## MinLex 416 Subgroups

Programs which generate, solve, and analyze Sudoku puzzles

### MinLex 416 Subgroups

Here is the minLex416 and the subgroups for each, in C code.
Two columns were added to the end of minLex416, the subgroup count and index.
The representation presented is human readable as the priority, while easily crunched by code.
These represent something constant in Sudoku.

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`////  subgroups.h//  minLexGrid////  Created by Wade Whitaker on 5/22/24.//#ifndef subgroups_h#define subgroups_h//typealias ReorderInputData = (row:Int,col:Int,rel:Int)typedef struct {    int        row;    int        col;    int        rel;} Reorder;//int *a = (int[]){3,4,5,6,7,8,0,1,2}; // compound literal//int *b = (int[]){{1,2,3},{4,5,6}};Reorder * subGroups[84] = {    (Reorder[]) { //  0        { 123456789, 123456789, 123456789 }    },    (Reorder[]) { //  1        { 123456789, 123456789, 123456789 },        { 132456789, 123897645, 123897645 }    },    (Reorder[]) { //  2        { 123456789, 123456789, 123456789 },        { 132456789, 132897645, 132897645 }    },    (Reorder[]) { //  3        { 123456789, 123456789, 123456789 },        { 132456789, 132987654, 132987654 }    },    (Reorder[]) { //  4        { 123456789, 123456789, 123456789 },        { 132456789, 321897645, 321897645 }    },    (Reorder[]) { //  5        { 123456789, 123456789, 123456789 },        { 132456789, 321987654, 321987654 }    },    (Reorder[]) { //  6        { 123456789, 123456789, 123456789 },        { 132456789, 564312789, 564312789 }    },    (Reorder[]) { //  7        { 123456789, 123456789, 123456789 },        { 132456789, 645231798, 645231798 }    },    (Reorder[]) { //  8        { 123456789, 123456789, 123456789 },        { 132456789, 654321798, 654321798 }    },    (Reorder[]) { //  9        { 123456789, 123456789, 123456789 },        { 132456789, 654321987, 654321987 }    },    (Reorder[]) { // 10        { 123456789, 123456789, 123456789 },        { 132456789, 789546123, 789546123 }    },    (Reorder[]) { // 11        { 123456789, 123456789, 123456789 },        { 132456789, 798456132, 798456132 }    },    (Reorder[]) { // 12        { 123456789, 123456789, 123456789 },        { 132456789, 798546132, 798546132 }    },    (Reorder[]) { // 13        { 123456789, 123456789, 123456789 },        { 132456789, 897546312, 897546312 }    },    (Reorder[]) { // 14        { 123456789, 123456789, 123456789 },        { 132456789, 987456321, 987456321 }    },    (Reorder[]) { // 15        { 123456789, 123456789, 123456789 },        { 213456789, 123789456, 456123789 }    },    (Reorder[]) { // 16        { 123456789, 123456789, 123456789 },        { 213456789, 132798465, 465132798 }    },    (Reorder[]) { // 17        { 123456789, 123456789, 123456789 },        { 213456789, 132798465, 475136298 }    },    (Reorder[]) { // 18        { 123456789, 123456789, 123456789 },        { 213456789, 321987654, 654321987 }    },    (Reorder[]) { // 19        { 123456789, 123456789, 123456789 },        { 213456789, 456123789, 189457623 }    },    (Reorder[]) { // 20        { 123456789, 123456789, 123456789 },        { 213456789, 456123789, 789456123 }    },    (Reorder[]) { // 21        { 123456789, 123456789, 123456789 },        { 213456789, 456123789, 893457612 }    },    (Reorder[]) { // 22        { 123456789, 123456789, 123456789 },        { 213456789, 546213798, 829547613 }    },    (Reorder[]) { // 23        { 123456789, 123456789, 123456789 },        { 213456789, 987654321, 216983754 }    },    (Reorder[]) { // 24        { 123456789, 123456789, 123456789 },        { 213456789, 987654321, 632981754 }    },    (Reorder[]) { // 25        { 123456789, 123456789, 123456789 },        { 321456789, 123879546, 689451723 }    },    (Reorder[]) { // 26        { 123456789, 123456789, 123456789 },        { 321456789, 123897645, 698451732 }    },    (Reorder[]) { // 27        { 123456789, 123456789, 123456789 },        { 321456789, 123978564, 689451723 }    },    (Reorder[]) { // 28        { 123456789, 123456789, 123456789 },        { 321456789, 123978564, 698451732 }    },    (Reorder[]) { // 29        { 123456789, 123456789, 123456789 },        { 321456789, 123987654, 698451732 }    },    (Reorder[]) { // 30        { 123456789, 123456789, 123456789 },        { 321456789, 213879546, 689541723 }    },    (Reorder[]) { // 31        { 123456789, 123456789, 123456789 },        { 321456789, 213897645, 698541732 }    },    (Reorder[]) { // 32        { 123456789, 123456789, 123456789 },        { 321456789, 213897645, 968542731 }    },    (Reorder[]) { // 33        { 123456789, 123456789, 123456789 },        { 321456789, 456123879, 132789456 }    },    (Reorder[]) { // 34        { 123456789, 123456789, 123456789 },        { 321456789, 456123987, 213789456 }    },    (Reorder[]) { // 35        { 123456789, 123456789, 123456789 },        { 321456789, 465132987, 213798465 }    },    (Reorder[]) { // 36        { 123456789, 123456789, 123456789 },        { 321456789, 564312789, 723896145 }    },    (Reorder[]) { // 37        { 123456789, 123456789, 123456789 },        { 321456789, 564312798, 371896245 }    },    (Reorder[]) { // 38        { 123456789, 123456789, 123456789 },        { 321456789, 654321789, 723986154 }    },    (Reorder[]) { // 39        { 123456789, 123456789, 123456789 },        { 321456789, 654321798, 371986254 }    },    (Reorder[]) { // 40        { 123456789, 123456789, 123456789 },        { 321456789, 654321798, 732986154 }    },    (Reorder[]) { // 41        { 123456789, 123456789, 123456789 },        { 321456789, 654321879, 732986154 }    },    (Reorder[]) { // 42        { 123456789, 123456789, 123456789 },        { 321456789, 654321987, 732986154 }    },    (Reorder[]) { // 43        { 123456789, 123456789, 123456789 },        { 321456789, 789456123, 145237689 }    },    (Reorder[]) { // 44        { 123456789, 123456789, 123456789 },        { 321456789, 789465123, 145237698 }    },    (Reorder[]) { // 45        { 123456789, 123456789, 123456789 },        { 321456789, 798456132, 145237689 }    },    (Reorder[]) { // 46        { 123456789, 123456789, 123456789 },        { 321456789, 798465132, 145237698 }    },    (Reorder[]) { // 47        { 123456789, 123456789, 123456789 },        { 321456789, 879456213, 154327689 }    },    (Reorder[]) { // 48        { 123456789, 123456789, 123456789 },        { 321456789, 897456312, 453127689 }    },    (Reorder[]) { // 49        { 123456789, 123456789, 123456789 },        { 321456789, 897456312, 543217689 }    },    (Reorder[]) { // 50        { 123456789, 123456789, 123456789 },        { 321456789, 978456231, 154327689 }    },    (Reorder[]) { // 51        { 123456789, 123456789, 123456789 },        { 321456789, 987456321, 453127689 }    },    (Reorder[]) { // 52        { 123456789, 123456789, 123456789 },        { 321456789, 987465321, 154327698 }    },    (Reorder[]) { // 53        { 123456789, 123456789, 123456789 },        { 321456789, 987654321, 645231987 }    },    (Reorder[]) { // 54        { 123456789, 123456789, 123456789 },        { 123456789, 789321654, 654987123 },        { 123456789, 654987123, 789321654 }    },    (Reorder[]) { // 55        { 123456789, 123456789, 123456789 },        { 312456789, 987213645, 829316754 },        { 231456789, 546897321, 524986713 }    },    (Reorder[]) { // 56        { 123456789, 123456789, 123456789 },        { 123456789, 132465798, 132465798 },        { 213456789, 456123789, 789456123 },        { 213456789, 465132798, 798465132 }    },    (Reorder[]) { // 57        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 213456789, 456123789, 789456123 },        { 213456789, 645312978, 897564231 },        { 213456789, 564231897, 978645312 }    },    (Reorder[]) { // 58        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 213456789, 123789456, 456123789 },        { 213456789, 312978645, 564231897 },        { 213456789, 231897564, 645312978 }    },    (Reorder[]) { // 59        { 123456789, 123456789, 123456789 },        { 132456789, 123897645, 123897645 },        { 123456789, 978312645, 564897231 },        { 132456789, 978456231, 978456231 },        { 123456789, 564897231, 978312645 },        { 132456789, 564312789, 564312789 }    },    (Reorder[]) { // 60        { 123456789, 123456789, 123456789 },        { 132456789, 123897645, 123897645 },        { 312456789, 897123645, 189236745 },        { 321456789, 897456312, 145237689 },        { 231456789, 456897312, 145896723 },        { 213456789, 456123789, 189457623 }    },    (Reorder[]) { // 61        { 123456789, 123456789, 123456789 },        { 132456789, 123987654, 123987654 },        { 312456789, 987123654, 189326754 },        { 321456789, 987456321, 154327689 },        { 231456789, 456987321, 154986723 },        { 213456789, 456123789, 189457623 }    },    (Reorder[]) { // 62        { 123456789, 123456789, 123456789 },        { 132456789, 132897645, 132897645 },        { 123456789, 789321654, 654987123 },        { 132456789, 798546132, 798546132 },        { 123456789, 654987123, 789321654 },        { 132456789, 645231798, 645231798 }    },    (Reorder[]) { // 63        { 123456789, 123456789, 123456789 },        { 132456789, 213978564, 213978564 },        { 312456789, 879312654, 897132546 },        { 321456789, 789465123, 645231798 },        { 231456789, 564987213, 465879312 },        { 213456789, 654321879, 987654321 }    },    (Reorder[]) { // 64        { 123456789, 123456789, 123456789 },        { 213456789, 123897645, 