 15\ 6 0 0 0 0 0 0 144 93 160 170 0 143 92 158 168 0 145 94\ 159 171 0 146 95 161 169 172| ==> list simplexSymmetryGroup = G25Action(); list orb = findOrbits(simplexSymmetryGroup,nrows(Q)); list simplexOrbitRepresentatives; for (int i=1;i<=size(orb);i++){simplexOrbitRepresentatives[i]=orb[i][1];} list afaceOrbitRepresentatives=afaces(J,simplexOrbitRepresentatives); list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q); list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup); list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits); list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q); list listOfMinimalOrbitConeOrbits = minimalOrbitConeOrbits(listOfOrbitConeOrbits); list Asigma = groupActionOnQImage(simplexSymmetryGroup,Q); groupActionOnHashes(Asigma,listOfOrbitConeOrbits); ==> [1]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\ 25| ==> ==> [2]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 2 4 3 5 7 6 9 8 10 11 13 12 14 16 15 17 19 18 23 24 25 20 21\ 22| ==> ==> [3]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 3 2 4 6 5 7 8 10 9 12 11 13 15 14 16 20 21 22 17 18 19 23 25\ 24| ==> ==> [4]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 4 2 3 7 5 6 9 10 8 13 11 12 16 14 15 23 24 25 17 19 18 20 22\ 21| ==> ==> [5]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 3 4 2 6 7 5 10 8 9 12 13 11 15 16 14 20 22 21 23 25 24 17 18\ 19| ==> ==> [6]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 4 3 2 7 6 5 10 9 8 13 12 11 16 15 14 23 25 24 20 22 21 17 19\ 18| ==> ==> [7]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 5 6 7 2 3 4 8 9 10 14 15 16 11 12 13 17 19 18 20 22 21 23 25\ 24| ==> ==> [8]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 5 7 6 2 4 3 9 8 10 14 16 15 11 13 12 17 18 19 23 25 24 20 22\ 21| ==> ==> [9]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 6 5 7 3 2 4 8 10 9 15 14 16 12 11 13 20 22 21 17 19 18 23 24\ 25| ==> ==> [10]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 7 5 6 4 2 3 9 10 8 16 14 15 13 11 12 23 25 24 17 18 19 20 21\ 22| ==> ==> [11]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 6 7 5 3 4 2 10 8 9 15 16 14 12 13 11 20 21 22 23 24 25 17 19\ 18| ==> ==> [12]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 1 7 6 5 4 3 2 10 9 8 16 15 14 13 12 11 23 24 25 20 21 22 17 18\ 19| ==> ==> [13]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 1 3 4 5 8 9 6 7 10 11 13 12 17 18 19 14 15 16 21 20 22 24 23\ 25| ==> ==> [14]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 1 4 3 5 9 8 7 6 10 11 12 13 17 19 18 14 16 15 24 23 25 21 20\ 22| ==> ==> [15]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 1 2 4 6 8 10 5 7 9 12 13 11 20 21 22 15 14 16 18 17 19 25 23\ 24| ==> ==> [16]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 1 2 3 7 9 10 5 6 8 13 12 11 23 24 25 16 14 15 19 17 18 22 20\ 21| ==> ==> [17]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 1 4 2 6 10 8 7 5 9 12 11 13 20 22 21 15 16 14 25 23 24 18 17\ 19| ==> ==> [18]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 1 3 2 7 10 9 6 5 8 13 11 12 23 25 24 16 15 14 22 20 21 19 17\ 18| ==> ==> [19]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 1 6 7 2 8 9 3 4 10 14 16 15 17 19 18 11 12 13 22 20 21 25 23\ 24| ==> ==> [20]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 1 7 6 2 9 8 4 3 10 14 15 16 17 18 19 11 13 12 25 23 24 