457126389 },        { 312456789, 897123654, 893216745 },        { 132456789, 897546312, 897546312 },        { 231456789, 456987312, 543896712 },        { 321456789, 456123798, 217896345 }    },    (Reorder[]) { // 65        { 123456789, 123456789, 123456789 },        { 213456789, 123897645, 457126389 },        { 123456789, 897123645, 456897312 },        { 213456789, 897456312, 126893745 },        { 123456789, 456897312, 897123645 },        { 213456789, 456123789, 893457612 }    },    (Reorder[]) { // 66        { 123456789, 123456789, 123456789 },        { 213456789, 132798465, 465132798 },        { 123456789, 897231564, 645978312 },        { 213456789, 879546213, 213879546 },        { 123456789, 645978312, 897231564 },        { 213456789, 654321987, 987654321 }    },    (Reorder[]) { // 67        { 123456789, 123456789, 123456789 },        { 231456789, 123564789, 896127345 },        { 312456789, 123645789, 457893612 },        { 132456789, 987546321, 987546321 },        { 321456789, 987465321, 543217698 },        { 213456789, 987654321, 216983754 }    },    (Reorder[]) { // 68        { 123456789, 123456789, 123456789 },        { 231456789, 231564789, 968317245 },        { 312456789, 312645789, 574892631 },        { 132456789, 465132798, 465132798 },        { 321456789, 654321798, 371986254 },        { 213456789, 546213798, 829547613 }    },    (Reorder[]) { // 69        { 123456789, 123456789, 123456789 },        { 231456789, 312564789, 689237145 },        { 312456789, 231645789, 745891623 },        { 132456789, 645231789, 645231789 },        { 321456789, 564312789, 723896145 },        { 213456789, 456123789, 189457623 }    },    (Reorder[]) { // 70        { 123456789, 123456789, 123456789 },        { 231456789, 312564978, 689237145 },        { 312456789, 231645897, 745891623 },        { 132456789, 798546132, 798546132 },        { 321456789, 879465213, 154327698 },        { 213456789, 987654321, 632981754 }    },    (Reorder[]) { // 71        { 123456789, 123456789, 123456789 },        { 321456789, 123789456, 689451723 },        { 231456789, 789123456, 723451689 },        { 132456789, 789456123, 789456123 },        { 312456789, 456789123, 623457189 },        { 213456789, 456123789, 189457623 }    },    (Reorder[]) { // 72        { 123456789, 123456789, 123456789 },        { 321456789, 123987654, 689451723 },        { 123456789, 789321654, 654987123 },        { 321456789, 789456123, 154327689 },        { 123456789, 654987123, 789321654 },        { 321456789, 654321789, 723986154 }    },    (Reorder[]) { // 73        { 123456789, 123456789, 123456789 },        { 321456789, 213978564, 689541723 },        { 312456789, 897132546, 198326745 },        { 213456789, 987654321, 632981754 },        { 231456789, 465879312, 154896732 },        { 132456789, 645231798, 645231798 }    },    (Reorder[]) { // 74        { 123456789, 123456789, 123456789 },        { 123456789, 132465798, 132465798 },        { 213456789, 123789456, 456123789 },        { 213456789, 132798465, 465132798 },        { 312456789, 789123465, 789132456 },        { 312456789, 798132456, 798123465 },        { 132456789, 789465123, 789465123 },        { 132456789, 798456132, 798456132 },        { 231456789, 456798123, 465789123 },        { 231456789, 465789132, 456798132 },        { 321456789, 456123798, 132789456 },        { 321456789, 465132789, 123798465 }    },    (Reorder[]) { // 75        { 123456789, 123456789, 123456789 },        { 123456789, 132465798, 132465798 },        { 213456789, 123789456, 456123789 },        { 213456789, 132798465, 465132798 },        { 123456789, 789123456, 456789123 },        { 123456789, 798132465, 465798132 },        { 213456789, 789456123, 123789456 },        { 213456789, 798465132, 132798465 },        { 123456789, 456789123, 789123456 },        { 123456789, 465798132, 798132465 },        { 213456789, 456123789, 789456123 },        { 213456789, 465132798, 798465132 }    },    (Reorder[]) { // 76        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 213456789, 132798465, 465132798 },        { 213456789, 321987654, 654321987 },        { 213456789, 213879546, 546213879 },        { 312456789, 789123645, 789231456 },        { 312456789, 978312564, 897312564 },        { 312456789, 897231456, 978123645 },        { 132456789, 798654132, 798654132 },        { 132456789, 987546321, 987546321 },        { 132456789, 879465213, 879465213 },        { 231456789, 456897123, 645789123 },        { 231456789, 645789312, 456897231 },        { 231456789, 564978231, 564978312 },        { 321456789, 465132879, 213798465 },        { 321456789, 654321798, 132987654 },        { 321456789, 546213987, 321879546 }    },    (Reorder[]) { // 77        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 132456789, 132798465, 132798465 },        { 132456789, 321987654, 321987654 },        { 132456789, 213879546, 213879546 },        { 231456789, 978312645, 123564897 },        { 231456789, 897231564, 231645978 },        { 231456789, 789123456, 312456789 },        { 213456789, 987654321, 132987654 },        { 213456789, 879546213, 321879546 },        { 213456789, 798465132, 213798465 },        { 312456789, 645978312, 312564897 },        { 312456789, 564897231, 123645978 },        { 312456789, 456789123, 231456789 },        { 321456789, 654321987, 213987654 },        { 321456789, 546213879, 132879546 },        { 321456789, 465132798, 321798465 }    },    (Reorder[]) { // 78        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 321456789, 132987654, 798465132 },        { 321456789, 321879546, 987654321 },        { 321456789, 213798465, 879546213 },        { 123456789, 978123456, 456789231 },        { 123456789, 897312645, 564897312 },        { 123456789, 789231564, 645978123 },        { 321456789, 987654321, 465132987 },        { 321456789, 879546213, 654321879 },        { 321456789, 798465132, 546213798 },        { 123456789, 645978123, 789231564 },        { 123456789, 564897312, 897312645 },        { 123456789, 456789231, 978123456 },        { 321456789, 654321879, 132987654 },        { 321456789, 546213798, 321879546 },        { 321456789, 465132987, 213798465 }    },    (Reorder[]) { // 79        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 231456789, 123456978, 789123456 },        { 231456789, 312645897, 897231564 },        { 231456789, 231564789, 978312645 },        { 312456789, 123456897, 456789123 },        { 312456789, 312645789, 564897231 },        { 312456789, 231564978, 645978312 },        { 132456789, 654321987, 654321987 },        { 132456789, 546213879, 546213879 },        { 132456789, 465132798, 465132798 },        { 321456789, 654321798, 321987654 },        { 321456789, 546213987, 213879546 },        { 321456789, 465132879, 132798465 },        { 213456789, 654321879, 987654321 },        { 213456789, 546213798, 879546213 },        { 213456789, 465132987, 798465132 }    },    (Reorder[]) { // 80        { 123456789, 123456789, 123456789 },        { 231456789, 123456789, 896127345 },        { 312456789, 123456789, 457893612 },        { 132456789, 123897645, 123897645 },        { 321456789, 123897645, 896453712 },        { 213456789, 123897645, 457126389 },        { 123456789, 897123645, 456897312 },        { 231456789, 897123645, 127453689 },        { 312456789, 897123645, 893126745 },        { 132456789, 897456312, 897456312 },        { 321456789, 897456312, 453127689 },        { 213456789, 897456312, 126893745 },        { 123456789, 456897312, 897123645 },        { 231456789, 456897312, 453896712 },        { 312456789, 456897312, 126457389 },        { 132456789, 456123789, 456123789 },        { 321456789, 456123789, 127896345 },        { 213456789, 456123789, 893457612 }    },    (Reorder[]) { // 81        { 123456789, 123456789, 123456789 },        { 231456789, 231564897, 968317245 },        { 312456789, 312645978, 574892631 },        { 132456789, 321987654, 321987654 },        { 321456789, 213879546, 869542713 },        { 213456789, 132798465, 475136298 },        { 123456789, 978312645, 564897231 },        { 231456789, 789123456, 173452689 },        { 312456789, 897231564, 928316745 },        { 132456789, 879546213, 879546213 },        { 321456789, 798465132, 425137698 },        { 213456789, 987654321, 361982754 },        { 123456789, 564897231, 978312645 },        { 231456789, 645978312, 524896731 },        { 312456789, 456789123, 163457289 },        { 132456789, 465132798, 465132798 },        { 321456789, 654321987, 371986254 },        { 213456789, 546213879, 829547613 }    },    (Reorder[]) { // 82        { 123456789, 123456789, 123456789 },        { 123456789, 312645978, 231564897 },        { 123456789, 231564897, 312645978 },        { 231456789, 123564978, 897123645 },        { 231456789, 312456897, 978231456 },        { 231456789, 231645789, 789312564 },        { 312456789, 123645897, 456897312 },        { 312456789, 312564789, 564978123 },        { 312456789, 231456978, 645789231 },        { 132456789, 123897645, 123897645 },        { 132456789, 312789564, 231978456 },        { 132456789, 231978456, 312789564 },        { 321456789, 123978564, 897456312 },        { 321456789, 312897456, 978564123 },        { 321456789, 231789645, 789645231 },        { 213456789, 123789456, 456123789 },        { 213456789, 312978645, 564231897 },        { 213456789, 231897564, 645312978 },        { 123456789, 789123456, 456789123 },        { 123456789, 978312645, 564897231 },        { 123456789, 897231564, 645978312 },        { 231456789, 789231645, 123645897 },        { 231456789, 978123564, 231456978 },        { 231456789, 897312456, 312564789 },        { 312456789, 789312564, 897312456 },        { 312456789, 978231456, 978123564 },        { 312456789, 897123645, 789231645 },        { 132456789, 789564312, 897645123 },        { 132456789, 978456231, 978456231 },        { 132456789, 897645123, 789564312 },        { 321456789, 789645231, 456312897 },        { 321456789, 978564123, 564123978 },        { 321456789, 897456312, 645231789 },        { 213456789, 789456123, 123789456 },        { 213456789, 978645312, 231897564 },        { 213456789, 897564231, 312978645 },        { 123456789, 456789123, 789123456 },        { 123456789, 645978312, 897231564 },        { 123456789, 564897231, 978312645 },        { 231456789, 456897312, 645897123 },        { 231456789, 645789231, 456978231 },        { 231456789, 564978123, 564789312 },        { 312456789, 456978231, 312456897 },        { 312456789, 645897123, 123564978 },        { 312456789, 564789312, 231645789 },        { 132456789, 456231978, 645123897 },        { 132456789, 645123897, 456231978 },        { 132456789, 564312789, 564312789 },        { 321456789, 456312897, 312897456 },        { 321456789, 645231789, 123978564 },        { 321456789, 564123978, 231789645 },        { 213456789, 456123789, 789456123 },        { 213456789, 645312978, 897564231 },        { 213456789, 564231897, 978645312 }    },    (Reorder[]) { // 83        { 123456789, 123456789, 123456789 },        { 123456789, 132465798, 132465798 },        { 123456789, 312645978, 231564897 },        { 123456789, 321654987, 321654987 },        { 123456789, 231564897, 312645978 },        { 123456789, 213546879, 213546879 },        { 231456789, 123456789, 789123456 },        { 231456789, 132465798, 798132465 },        { 231456789, 312645978, 897231564 },        { 231456789, 321654987, 987321654 },        { 231456789, 231564897, 978312645 },        { 231456789, 213546879, 879213546 },        { 312456789, 123456789, 456789123 },        { 312456789, 132465798, 465798132 },        { 312456789, 312645978, 564897231 },        { 312456789, 321654987, 654987321 },        { 312456789, 231564897, 645978312 },        { 312456789, 213546879, 546879213 },        { 132456789, 123789456, 123789456 },        { 132456789, 132798465, 132798465 },        { 132456789, 312978645, 231897564 },        { 132456789, 321987654, 321987654 },        { 132456789, 231897564, 312978645 },        { 132456789, 213879546, 213879546 },        { 321456789, 123789456, 789456123 },        { 321456789, 132798465, 798465132 },        { 321456789, 312978645, 897564231 },        { 321456789, 321987654, 987654321 },        { 321456789, 231897564, 978645312 },        { 321456789, 213879546, 879546213 },        { 213456789, 123789456, 456123789 },        { 213456789, 132798465, 465132798 },        { 213456789, 312978645, 564231897 },        { 213456789, 321987654, 654321987 },        { 213456789, 231897564, 645312978 },        { 213456789, 213879546, 546213879 },        { 123456789, 789123456, 456789123 },        { 123456789, 798132465, 465798132 },        { 123456789, 978312645, 564897231 },        { 123456789, 987321654, 654987321 },        { 123456789, 897231564, 645978312 },        { 123456789, 879213546, 546879213 },        { 231456789, 789123456, 123456789 },        { 231456789, 798132465, 132465798 },        { 231456789, 978312645, 231564897 },        { 231456789, 987321654, 321654987 },        { 231456789, 897231564, 312645978 },        { 231456789, 879213546, 213546879 },        { 312456789, 789123456, 789123456 },        { 312456789, 798132465, 798132465 },        { 312456789, 978312645, 897231564 },        { 312456789, 987321654, 987321654 },        { 312456789, 897231564, 978312645 },        { 312456789, 879213546, 879213546 },        { 132456789, 789456123, 789456123 },        { 132456789, 798465132, 798465132 },        { 132456789, 978645312, 897564231 },        { 132456789, 987654321, 987654321 },        { 132456789, 897564231, 978645312 },        { 132456789, 879546213, 879546213 },        { 321456789, 789456123, 456123789 },        { 321456789, 798465132, 465132798 },        { 321456789, 978645312, 564231897 },        { 321456789, 987654321, 654321987 },        { 321456789, 897564231, 645312978 },        { 321456789, 879546213, 546213879 },        { 213456789, 789456123, 123789456 },        { 213456789, 798465132, 132798465 },        { 213456789, 978645312, 231897564 },        { 213456789, 987654321, 321987654 },        { 213456789, 897564231, 312978645 },        { 213456789, 879546213, 213879546 },        { 123456789, 456789123, 789123456 },        { 123456789, 465798132, 798132465 },        { 123456789, 645978312, 897231564 },        { 123456789, 654987321, 987321654 },        { 123456789, 564897231, 978312645 },        { 123456789, 546879213, 879213546 },        { 231456789, 456789123, 456789123 },        { 231456789, 465798132, 465798132 },        { 231456789, 645978312, 564897231 },        { 231456789, 654987321, 654987321 },        { 231456789, 564897231, 645978312 },        { 231456789, 546879213, 546879213 },        { 312456789, 456789123, 123456789 },        { 312456789, 465798132, 132465798 },        { 312456789, 645978312, 231564897 },        { 312456789, 654987321, 321654987 },        { 312456789, 564897231, 312645978 },        { 312456789, 546879213, 213546879 },        { 132456789, 456123789, 456123789 },        { 132456789, 465132798, 465132798 },        { 132456789, 645312978, 564231897 },        { 132456789, 654321987, 654321987 },        { 132456789, 564231897, 645312978 },        { 132456789, 546213879, 546213879 },        { 321456789, 456123789, 123789456 },        { 321456789, 465132798, 132798465 },        { 321456789, 645312978, 231897564 },        { 321456789, 654321987, 321987654 },        { 321456789, 564231897, 312978645 },        { 321456789, 546213879, 213879546 },        { 213456789, 456123789, 789456123 },        { 213456789, 465132798, 798465132 },        { 213456789, 645312978, 897564231 },        { 213456789, 654321987, 987654321 },        { 213456789, 564231897, 978645312 },        { 213456789, 546213879, 879546213 }    }};typedef struct {    int        number;    int        row1;    int        row2;    int        row3;    int        count;    int        subgroup;} minLex416Data;minLex416Data minLex416[416] = {    {  1, 123456789, 456789123, 789123456, 108, 83 },    {  2, 123456789, 456789123, 789123465,   4, 56 },    {  3, 123456789, 456789123, 789123564,   6, 57 },    {  4, 123456789, 456789123, 789132465,  12, 74 },    {  5, 123456789, 456789123, 789132546,   2, 18 },    {  6, 123456789, 456789123, 789132564,   1,  0 },    {  7, 123456789, 456789123, 789231564,   6, 58 },    {  8, 123456789, 456789123, 789231645,  18, 76 },    {  9, 123456789, 456789123, 798132465,  12, 75 },    { 10, 123456789, 456789123, 798132546,   2, 20 },    { 11, 123456789, 456789123, 798132564,   2, 20 },    { 12, 123456789, 456789123, 798213564,   2,  4 },    { 13, 123456789, 456789123, 798213654,   6, 66 },    { 14, 123456789, 456789123, 798231564,   2, 15 },    { 15, 123456789, 456789123, 798231645,   2, 16 },    { 16, 123456789, 456789123, 897231564,  54, 82 },    { 17, 123456789, 456789123, 897231645,   6, 57 },    { 18, 123456789, 456789132, 789123546,   2,  9 },    { 19, 123456789, 456789132, 789132546,   2, 53 },    { 20, 123456789, 456789132, 789132564,   1,  0 },    { 21, 123456789, 456789132, 789213456,   2,  5 },    { 22, 123456789, 456789132, 789213645,   1,  0 },    { 23, 123456789, 456789132, 789213654,   2, 34 },    { 24, 123456789, 456789132, 789231546,   1,  0 },    { 25, 123456789, 456789132, 789231564,   2, 35 },    { 26, 123456789, 456789132, 879231564,   2,  2 },    { 27, 123456789, 456789231, 789123645,  18, 79 },    { 28, 123456789, 456789231, 789132546,   2, 33 },    { 29, 123456789, 456789231, 789231564,  18, 78 },    { 30, 123456789, 456789231, 789312456,  18, 77 },    { 31, 123456789, 456789231, 798213645,   6, 63 },    { 32, 123456789, 457189236, 689237145,   2, 43 },    { 33, 123456789, 457189236, 689237154,   1,  0 },    { 34, 123456789, 457189236, 689237415,   1,  0 },    { 35, 123456789, 457189236, 689237451,   1,  0 },    { 36, 123456789, 457189236, 689237514,   2, 41 },    { 37, 123456789, 457189236, 689237541,   1,  0 },    { 38, 123456789, 457189236, 689273145,   1,  0 },    { 39, 123456789, 457189236, 689273154,   1,  0 },    { 40, 123456789, 457189236, 689273415,   1,  0 },    { 41, 123456789, 457189236, 689273451,   2, 24 },    { 42, 123456789, 457189236, 689273514,   1,  0 },    { 43, 123456789, 457189236, 689273541,   1,  0 },    { 44, 123456789, 457189236, 689327145,   1,  0 },    { 45, 123456789, 457189236, 689327154,   2, 38 },    { 46, 123456789, 457189236, 689327415,   1,  0 },    { 47, 123456789, 457189236, 689327451,   1,  0 },    { 48, 123456789, 457189236, 689327514,   1,  0 },    { 49, 123456789, 457189236, 689327541,   1,  0 },    { 50, 123456789, 457189236, 689372145,   1,  0 },    { 51, 123456789, 457189236, 689372154,   1,  0 },    { 52, 123456789, 457189236, 689372415,   1,  0 },    { 53, 123456789, 457189236, 689372451,   2, 24 },    { 54, 123456789, 457189236, 689372514,   2, 27 },    { 55, 123456789, 457189236, 689372541,   1,  0 },    { 56, 123456789, 457189236, 689723145,   1,  0 },    { 57, 123456789, 457189236, 689723154,   1,  0 },    { 58, 123456789, 457189236, 689723415,   1,  0 },    { 59, 123456789, 457189236, 689723514,   1,  0 },    { 60, 123456789, 457189236, 689723541,   