22 20\ 21| ==> ==> [21]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 1 5 7 3 8 10 2 4 9 15 16 14 20 22 21 12 11 13 19 17 18 24 23\ 25| ==> ==> [22]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 1 5 6 4 9 10 2 3 8 16 15 14 23 25 24 13 11 12 18 17 19 21 20\ 22| ==> ==> [23]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 1 7 5 3 10 8 4 2 9 15 14 16 20 21 22 12 13 11 24 23 25 19 17\ 18| ==> ==> [24]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 1 6 5 4 10 9 3 2 8 16 14 15 23 24 25 13 12 11 21 20 22 18 17\ 19| ==> ==> [25]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 3 1 4 8 5 9 6 10 7 13 11 12 18 17 19 21 20 22 14 15 16 24 25\ 23| ==> ==> [26]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 4 1 3 9 5 8 7 10 6 12 11 13 19 17 18 24 23 25 14 16 15 21 22\ 20| ==> ==> [27]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 2 1 4 8 6 10 5 9 7 13 12 11 21 20 22 18 17 19 15 14 16 25 24\ 23| ==> ==> [28]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 2 1 3 9 7 10 5 8 6 12 13 11 24 23 25 19 17 18 16 14 15 22 21\ 20| ==> ==> [29]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 4 1 2 10 6 8 7 9 5 11 12 13 22 20 21 25 23 24 15 16 14 18 19\ 17| ==> ==> [30]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 3 1 2 10 7 9 6 8 5 11 13 12 25 23 24 22 20 21 16 15 14 19 18\ 17| ==> ==> [31]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 6 1 7 8 2 9 3 10 4 16 14 15 19 17 18 22 20 21 11 12 13 25 24\ 23| ==> ==> [32]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 7 1 6 9 2 8 4 10 3 15 14 16 18 17 19 25 23 24 11 13 12 22 21\ 20| ==> ==> [33]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 5 1 7 8 3 10 2 9 4 16 15 14 22 20 21 19 17 18 12 11 13 24 25\ 23| ==> ==> [34]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 5 1 6 9 4 10 2 8 3 15 16 14 25 23 24 18 17 19 13 11 12 21 22\ 20| ==> ==> [35]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 7 1 5 10 3 8 4 9 2 14 15 16 21 20 22 24 23 25 12 13 11 19 18\ 17| ==> ==> [36]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 6 1 5 10 4 9 3 8 2 14 16 15 24 23 25 21 20 22 13 12 11 18 19\ 17| ==> ==> [37]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 3 4 1 8 9 5 10 6 7 13 12 11 18 19 17 21 22 20 24 25 23 14 15\ 16| ==> ==> [38]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 4 3 1 9 8 5 10 7 6 12 13 11 19 18 17 24 25 23 21 22 20 14 16\ 15| ==> ==> [39]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 2 4 1 8 10 6 9 5 7 13 11 12 21 22 20 18 19 17 25 24 23 15 14\ 16| ==> ==> [40]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 2 3 1 9 10 7 8 5 6 12 11 13 24 25 23 19 18 17 22 21 20 16 14\ 15| ==> ==> [41]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 4 2 1 10 8 6 9 7 5 11 13 12 22 21 20 25 24 23 18 19 17 15 16\ 14| ==> ==> [42]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 3 2 1 10 9 7 8 6 5 11 12 13 25 24 23 22 21 20 19 18 17 16 15\ 14| ==> ==> [43]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 6 7 1 8 9 2 10 3 4 16 15 14 19 18 17 22 21 20 25 24 23 11 12\ 13| ==> ==> [44]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 7 6 1 9 8 2 10 4 3 15 16 14 18 19 17 25 24 23 22 21 20 11 13\ 12| ==> ==> [45]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 5 7 1 8 10 3 9 2 4 16 14 15 22 21 20 19 18 17 24 25 23 12 11\ 13| ==> ==> [46]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 