1,  0 },    { 61, 123456789, 457189236, 689732145,   1,  0 },    { 62, 123456789, 457189236, 689732154,   1,  0 },    { 63, 123456789, 457189236, 689732415,   1,  0 },    { 64, 123456789, 457189236, 689732514,   1,  0 },    { 65, 123456789, 457189236, 689732541,   1,  0 },    { 66, 123456789, 457189236, 698237145,   1,  0 },    { 67, 123456789, 457189236, 698237154,   2, 29 },    { 68, 123456789, 457189236, 698237415,   1,  0 },    { 69, 123456789, 457189236, 698237514,   1,  0 },    { 70, 123456789, 457189236, 698237541,   1,  0 },    { 71, 123456789, 457189236, 698273145,   2, 44 },    { 72, 123456789, 457189236, 698273154,   1,  0 },    { 73, 123456789, 457189236, 698273415,   1,  0 },    { 74, 123456789, 457189236, 698273514,   1,  0 },    { 75, 123456789, 457189236, 698273541,   2, 24 },    { 76, 123456789, 457189236, 698327145,   1,  0 },    { 77, 123456789, 457189236, 698327154,   1,  0 },    { 78, 123456789, 457189236, 698327415,   1,  0 },    { 79, 123456789, 457189236, 698327541,   1,  0 },    { 80, 123456789, 457189236, 698372145,   1,  0 },    { 81, 123456789, 457189236, 698372154,   1,  0 },    { 82, 123456789, 457189236, 698372415,   1,  0 },    { 83, 123456789, 457189236, 698372514,   1,  0 },    { 84, 123456789, 457189236, 698372541,   2, 24 },    { 85, 123456789, 457189236, 698723145,   1,  0 },    { 86, 123456789, 457189236, 698723154,   1,  0 },    { 87, 123456789, 457189236, 698723415,   1,  0 },    { 88, 123456789, 457189236, 698723514,   1,  0 },    { 89, 123456789, 457189236, 698732145,   1,  0 },    { 90, 123456789, 457189236, 698732154,   1,  0 },    { 91, 123456789, 457189236, 698732415,   1,  0 },    { 92, 123456789, 457189236, 698732514,   1,  0 },    { 93, 123456789, 457189236, 869237145,   1,  0 },    { 94, 123456789, 457189236, 869237514,   1,  0 },    { 95, 123456789, 457189236, 869273145,   1,  0 },    { 96, 123456789, 457189236, 869273154,   1,  0 },    { 97, 123456789, 457189236, 869273415,   2, 24 },    { 98, 123456789, 457189236, 869273514,   2,  2 },    { 99, 123456789, 457189236, 869327154,   1,  0 },    {100, 123456789, 457189236, 869327415,   1,  0 },    {101, 123456789, 457189236, 869327514,   2, 47 },    {102, 123456789, 457189236, 869372145,   1,  0 },    {103, 123456789, 457189236, 869372154,   1,  0 },    {104, 123456789, 457189236, 869372415,   6, 73 },    {105, 123456789, 457189236, 869372514,   1,  0 },    {106, 123456789, 457189236, 869723145,   1,  0 },    {107, 123456789, 457189236, 869723154,   1,  0 },    {108, 123456789, 457189236, 869723514,   1,  0 },    {109, 123456789, 457189236, 869732145,   1,  0 },    {110, 123456789, 457189236, 869732154,   1,  0 },    {111, 123456789, 457189236, 896237145,   1,  0 },    {112, 123456789, 457189236, 896237154,   1,  0 },    {113, 123456789, 457189236, 896237514,   1,  0 },    {114, 123456789, 457189236, 896273145,   2, 24 },    {115, 123456789, 457189236, 896273154,   1,  0 },    {116, 123456789, 457189236, 896273514,   1,  0 },    {117, 123456789, 457189236, 896327145,   1,  0 },    {118, 123456789, 457189236, 896327154,   1,  0 },    {119, 123456789, 457189236, 896327514,   1,  0 },    {120, 123456789, 457189236, 896372145,   2, 24 },    {121, 123456789, 457189236, 896372154,   1,  0 },    {122, 123456789, 457189236, 896372514,   2,  1 },    {123, 123456789, 457189236, 896723154,   1,  0 },    {124, 123456789, 457189236, 896723514,   2,  8 },    {125, 123456789, 457189236, 896732154,   1,  0 },    {126, 123456789, 457189236, 896732514,   1,  0 },    {127, 123456789, 457189236, 968237154,   1,  0 },    {128, 123456789, 457189236, 968237514,   1,  0 },    {129, 123456789, 457189236, 968273514,   2, 24 },    {130, 123456789, 457189236, 968327154,   1,  0 },    {131, 123456789, 457189236, 968327514,   1,  0 },    {132, 123456789, 457189236, 968372154,   1,  0 },    {133, 123456789, 457189236, 968372514,   6, 70 },    {134, 123456789, 457189236, 968723154,   1,  0 },    {135, 123456789, 457189236, 968732154,   1,  0 },    {136, 123456789, 457189236, 986237154,   1,  0 },    {137, 123456789, 457189236, 986273154,   2, 24 },    {138, 123456789, 457189236, 986327154,   1,  0 },    {139, 123456789, 457189236, 986372154,   2, 24 },    {140, 123456789, 457189263, 689237145,   1,  0 },    {141, 123456789, 457189263, 689237415,   1,  0 },    {142, 123456789, 457189263, 689237451,   2, 42 },    {143, 123456789, 457189263, 689237514,   1,  0 },    {144, 123456789, 457189263, 689273154,   2, 46 },    {145, 123456789, 457189263, 689273415,   1,  0 },    {146, 123456789, 457189263, 689273451,   1,  0 },    {147, 123456789, 457189263, 689273514,   1,  0 },    {148, 123456789, 457189263, 689273541,   2, 25 },    {149, 123456789, 457189263, 689327154,   2, 38 },    {150, 123456789, 457189263, 689327415,   1,  0 },    {151, 123456789, 457189263, 689327514,   1,  0 },    {152, 123456789, 457189263, 689327541,   1,  0 },    {153, 123456789, 457189263, 689372145,   1,  0 },    {154, 123456789, 457189263, 689372154,   1,  0 },    {155, 123456789, 457189263, 689372415,   1,  0 },    {156, 123456789, 457189263, 689372451,   1,  0 },    {157, 123456789, 457189263, 689372514,   1,  0 },    {158, 123456789, 457189263, 689723145,   1,  0 },    {159, 123456789, 457189263, 689723154,   1,  0 },    {160, 123456789, 457189263, 689723451,   1,  0 },    {161, 123456789, 457189263, 689732145,   1,  0 },    {162, 123456789, 457189263, 689732154,   1,  0 },    {163, 123456789, 457189263, 689732415,   1,  0 },    {164, 123456789, 457189263, 689732451,   1,  0 },    {165, 123456789, 457189263, 689732514,   1,  0 },    {166, 123456789, 457189263, 689732541,   1,  0 },    {167, 123456789, 457189263, 698237154,   2, 45 },    {168, 123456789, 457189263, 698237415,   1,  0 },    {169, 123456789, 457189263, 698237451,   1,  0 },    {170, 123456789, 457189263, 698237514,   1,  0 },    {171, 123456789, 457189263, 698273145,   1,  0 },    {172, 123456789, 457189263, 698273415,   1,  0 },    {173, 123456789, 457189263, 698273451,   1,  0 },    {174, 123456789, 457189263, 698273514,   1,  0 },    {175, 123456789, 457189263, 698327145,   2, 26 },    {176, 123456789, 457189263, 698327154,   1,  0 },    {177, 123456789, 457189263, 698327415,   1,  0 },    {178, 123456789, 457189263, 698327451,   1,  0 },    {179, 123456789, 457189263, 698327514,   1,  0 },    {180, 123456789, 457189263, 698372154,   1,  0 },    {181, 123456789, 457189263, 698372415,   1,  0 },    {182, 123456789, 457189263, 698372514,   1,  0 },    {183, 123456789, 457189263, 698372541,   1,  0 },    {184, 123456789, 457189263, 698732145,   1,  0 },    {185, 123456789, 457189263, 698732154,   1,  0 },    {186, 123456789, 457189263, 698732451,   1,  0 },    {187, 123456789, 457189263, 869237154,   1,  0 },    {188, 123456789, 457189263, 869237415,   1,  0 },    {189, 123456789, 457189263, 869237514,   1,  0 },    {190, 123456789, 457189263, 869273451,   2, 30 },    {191, 123456789, 457189263, 869327415,   1,  0 },    {192, 123456789, 457189263, 869327451,   1,  0 },    {193, 123456789, 457189263, 869327514,   1,  0 },    {194, 123456789, 457189263, 869372145,   1,  0 },    {195, 123456789, 457189263, 869372154,   1,  0 },    {196, 123456789, 457189263, 869372514,   1,  0 },    {197, 123456789, 457189263, 896237145,   1,  0 },    {198, 123456789, 457189263, 896237154,   1,  0 },    {199, 123456789, 457189263, 896237451,   1,  0 },    {200, 123456789, 457189263, 896327145,   1,  0 },    {201, 123456789, 457189263, 896327154,   1,  0 },    {202, 123456789, 457189263, 896327415,   1,  0 },    {203, 123456789, 457189263, 896327451,   1,  0 },    {204, 123456789, 457189263, 896327514,   1,  0 },    {205, 123456789, 457189263, 896327541,   1,  0 },    {206, 123456789, 457189263, 896372145,   1,  0 },    {207, 123456789, 457189263, 896372154,   1,  0 },    {208, 123456789, 457189263, 896372451,   1,  0 },    {209, 123456789, 457189263, 968327145,   1,  0 },    {210, 123456789, 457189263, 968327154,   2, 31 },    {211, 123456789, 457189263, 968327415,   1,  0 },    {212, 123456789, 457189263, 968327514,   1,  0 },    {213, 123456789, 457189263, 968327541,   2, 50 },    {214, 123456789, 457189263, 968372145,   2, 36 },    {215, 123456789, 457189263, 986327145,   1,  0 },    {216, 123456789, 457189263, 986327154,   1,  0 },    {217, 123456789, 457189263, 986327451,   1,  0 },    {218, 123456789, 457189326, 689237451,   1,  0 },    {219, 123456789, 457189326, 689237514,   2, 41 },    {220, 123456789, 457189326, 689237541,   1,  0 },    {221, 123456789, 457189326, 689273145,   1,  0 },    {222, 123456789, 457189326, 689273451,   1,  0 },    {223, 123456789, 457189326, 689273541,   1,  0 },    {224, 123456789, 457189326, 689327154,   6, 72 },    {225, 123456789, 457189326, 689327451,   1,  0 },    {226, 123456789, 457189326, 689327541,   1,  0 },    {227, 123456789, 457189326, 689372415,   1,  0 },    {228, 123456789, 457189326, 689372541,   1,  0 },    {229, 123456789, 457189326, 689723145,   1,  0 },    {230, 123456789, 457189326, 689723415,   1,  0 },    {231, 123456789, 457189326, 689732145,   1,  0 },    {232, 123456789, 457189326, 689732415,   1,  0 },    {233, 123456789, 457189326, 689732514,   1,  0 },    {234, 123456789, 457189326, 689732541,   1,  0 },    {235, 123456789, 457189326, 698237145,   3, 54 },    {236, 123456789, 457189326, 698237541,   1,  0 },    {237, 123456789, 457189326, 698273514,   2, 28 },    {238, 123456789, 457189326, 698273541,   1,  0 },    {239, 123456789, 457189326, 698732415,   1,  0 },    {240, 123456789, 457189326, 869372514,   6, 62 },    {241, 123456789, 457189623, 689237145,   2, 40 },    {242, 123456789, 457189623, 689237154,   1,  0 },    {243, 123456789, 457189623, 689273145,   1,  0 },    {244, 123456789, 457189623, 689273154,   1,  0 },    {245, 123456789, 457189623, 689273541,   2, 10 },    {246, 123456789, 457189623, 689327145,   1,  0 },    {247, 123456789, 457189623, 689327154,   2, 38 },    {248, 123456789, 457189623, 689372145,   1,  0 },    {249, 123456789, 457189623, 689372154,   1,  0 },    {250, 123456789, 457189623, 689372514,   2, 12 },    {251, 123456789, 457189623, 689723145,   2, 19 },    {252, 123456789, 457189623, 689723154,   2, 19 },    {253, 123456789, 457189623, 689723415,   2, 19 },    {254, 123456789, 457189623, 689723451,   6, 71 },    {255, 123456789, 457189623, 689723514,   2, 19 },    {256, 123456789, 457189623, 689723541,   2, 19 },    {257, 123456789, 457189623, 689732145,   1,  0 },    {258, 123456789, 457189623, 689732154,   1,  0 },    {259, 123456789, 457189623, 689732415,   2, 11 },    {260, 123456789, 457189623, 689732451,   1,  0 },    {261, 123456789, 457189623, 689732514,   1,  0 },    {262, 123456789, 457189623, 689732541,   1,  0 },    {263, 123456789, 457189623, 698237145,   1,  0 },    {264, 123456789, 457189623, 698237154,   1,  0 },    {265, 123456789, 457189623, 698237541,   1,  0 },    {266, 123456789, 457189623, 698273145,   1,  0 },    {267, 123456789, 457189623, 698273154,   1,  0 },    {268, 123456789, 457189623, 698327145,   1,  0 },    {269, 123456789, 457189623, 698327154,   1,  0 },    {270, 123456789, 457189623, 698327514,   1,  0 },    {271, 123456789, 457189623, 698372145,   1,  0 },    {272, 123456789, 457189623, 698372154,   1,  0 },    {273, 123456789, 457189623, 698732145,   2, 19 },    {274, 123456789, 457189623, 698732154,   2, 19 },    {275, 123456789, 457189623, 698732415,   2, 19 },    {276, 123456789, 457189623, 698732514,   2, 19 },    {277, 123456789, 457189623, 698732541,   2, 19 },    {278, 123456789, 457189623, 869237145,   1,  0 },    {279, 123456789, 457189623, 869273145,   2, 19 },    {280, 123456789, 457189623, 869273154,   2, 19 },    {281, 123456789, 457189623, 869273451,   2, 19 },    {282, 123456789, 457189623, 869327154,   1,  0 },    {283, 123456789, 457189623, 869372145,   1,  0 },    {284, 123456789, 457189623, 869372154,   2,  7 },    {285, 123456789, 457189623, 896237145,   2, 19 },    {286, 123456789, 457189623, 896237154,   2, 19 },    {287, 123456789, 457189623, 896237415,   2, 19 },    {288, 123456789, 457189623, 896237451,   2, 19 },    {289, 123456789, 457189623, 896237514,   6, 60 },    {290, 123456789, 457189623, 896237541,   2, 19 },    {291, 123456789, 457189623, 896327145,   1,  0 },    {292, 123456789, 457189623, 896327154,   1,  0 },    {293, 123456789, 457189623, 896327415,   1,  0 },    {294, 123456789, 457189623, 896327451,   1,  0 },    {295, 123456789, 457189623, 896327514,   1,  0 },    {296, 123456789, 457189623, 896372145,   1,  0 },    {297, 123456789, 457189623, 896372154,   1,  0 },    {298, 123456789, 457189623, 896372451,   2, 52 },    {299, 123456789, 457189623, 968327145,   1,  0 },    {300, 123456789, 457189623, 968327154,   1,  0 },    {301, 123456789, 457189623, 968327415,   1,  0 },    {302, 123456789, 457189623, 968372145,   6, 69 },    {303, 123456789, 457189623, 968372154,   2, 19 },    {304, 123456789, 457189623, 986327145,   2, 19 },    {305, 123456789, 457189623, 986327154,   2, 19 },    {306, 123456789, 457189623, 986327415,   2, 19 },    {307, 123456789, 457189623, 986327451,   6, 61 },    {308, 123456789, 457189623, 986327514,   2, 19 },    {309, 123456789, 457189623, 986327541,   2, 19 },    {310, 123456789, 457189632, 689237145,   2, 40 },    {311, 123456789, 457189632, 689273145,   1,  0 },    {312, 123456789, 457189632, 689273154,   1,  0 },    {313, 123456789, 457189632, 689273514,   1,  0 },    {314, 123456789, 457189632, 689327154,   2, 38 },    {315, 123456789, 457189632, 689372145,   1,  0 },    {316, 123456789, 457189632, 689372154,   1,  0 },    {317, 123456789, 457189632, 689723145,   1,  0 },    {318, 123456789, 457189632, 689723514,   1,  0 },    {319, 123456789, 457189632, 689732145,   1,  0 },    {320, 123456789, 457189632, 689732154,   1,  0 },    {321, 123456789, 457189632, 689732514,   1,  0 },    {322, 123456789, 457189632, 689732541,   1,  0 },    {323, 123456789, 457189632, 698237145,   1,  0 },    {324, 123456789, 457189632, 698237154,   1,  0 },    {325, 123456789, 457189632, 698237514,   1,  0 },    {326, 123456789, 457189632, 698273145,   1,  0 },    {327, 123456789, 457189632, 698327145,   1,  0 },    {328, 123456789, 457189632, 698327154,   1,  0 },    {329, 123456789, 457189632, 698327541,   1,  0 },    {330, 123456789, 457189632, 698372154,   1,  0 },    {331, 123456789, 457189632, 698732145,   1,  0 },    {332, 123456789, 457189632, 698732514,   1,  0 },    {333, 123456789, 457189632, 869273145,   1,  0 },    {334, 123456789, 457189632, 869372145,   2,  7 },    {335, 123456789, 457189632, 896237145,   1,  0 },    {336, 123456789, 457189632, 896237415,   1,  0 },    {337, 123456789, 457189632, 896327145,   1,  0 },    {338, 123456789, 457189632, 896327154,   1,  0 },    {339, 123456789, 457189632, 896327451,   1,  0 },    {340, 123456789, 457189632, 896327541,   1,  0 },    {341, 123456789, 457189632, 896372145,   1,  0 },    {342, 123456789, 457189632, 896372154,   1,  0 },    {343, 123456789, 457189632, 896372451,   1,  0 },    {344, 123456789, 457189632, 968327145,   1,  0 },    {345, 123456789, 457189632, 968327154,   1,  0 },    {346, 123456789, 457189632, 968327451,   2,  3 },    {347, 123456789, 457189632, 986327145,   1,  0 },    {348, 123456789, 457289163, 689173452,  18, 81 },    {349, 123456789, 457289163, 689713254,   2, 17 },    {350, 123456789, 457289163, 698137425,   2, 17 },    {351, 123456789, 457289163, 698137524,   1,  0 },    {352, 123456789, 457289163, 698317254,   2, 32 },    {353, 123456789, 457289163, 698317524,   2, 17 },    {354, 123456789, 457289163, 698713254,   2, 17 },    {355, 123456789, 457289163, 869713245,   1,  0 },    {356, 123456789, 457289163, 869731245,   1,  0 },    {357, 123456789, 457289163, 869731524,   1,  0 },    {358, 123456789, 457289163, 896317245,   1,  0 },    {359, 123456789, 457289163, 896731524,   6, 59 },    {360, 123456789, 457289613, 689173245,   2, 39 },    {361, 123456789, 457289613, 689713245,   1,  0 },    {362, 123456789, 457289613, 689713254,   1,  0 },    {363, 123456789, 457289613, 698137254,   1,  0 },    {364, 123456789, 457289613, 698317245,   1,  0 },    {365, 123456789, 457289613, 698317254,   1,  0 },    {366, 123456789, 457289613, 698713245,   1,  0 },    {367, 123456789, 457289613, 869713245,   1,  0 },    {368, 123456789, 457289613, 869731245,   1,  0 },    {369, 123456789, 457289613, 869731254,   1,  0 },    {370, 123456789, 457289613, 896137245,   1,  0 },    {371, 123456789, 457289613, 896137254,   1,  0 },    {372, 123456789, 457289613, 896317245,   1,  0 },    {373, 123456789, 457289613, 896317425,   1,  0 },    {374, 123456789, 457289613, 896731245,   1,  0 },    {375, 123456789, 457289613, 896731254,   2,  6 },    {376, 123456789, 457289613, 968137245,   1,  0 },    {377, 123456789, 457289613, 968137254,   2, 37 },    {378, 123456789, 457289613, 968731245,   1,  0 },    {379, 123456789, 457289613, 986137245,   1,  0 },    {380, 123456789, 457289631, 689173245,   6, 68 },    {381, 123456789, 457289631, 689713254,   1,  0 },    {382, 123456789, 457289631, 698317254,   1,  0 },    {383, 123456789, 457289631, 869713245,   2, 22 },    {384, 123456789, 457289631, 869713254,   2, 22 },    {385, 123456789, 457289631, 869731245,   1,  0 },    {386, 123456789, 457289631, 869731254,   1,  0 },    {387, 123456789, 457289631, 896137245,   1,  0 },    {388, 123456789, 457289631, 896137254,   1,  0 },    {389, 123456789, 457289631, 896137425,   3, 55 },    {390, 123456789, 457289631, 896317245,   2, 22 },    {391, 123456789, 457289631, 896317254,   2, 22 },    {392, 123456789, 457289631, 896731245,   2,  6 },    {393, 123456789, 457289631, 968137254,   2, 37 },    {394, 123456789, 457289631, 968731245,   2, 22 },    {395, 123456789, 457289631, 968731254,   2, 22 },    {396, 123456789, 457289631, 986137245,   2, 22 },    {397, 123456789, 457289631, 986137254,   2, 22 },    {398, 123456789, 457389612, 896127345,   2, 48 },    {399, 123456789, 457389612, 896127354,   1,  0 },    {400, 123456789, 457389612, 896172345,   2, 23 },    {401, 123456789, 457389612, 896172354,   2, 13 },    {402, 123456789, 457389612, 896217345,   1,  0 },    {403, 123456789, 457389612, 896217354,   1,  0 },    {404, 123456789, 457389612, 896271345,   6, 67 },    {405, 123456789, 457389612, 896271354,   1,  0 },    {406, 123456789, 457389612, 896712354,   1,  0 },    {407, 123456789, 457389612, 896721354,   2, 14 },    {408, 123456789, 457389612, 986172354,   2, 23 },    {409, 123456789, 457389612, 986217354,   1,  0 },    {410, 123456789, 457389621, 896127345,   1,  0 },    {411, 123456789, 457389621, 896217354,   2, 49 },    {412, 123456789, 457389621, 986127354,   2, 51 },    {413, 123456789, 457893612, 896127345,  36, 80 },    {414, 123456789, 457893612, 896127354,   4, 21 },    {415, 123456789, 457893612, 896217354,  12, 64 },    {416, 123456789, 457893612, 986217354,  12, 65 }};#endif /* subgroups_h */`
Sojourner9

Posts: 34
Joined: 10 March 2018

### Re: MinLex 416 Subgroups

Hi,
It happens that I am just working (again) on the mapping of a band to the minlex form and reverse.