5 6 1 9 10 4 8 2 3 15 14 16 25 24 23 18 19 17 21 22 20 13 11\ 12| ==> ==> [47]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 7 5 1 10 8 3 9 4 2 14 16 15 21 22 20 24 25 23 19 18 17 12 13\ 11| ==> ==> [48]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 6 5 1 10 9 4 8 3 2 14 15 16 24 25 23 21 22 20 18 19 17 13 12\ 11| ==> ==> [49]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 5 8 9 1 3 4 6 7 10 17 18 19 11 13 12 14 16 15 21 22 20 24 25\ 23| ==> ==> [50]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 5 9 8 1 4 3 7 6 10 17 19 18 11 12 13 14 15 16 24 25 23 21 22\ 20| ==> ==> [51]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 2 8 9 1 6 7 3 4 10 17 19 18 14 16 15 11 13 12 22 21 20 25 24\ 23| ==> ==> [52]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 2 9 8 1 7 6 4 3 10 17 18 19 14 15 16 11 12 13 25 24 23 22 21\ 20| ==> ==> [53]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 6 8 10 1 2 4 5 7 9 20 21 22 12 13 11 15 16 14 18 19 17 25 24\ 23| ==> ==> [54]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 7 9 10 1 2 3 5 6 8 23 24 25 13 12 11 16 15 14 19 18 17 22 21\ 20| ==> ==> [55]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 6 10 8 1 4 2 7 5 9 20 22 21 12 11 13 15 14 16 25 24 23 18 19\ 17| ==> ==> [56]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 7 10 9 1 3 2 6 5 8 23 25 24 13 11 12 16 14 15 22 21 20 19 18\ 17| ==> ==> [57]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 3 8 10 1 5 7 2 4 9 20 22 21 15 16 14 12 13 11 19 18 17 24 25\ 23| ==> ==> [58]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 4 9 10 1 5 6 2 3 8 23 25 24 16 15 14 13 12 11 18 19 17 21 22\ 20| ==> ==> [59]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 3 10 8 1 7 5 4 2 9 20 21 22 15 14 16 12 11 13 24 25 23 19 18\ 17| ==> ==> [60]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 4 10 9 1 6 5 3 2 8 23 24 25 16 14 15 13 11 12 21 22 20 18 19\ 17| ==> ==> [61]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 8 5 9 3 1 4 6 10 7 18 17 19 13 11 12 21 22 20 14 16 15 24 23\ 25| ==> ==> [62]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 9 5 8 4 1 3 7 10 6 19 17 18 12 11 13 24 25 23 14 15 16 21 20\ 22| ==> ==> [63]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 8 2 9 6 1 7 3 10 4 19 17 18 16 14 15 22 21 20 11 13 12 25 23\ 24| ==> ==> [64]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 9 2 8 7 1 6 4 10 3 18 17 19 15 14 16 25 24 23 11 12 13 22 20\ 21| ==> ==> [65]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 8 6 10 2 1 4 5 9 7 21 20 22 13 12 11 18 19 17 15 16 14 25 23\ 24| ==> ==> [66]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 9 7 10 2 1 3 5 8 6 24 23 25 12 13 11 19 18 17 16 15 14 22 20\ 21| ==> ==> [67]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 10 6 8 4 1 2 7 9 5 22 20 21 11 12 13 25 24 23 15 14 16 18 17\ 19| ==> ==> [68]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 10 7 9 3 1 2 6 8 5 25 23 24 11 13 12 22 21 20 16 14 15 19 17\ 18| ==> ==> [69]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 8 3 10 5 1 7 2 9 4 22 20 21 16 15 14 19 18 17 12 13 11 24 23\ 25| ==> ==> [70]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 9 4 10 5 1 6 2 8 3 25 23 24 15 16 14 18 19 17 13 12 11 21 20\ 22| ==> ==> [71]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 10 3 8 7 1 5 4 9 2 21 20 22 14 15 16 24 25 23 12 11 