I don't want to pollute this thread, but this already exists in other forms.

Here is the minlex table of the 416 band1 that I picked years ago somewhere here. This table shows only the last 26 digits, after the start 12345678945
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`   "6789123789123456", "6789123789123465", "6789123789123564", "6789123789132465",   "6789123789132546", "6789123789132564", "6789123789231564", "6789123789231645",   "6789123798132465", "6789123798132546", "6789123798132564", "6789123798213564",   "6789123798213654", "6789123798231564", "6789123798231645", "6789123897231564",   "6789123897231645", "6789132789123546", "6789132789132546", "6789132789132564",   "6789132789213456", "6789132789213645", "6789132789213654", "6789132789231546",   "6789132789231564", "6789132879231564", "6789231789123645", "6789231789132546",   "6789231789231564", "6789231789312456", "6789231798213645", "7189236689237145", //31    "7189236689237154", "7189236689237415", "7189236689237451", "7189236689237514",   "7189236689237541", "7189236689273145", "7189236689273154", "7189236689273415",//40   "7189236689273451", "7189236689273514", "7189236689273541", "7189236689327145",   "7189236689327154", "7189236689327415", "7189236689327451", "7189236689327514",   "7189236689327541", "7189236689372145", "7189236689372154", "7189236689372415",   "7189236689372451", "7189236689372514", "7189236689372541", "7189236689723145",   "7189236689723154", "7189236689723415", "7189236689723514", "7189236689723541",   "7189236689732145", "7189236689732154", "7189236689732415", "7189236689732514",   "7189236689732541", "7189236698237145", "7189236698237154", "7189236698237415",   "7189236698237514", "7189236698237541", "7189236698273145", "7189236698273154",   "7189236698273415", "7189236698273514", "7189236698273541", "7189236698327145",   "7189236698327154", "7189236698327415", "7189236698327541", "7189236698372145",//80   "7189236698372154", "7189236698372415", "7189236698372514", "7189236698372541",   "7189236698723145", "7189236698723154", "7189236698723415", "7189236698723514",   "7189236698732145", "7189236698732154", "7189236698732415", "7189236698732514",   "7189236869237145", "7189236869237514", "7189236869273145", "7189236869273154",   "7189236869273415", "7189236869273514", "7189236869327154", "7189236869327415",   "7189236869327514", "7189236869372145", "7189236869372154", "7189236869372415",   "7189236869372514", "7189236869723145", "7189236869723154", "7189236869723514",   "7189236869732145", "7189236869732154", "7189236896237145", "7189236896237154",   "7189236896237514", "7189236896273145", "7189236896273154", "7189236896273514",   "7189236896327145", "7189236896327154", "7189236896327514", "7189236896372145",//120   "7189236896372154", "7189236896372514", "7189236896723154", "7189236896723514",   "7189236896732154", "7189236896732514", "7189236968237154", "7189236968237514",   "7189236968273514", "7189236968327154", "7189236968327514", "7189236968372154",   "7189236968372514", "7189236968723154", "7189236968732154", "7189236986237154",   "7189236986273154", "7189236986327154", "7189236986372154", "7189263689237145",//  139   "7189263689237415", "7189263689237451", "7189263689237514", "7189263689273154",   "7189263689273415", "7189263689273451", "7189263689273514", "7189263689273541",   "7189263689327154", "7189263689327415", "7189263689327514", "7189263689327541",   "7189263689372145", "7189263689372154", "7189263689372415", "7189263689372451",   "7189263689372514", "7189263689723145", "7189263689723154", "7189263689723451",//160   "7189263689732145", "7189263689732154", "7189263689732415", "7189263689732451",   "7189263689732514", "7189263689732541", "7189263698237154", "7189263698237415",   "7189263698237451", "7189263698237514", "7189263698273145", "7189263698273415",   "7189263698273451", "7189263698273514", "7189263698327145", "7189263698327154",   "7189263698327415", "7189263698327451", "7189263698327514", "7189263698372154",   "7189263698372415", "7189263698372514", "7189263698372541", "7189263698732145",   "7189263698732154", "7189263698732451", "7189263869237154", "7189263869237415",   "7189263869237514", "7189263869273451", "7189263869327415", "7189263869327451",   "7189263869327514", "7189263869372145", "7189263869372154", "7189263869372514",   "7189263896237145", "7189263896237154", "7189263896237451", "7189263896327145",//200   "7189263896327154", "7189263896327415", "7189263896327451", "7189263896327514",   "7189263896327541", "7189263896372145", "7189263896372154", "7189263896372451",   "7189263968327145", "7189263968327154", "7189263968327415", "7189263968327514",   "7189263968327541", "7189263968372145", "7189263986327145", "7189263986327154",   "7189263986327451", "7189326689237451", "7189326689237514", "7189326689237541",// 217   "7189326689273145", "7189326689273451", "7189326689273541", "7189326689327154",   "7189326689327451", "7189326689327541", "7189326689372415", "7189326689372541",   "7189326689723145", "7189326689723415", "7189326689732145", "7189326689732415",   "7189326689732514", "7189326689732541", "7189326698237145", "7189326698237541",   "7189326698273514", "7189326698273541", "7189326698732415", "7189326869372514",// 236   "7189623689237145", "7189623689237154", "7189623689273145", "7189623689273154",   "7189623689273541", "7189623689327145", "7189623689327154", "7189623689372145",   "7189623689372154", "7189623689372514", "7189623689723145", "7189623689723154",   "7189623689723415", "7189623689723451", "7189623689723514", "7189623689723541",   "7189623689732145", "7189623689732154", "7189623689732415", "7189623689732451",   "7189623689732514", "7189623689732541", "7189623698237145", "7189623698237154",   "7189623698237541", "7189623698273145", "7189623698273154", "7189623698327145",   "7189623698327154", "7189623698327514", "7189623698372145", "7189623698372154",   "7189623698732145", "7189623698732154", "7189623698732415", "7189623698732514",   "7189623698732541", "7189623869237145", "7189623869273145", "7189623869273154",//280   "7189623869273451", "7189623869327154", "7189623869372145", "7189623869372154",   "7189623896237145", "7189623896237154", "7189623896237415", "7189623896237451",   "7189623896237514", "7189623896237541", "7189623896327145", "7189623896327154",   "7189623896327415", "7189623896327451", "7189623896327514", "7189623896372145",   "7189623896372154", "7189623896372451", "7189623968327145", "7189623968327154",//300   "7189623968327415", "7189623968372145", "7189623968372154", "7189623986327145",    "7189623986327154", "7189623986327415", "7189623986327451", "7189623986327514",   "7189623986327541", "7189632689237145", "7189632689273145", "7189632689273154", // 