13 19 17\ 18| ==> ==> [72]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 10 4 9 6 1 5 3 8 2 24 23 25 14 16 15 21 22 20 13 11 12 18 17\ 19| ==> ==> [73]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 8 9 5 3 4 1 10 6 7 18 19 17 13 12 11 21 20 22 24 23 25 14 16\ 15| ==> ==> [74]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 2 9 8 5 4 3 1 10 7 6 19 18 17 12 13 11 24 23 25 21 20 22 14 15\ 16| ==> ==> [75]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 8 9 2 6 7 1 10 3 4 19 18 17 16 15 14 22 20 21 25 23 24 11 13\ 12| ==> ==> [76]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 5 9 8 2 7 6 1 10 4 3 18 19 17 15 16 14 25 23 24 22 20 21 11 12\ 13| ==> ==> [77]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 8 10 6 2 4 1 9 5 7 21 22 20 13 11 12 18 17 19 25 23 24 15 16\ 14| ==> ==> [78]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 9 10 7 2 3 1 8 5 6 24 25 23 12 11 13 19 17 18 22 20 21 16 15\ 14| ==> ==> [79]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 3 10 8 6 4 2 1 9 7 5 22 21 20 11 13 12 25 23 24 18 17 19 15 14\ 16| ==> ==> [80]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 4 10 9 7 3 2 1 8 6 5 25 24 23 11 12 13 22 20 21 19 17 18 16 14\ 15| ==> ==> [81]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 8 10 3 5 7 1 9 2 4 22 21 20 16 14 15 19 17 18 24 23 25 12 13\ 11| ==> ==> [82]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 9 10 4 5 6 1 8 2 3 25 24 23 15 14 16 18 17 19 21 20 22 13 12\ 11| ==> ==> [83]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 6 10 8 3 7 5 1 9 4 2 21 22 20 14 16 15 24 23 25 19 17 18 12 11\ 13| ==> ==> [84]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 7 10 9 4 6 5 1 8 3 2 24 25 23 14 15 16 21 20 22 18 17 19 13 11\ 12| ==> ==> [85]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 8 2 5 9 3 6 10 1 4 7 18 19 17 21 22 20 13 11 12 16 14 15 23 24\ 25| ==> ==> [86]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 9 2 5 8 4 7 10 1 3 6 19 18 17 24 25 23 12 11 13 15 14 16 20 21\ 22| ==> ==> [87]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 8 5 2 9 6 3 10 1 7 4 19 18 17 22 21 20 16 14 15 13 11 12 23 25\ 24| ==> ==> [88]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 9 5 2 8 7 4 10 1 6 3 18 19 17 25 24 23 15 14 16 12 11 13 20 22\ 21| ==> ==> [89]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 8 3 6 10 2 5 9 1 4 7 21 22 20 18 19 17 13 12 11 16 15 14 23 25\ 24| ==> ==> [90]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 9 4 7 10 2 5 8 1 3 6 24 25 23 19 18 17 12 13 11 15 16 14 20 22\ 21| ==> ==> [91]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 8 6 3 10 5 2 9 1 7 4 22 21 20 19 18 17 16 15 14 13 12 11 23 24\ 25| ==> ==> [92]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 9 7 4 10 5 2 8 1 6 3 25 24 23 18 19 17 15 16 14 12 13 11 20 21\ 22| ==> ==> [93]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 10 3 6 8 4 7 9 1 2 5 22 21 20 25 24 23 11 12 13 14 15 16 17 18\ 19| ==> ==> [94]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 10 4 7 9 3 6 8 1 2 5 25 24 23 22 21 20 11 13 12 14 16 15 17 19\ 18| ==> ==> [95]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\ 24 25| ==> | 10 6 3 8 7 4 9 1 5 2 21 22 20 24 25 23 14 15 16 11 12 13 17 19\ 18| ==> ==> [96]: ==> | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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13| ==> ```