309   "7189632689273514", "7189632689327154", "7189632689372145", "7189632689372154",   "7189632689723145", "7189632689723514", "7189632689732145", "7189632689732154",//320   "7189632689732514", "7189632689732541", "7189632698237145", "7189632698237154",   "7189632698237514", "7189632698273145", "7189632698327145", "7189632698327154",   "7189632698327541", "7189632698372154", "7189632698732145", "7189632698732514",   "7189632869273145", "7189632869372145", "7189632896237145", "7189632896237415",   "7189632896327145", "7189632896327154", "7189632896327451", "7189632896327541",   "7189632896372145", "7189632896372154", "7189632896372451", "7189632968327145",   "7189632968327154", "7189632968327451", "7189632986327145", "7289163689173452",   "7289163689713254", "7289163698137425", "7289163698137524", "7289163698317254",   "7289163698317524", "7289163698713254", "7289163869713245", "7289163869731245",   "7289163869731524", "7289163896317245", "7289163896731524", "7289613689173245",//360   "7289613689713245", "7289613689713254", "7289613698137254", "7289613698317245",   "7289613698317254", "7289613698713245", "7289613869713245", "7289613869731245",   "7289613869731254", "7289613896137245", "7289613896137254", "7289613896317245",   "7289613896317425", "7289613896731245", "7289613896731254", "7289613968137245",   "7289613968137254", "7289613968731245", "7289613986137245", "7289631689173245",//380   "7289631689713254", "7289631698317254", "7289631869713245", "7289631869713254",   "7289631869731245", "7289631869731254", "7289631896137245", "7289631896137254",   "7289631896137425", "7289631896317245", "7289631896317254", "7289631896731245",   "7289631968137254", "7289631968731245", "7289631968731254", "7289631986137245",   "7289631986137254", "7389612896127345", "7389612896127354", "7389612896172345",//400   "7389612896172354", "7389612896217345", "7389612896217354", "7389612896271345",    "7389612896271354", "7389612896712354", "7389612896721354", "7389612986172354",   "7389612986217354", "7389621896127345", "7389621896217354", "7389621986127354",   "7893612896127345", "7893612896127354", "7893612896217354", "7893612986217354",`

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`{0,{0,1,2},{0,2,1,3,5,4,6,8,7},{0,2,1,3,5,4,6,8,7}},{0,{0,1,2},{1,0,2,4,3,5,7,6,8},{1,0,2,4,3,5,7,6,8}},{0,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6}},{0,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7}},{0,{0,1,2},{2,1,0,5,4,3,8,7,6},{2,1,0,5,4,3,8,7,6}},{0,{0,2,1},{0,1,2,6,7,8,3,4,5},{0,1,2,6,7,8,3,4,5}},{0,{0,2,1},{0,2,1,6,8,7,3,5,4},{0,2,1,6,8,7,3,5,4}},{0,{0,2,1},{1,0,2,7,6,8,4,3,5},{1,0,2,7,6,8,4,3,5}},{0,{0,2,1},{2,0,1,8,6,7,5,3,4},{1,2,0,7,8,6,4,5,3}},{0,{0,2,1},{1,2,0,7,8,6,4,5,3},{2,0,1,8,6,7,5,3,4}},{0,{0,2,1},{2,1,0,8,7,6,5,4,3},{2,1,0,8,7,6,5,4,3}},{0,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8}},{0,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7}},{0,{1,0,2},{1,0,2,7,6,8,4,3,5},{4,3,5,1,0,2,7,6,8}},{0,{1,0,2},{2,0,1,8,6,7,5,3,4},{4,5,3,1,2,0,7,8,6}},{0,{1,0,2},{1,2,0,7,8,6,4,5,3},{5,3,4,2,0,1,8,6,7}},{0,{1,0,2},{2,1,0,8,7,6,5,4,3},{5,4,3,2,1,0,8,7,6}},{0,{1,2,0},{0,1,2,3,4,5,6,7,8},{6,7,8,0,1,2,3,4,5}},{0,{1,2,0},{0,2,1,3,5,4,6,8,7},{6,8,7,0,2,1,3,5,4}},{0,{1,2,0},{1,0,2,4,3,5,7,6,8},{7,6,8,1,0,2,4,3,5}},//20{0,{1,2,0},{2,0,1,5,3,4,8,6,7},{7,8,6,1,2,0,4,5,3}},{0,{1,2,0},{1,2,0,4,5,3,7,8,6},{8,6,7,2,0,1,5,3,4}},{0,{1,2,0},{2,1,0,5,4,3,8,7,6},{8,7,6,2,1,0,5,4,3}},{0,{2,0,1},{0,1,2,3,4,5,6,7,8},{3,4,5,6,7,8,0,1,2}},{0,{2,0,1},{0,2,1,3,5,4,6,8,7},{3,5,4,6,8,7,0,2,1}},{0,{2,0,1},{1,0,2,4,3,5,7,6,8},{4,3,5,7,6,8,1,0,2}},{0,{2,0,1},{2,0,1,5,3,4,8,6,7},{4,5,3,7,8,6,1,2,0}},{0,{2,0,1},{1,2,0,4,5,3,7,8,6},{5,3,4,8,6,7,2,0,1}},{0,{2,0,1},{2,1,0,5,4,3,8,7,6},{5,4,3,8,7,6,2,1,0}},{0,{2,1,0},{0,1,2,6,7,8,3,4,5},{6,7,8,3,4,5,0,1,2}},//30{0,{2,1,0},{0,2,1,6,8,7,3,5,4},{6,8,7,3,5,4,0,2,1}},{0,{2,1,0},{1,0,2,7,6,8,4,3,5},{7,6,8,4,3,5,1,0,2}},{0,{2,1,0},{2,0,1,8,6,7,5,3,4},{7,8,6,4,5,3,1,2,0}},{0,{2,1,0},{1,2,0,7,8,6,4,5,3},{8,6,7,5,3,4,2,0,1}},{0,{2,1,0},{2,1,0,8,7,6,5,4,3},{8,7,6,5,4,3,2,1,0}},{0,{0,1,2},{3,4,5,6,7,8,0,1,2},{6,7,8,0,1,2,3,4,5}},{0,{0,1,2},{3,5,4,6,8,7,0,2,1},{6,8,7,0,2,1,3,5,4}},{0,{0,1,2},{4,3,5,7,6,8,1,0,2},{7,6,8,1,0,2,4,3,5}},{0,{0,1,2},{5,3,4,8,6,7,2,0,1},{7,8,6,1,2,0,4,5,3}},{0,{0,1,2},{4,5,3,7,8,6,1,2,0},{8,6,7,2,0,1,5,3,4}},//40{0,{0,1,2},{5,4,3,8,7,6,2,1,0},{8,7,6,2,1,0,5,4,3}},{0,{0,2,1},{3,4,5,0,1,2,6,7,8},{3,4,5,0,1,2,6,7,8}},{0,{0,2,1},{3,5,4,0,2,1,6,8,7},{3,5,4,0,2,1,6,8,7}},{0,{0,2,1},{4,3,5,1,0,2,7,6,8},{4,3,5,1,0,2,7,6,8}},{0,{0,2,1},{5,3,4,2,0,1,8,6,7},{4,5,3,1,2,0,7,8,6}},{0,{0,2,1},{4,5,3,1,2,0,7,8,6},{5,3,4,2,0,1,8,6,7}},{0,{0,2,1},{5,4,3,2,1,0,8,7,6},{5,4,3,2,1,0,8,7,6}},{0,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2}},{0,{1,0,2},{3,5,4,0,2,1,6,8,7},{6,8,7,3,5,4,0,2,1}},{0,{1,0,2},{4,3,5,1,0,2,7,6,8},{7,6,8,4,3,5,1,0,2}},//50{0,{1,0,2},{5,3,4,2,0,1,8,6,7},{7,8,6,4,5,3,1,2,0}},{0,{1,0,2},{4,5,3,1,2,0,7,8,6},{8,6,7,5,3,4,2,0,1}},{0,{1,0,2},{5,4,3,2,1,0,8,7,6},{8,7,6,5,4,3,2,1,0}},{0,{1,2,0},{3,4,5,6,7,8,0,1,2},{3,4,5,6,7,8,0,1,2}},{0,{1,2,0},{3,5,4,6,8,7,0,2,1},{3,5,4,6,8,7,0,2,1}},{0,{1,2,0},{4,3,5,7,6,8,1,0,2},{4,3,5,7,6,8,1,0,2}},{0,{1,2,0},{5,3,4,8,6,7,2,0,1},{4,5,3,7,8,6,1,2,0}},{0,{1,2,0},{4,5,3,7,8,6,1,2,0},{5,3,4,8,6,7,2,0,1}},{0,{1,2,0},{5,4,3,8,7,6,2,1,0},{5,4,3,8,7,6,2,1,0}},{0,{2,0,1},{3,4,5,6,7,8,0,1,2},{0,1,2,3,4,5,6,7,8}},//60{0,{2,0,1},{3,5,4,6,8,7,0,2,1},{0,2,1,3,5,4,6,8,7}},{0,{2,0,1},{4,3,5,7,6,8,1,0,2},{1,0,2,4,3,5,7,6,8}},{0,{2,0,1},{5,3,4,8,6,7,2,0,1},{1,2,0,4,5,3,7,8,6}},{0,{2,0,1},{4,5,3,7,8,6,1,2,0},{2,0,1,5,3,4,8,6,7}},{0,{2,0,1},{5,4,3,8,7,6,2,1,0},{2,1,0,5,4,3,8,7,6}},{0,{2,1,0},{3,4,5,0,1,2,6,7,8},{0,1,2,6,7,8,3,4,5}},{0,{2,1,0},{3,5,4,0,2,1,6,8,7},{0,2,1,6,8,7,3,5,4}},{0,{2,1,0},{4,3,5,1,0,2,7,6,8},{1,0,2,7,6,8,4,3,5}},{0,{2,1,0},{5,3,4,2,0,1,8,6,7},{1,2,0,7,8,6,4,5,3}},{0,{2,1,0},{4,5,3,1,2,0,7,8,6},{2,0,1,8,6,7,5,3,4}},//70{0,{2,1,0},{5,4,3,2,1,0,8,7,6},{2,1,0,8,7,6,5,4,3}},{0,{0,1,2},{6,7,8,0,1,2,3,4,5},{3,4,5,6,7,8,0,1,2}},{0,{0,1,2},{6,8,7,0,2,1,3,5,4},{3,5,4,6,8,7,0,2,1}},{0,{0,1,2},{7,6,8,1,0,2,4,3,5},{4,3,5,7,6,8,1,0,2}},{0,{0,1,2},{8,6,7,2,0,1,5,3,4},{4,5,3,7,8,6,1,2,0}},{0,{0,1,2},{7,8,6,1,2,0,4,5,3},{5,3,4,8,6,7,2,0,1}},{0,{0,1,2},{8,7,6,2,1,0,5,4,3},{5,4,3,8,7,6,2,1,0}},{0,{0,2,1},{6,7,8,3,4,5,0,1,2},{6,7,8,3,4,5,0,1,2}},{0,{0,2,1},{6,8,7,3,5,4,0,2,1},{6,8,7,3,5,4,0,2,1}},{0,{0,2,1},{7,6,8,4,3,5,1,0,2},{7,6,8,4,3,5,1,0,2}},//80{0,{0,2,1},{8,6,7,5,3,4,2,0,1},{7,8,6,4,5,3,1,2,0}},{0,{0,2,1},{7,8,6,4,5,3,1,2,0},{8,6,7,5,3,4,2,0,1}},{0,{0,2,1},{8,7,6,5,4,3,2,1,0},{8,7,6,5,4,3,2,1,0}},{0,{1,0,2},{6,7,8,3,4,5,0,1,2},{0,1,2,6,7,8,3,4,5}},{0,{1,0,2},{6,8,7,3,5,4,0,2,1},{0,2,1,6,8,7,3,5,4}},{0,{1,0,2},{7,6,8,4,3,5,1,0,2},{1,0,2,7,6,8,4,3,5}},{0,{1,0,2},{8,6,7,5,3,4,2,0,1},{1,2,0,7,8,6,4,5,3}},{0,{1,0,2},{7,8,6,4,5,3,1,2,0},{2,0,1,8,6,7,5,3,4}},{0,{1,0,2},{8,7,6,5,4,3,2,1,0},{2,1,0,8,7,6,5,4,3}},{0,{1,2,0},{6,7,8,0,1,2,3,4,5},{0,1,2,3,4,5,6,7,8}},//90{0,{1,2,0},{6,8,7,0,2,1,3,5,4},{0,2,1,3,5,4,6,8,7}},{0,{1,2,0},{7,6,8,1,0,2,4,3,5},{1,0,2,4,3,5,7,6,8}},{0,{1,2,0},{8,6,7,2,0,1,5,3,4},{1,2,0,4,5,3,7,8,6}},{0,{1,2,0},{7,8,6,1,2,0,4,5,3},{2,0,1,5,3,4,8,6,7}},{0,{1,2,0},{8,7,6,2,1,0,5,4,3},{2,1,0,5,4,3,8,7,6}},{0,{2,0,1},{6,7,8,0,1,2,3,4,5},{6,7,8,0,1,2,3,4,5}},{0,{2,0,1},{6,8,7,0,2,1,3,5,4},{6,8,7,0,2,1,3,5,4}},{0,{2,0,1},{7,6,8,1,0,2,4,3,5},{7,6,8,1,0,2,4,3,5}},{0,{2,0,1},{8,6,7,2,0,1,5,3,4},{7,8,6,1,2,0,4,5,3}},{0,{2,0,1},{7,8,6,1,2,0,4,5,3},{8,6,7,2,0,1,5,3,4}},//100{0,{2,0,1},{8,7,6,2,1,0,5,4,3},{8,7,6,2,1,0,5,4,3}},{0,{2,1,0},{6,7,8,3,4,5,0,1,2},{3,4,5,0,1,2,6,7,8}},{0,{2,1,0},{6,8,7,3,5,4,0,2,1},{3,5,4,0,2,1,6,8,7}},{0,{2,1,0},{7,6,8,4,3,5,1,0,2},{4,3,5,1,0,2,7,6,8}},{0,{2,1,0},{8,6,7,5,3,4,2,0,1},{4,5,3,1,2,0,7,8,6}},{0,{2,1,0},{7,8,6,4,5,3,1,2,0},{5,3,4,2,0,1,8,6,7}},{0,{2,1,0},{8,7,6,5,4,3,2,1,0},{5,4,3,2,1,0,8,7,6}},//107{1,{0,1,2},{0,2,1,3,5,4,6,8,7},{0,2,1,3,5,4,6,8,7}},{1,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2}},{1,{1,0,2},{3,5,4,0,2,1,6,8,7},{6,8,7,3,5,4,0,2,1}},{2,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6}},{2,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7}},{2,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2}},{2,{1,0,2},{5,3,4,2,0,1,8,6,7},{7,8,6,4,5,3,1,2,0}},{2,{1,0,2},{4,5,3,1,2,0,7,8,6},{8,6,7,5,3,4,2,0,1}},{3,{0,1,2},{0,2,1,3,5,4,6,8,7},{0,2,1,3,5,4,6,8,7}},{3,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8}},{3,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7}},{3,{1,2,0},{3,4,5,6,8,7,0,1,2},{3,5,4,6,7,8,0,1,2}},{3,{1,2,0},{3,5,4,6,7,8,0,2,1},{3,4,5,6,8,7,0,2,1}},{3,{2,1,0},{3,4,5,0,1,2,6,8,7},{0,2,1,6,7,8,3,4,5}},{3,{2,1,0},{3,5,4,0,2,1,6,7,8},{0,1,2,6,8,7,3,5,4}},{3,{0,2,1},{6,7,8,3,5,4,0,1,2},{6,7,8,3,5,4,0,1,2}},{3,{0,2,1},{6,8,7,3,4,5,0,2,1},{6,8,7,3,4,5,0,2,1}},{3,{2,0,1},{6,7,8,0,1,2,3,5,4},{6,7,8,0,2,1,3,4,5}},{3,{2,0,1},{6,8,7,0,2,1,3,4,5},{6,8,7,0,1,2,3,5,4}},{ 4,{1,0,2},{2,1,0,8,7,6,5,4,3},{5,4,3,2,1,0,8,7,6} },{ 6,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 6,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 6,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8} },{ 6,{1,0,2},{2,0,1,8,6,7,5,3,4},{4,5,3,1,2,0,7,8,6} },{ 6,{1,0,2},{1,2,0,7,8,6,4,5,3},{5,3,4,2,0,1,8,6,7} },{ 7,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 7,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 7,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7} },{ 7,{1,0,2},{1,0,2,7,6,8,4,3,5},{4,3,5,1,0,2,7,6,8} },{ 7,{1,0,2},{2,1,0,8,7,6,5,4,3},{5,4,3,2,1,0,8,7,6} },{ 7,{1,2,0},{3,4,5,7,8,6,0,1,2},{5,3,4,6,7,8,0,1,2} },{ 7,{1,2,0},{5,3,4,6,7,8,2,0,1},{3,4,5,7,8,6,1,2,0} },{ 7,{1,2,0},{4,5,3,8,6,7,1,2,0},{4,5,3,8,6,7,2,0,1} },{ 7,{2,1,0},{3,5,4,0,2,1,7,6,8},{1,0,2,6,8,7,3,5,4} },{ 7,{2,1,0},{4,3,5,1,0,2,8,7,6},{2,1,0,7,6,8,4,3,5} },{ 7,{2,1,0},{5,4,3,2,1,0,6,8,7},{0,2,1,8,7,6,5,4,3} },{ 7,{0,2,1},{6,8,7,5,4,3,0,2,1},{6,8,7,5,4,3,0,2,1} },{ 7,{0,2,1},{7,6,8,3,5,4,1,0,2},{7,6,8,3,5,4,1,0,2} },{ 7,{0,2,1},{8,7,6,4,3,5,2,1,0},{8,7,6,4,3,5,2,1,0} },{ 7,{2,0,1},{6,7,8,0,1,2,5,3,4},{6,7,8,1,2,0,3,4,5} },{ 7,{2,0,1},{8,6,7,2,0,1,4,5,3},{7,8,6,2,0,1,4,5,3} },{ 7,{2,0,1},{7,8,6,1,2,0,3,4,5},{8,6,7,0,1,2,5,3,4} },{ 8,{0,1,2},{0,2,1,3,5,4,6,8,7},{0,2,1,3,5,4,6,8,7} },{ 8,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8} },{ 8,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7} },{ 8,{0,1,2},{3,4,5,6,7,8,0,1,2},{6,7,8,0,1,2,3,4,5} },{ 8,{0,1,2},{3,5,4,6,8,7,0,2,1},{6,8,7,0,2,1,3,5,4} },{ 8,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2} },{ 8,{1,0,2},{3,5,4,0,2,1,6,8,7},{6,8,7,3,5,4,0,2,1} },{ 8,{0,1,2},{6,7,8,0,1,2,3,4,5},{3,4,5,6,7,8,0,1,2} },{ 8,{0,1,2},{6,8,7,0,2,1,3,5,4},{3,5,4,6,8,7,0,2,1} },{ 8,{1,0,2},{6,7,8,3,4,5,0,1,2},{0,1,2,6,7,8,3,4,5} },{ 8,{1,0,2},{6,8,7,3,5,4,0,2,1},{0,2,1,6,8,7,3,5,4} },{ 9,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2} },{ 10,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2} },{ 11,{0,2,1},{2,1,0,7,8,6,5,3,4},{2,1,0,7,8,6,5,3,4} },{ 12,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7} },{ 12,{0,1,2},{5,3,4,8,6,7,2,0,1},{7,8,6,1,2,0,4,5,3} },{ 12,{1,0,2},{5,4,3,2,1,0,8,7,6},{8,7,6,5,4,3,2,1,0} },{ 12,{0,1,2},{7,8,6,1,2,0,4,5,3},{5,3,4,8,6,7,2,0,1} },{ 12,{1,0,2},{7,6,8,4,3,5,1,0,2},{1,0,2,7,6,8,4,3,5} },{ 13,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8} },{ 14,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,5,4,0,2,1,6,8,7} },{ 15,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 15,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 15,{0,2,1},{0,1,2,7,8,6,5,3,4},{0,1,2,7,8,6,5,3,4} },{ 15,{0,2,1},{2,0,1,6,7,8,4,5,3},{1,2,0,8,6,7,3,4,5} },{ 15,{0,2,1},{1,2,0,8,6,7,3,4,5},{2,0,1,6,7,8,4,5,3} },{ 15,{1,0,2},{0,1,2,6,7,8,3,4,5},{3,4,5,0,1,2,6,7,8} },{ 15,{1,0,2},{2,0,1,8,6,7,5,3,4},{4,5,3,1,2,0,7,8,6} },{ 15,{1,0,2},{1,2,0,7,8,6,4,5,3},{5,3,4,2,0,1,8,6,7} },{ 15,{1,2,0},{0,1,2,4,5,3,8,6,7},{7,8,6,0,1,2,5,3,4} },{ 15,{1,2,0},{2,0,1,3,4,5,7,8,6},{8,6,7,1,2,0,3,4,5} },{ 15,{1,2,0},{1,2,0,5,3,4,6,7,8},{6,7,8,2,0,1,4,5,3} },{ 15,{2,0,1},{0,1,2,5,3,4,7,8,6},{3,4,5,7,8,6,2,0,1} },{ 15,{2,0,1},{2,0,1,4,5,3,6,7,8},{4,5,3,8,6,7,0,1,2} },{ 15,{2,0,1},{1,2,0,3,4,5,8,6,7},{5,3,4,6,7,8,1,2,0} },{ 15,{2,1,0},{0,1,2,8,6,7,4,5,3},{7,8,6,3,4,5,2,0,1} },{ 15,{2,1,0},{2,0,1,7,8,6,3,4,5},{8,6,7,4,5,3,0,1,2} },{ 15,{2,1,0},{1,2,0,6,7,8,5,3,4},{6,7,8,5,3,4,1,2,0} },{ 15,{0,1,2},{3,4,5,6,7,8,0,1,2},{6,7,8,0,1,2,3,4,5} },{ 15,{0,1,2},{5,3,4,8,6,7,2,0,1},{7,8,6,1,2,0,4,5,3} },{ 15,{0,1,2},{4,5,3,7,8,6,1,2,0},{8,6,7,2,0,1,5,3,4} },{ 15,{0,2,1},{3,4,5,1,2,0,8,6,7},{5,3,4,0,1,2,7,8,6} },{ 15,{0,2,1},{5,3,4,0,1,2,7,8,6},{3,4,5,1,2,0,8,6,7} },{ 15,{0,2,1},{4,5,3,2,0,1,6,7,8},{4,5,3,2,0,1,6,7,8} },{ 15,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2} },{ 15,{1,0,2},{5,3,4,2,0,1,8,6,7},{7,8,6,4,5,3,1,2,0} },{ 15,{1,0,2},{4,5,3,1,2,0,7,8,6},{8,6,7,5,3,4,2,0,1} },{ 15,{1,2,0},{3,4,5,7,8,6,2,0,1},{5,3,4,7,8,6,0,1,2} },{ 15,{1,2,0},{5,3,4,6,7,8,1,2,0},{3,4,5,8,6,7,1,2,0} },{ 15,{1,2,0},{4,5,3,8,6,7,0,1,2},{4,5,3,6,7,8,2,0,1} },{ 15,{2,0,1},{3,4,5,8,6,7,1,2,0},{2,0,1,3,4,5,7,8,6} },{ 15,{2,0,1},{5,3,4,7,8,6,0,1,2},{0,1,2,4,5,3,8,6,7} },{ 15,{2,0,1},{4,5,3,6,7,8,2,0,1},{1,2,0,5,3,4,6,7,8} },{ 15,{2,1,0},{3,4,5,2,0,1,7,8,6},{2,0,1,7,8,6,3,4,5} },{ 15,{2,1,0},{5,3,4,1,2,0,6,7,8},{0,1,2,8,6,7,4,5,3} },{ 15,{2,1,0},{4,5,3,0,1,2,8,6,7},{1,2,0,6,7,8,5,3,4} },{ 15,{0,1,2},{6,7,8,0,1,2,3,4,5},{3,4,5,6,7,8,0,1,2} },{ 15,{0,1,2},{8,6,7,2,0,1,5,3,4},{4,5,3,7,8,6,1,2,0} },{ 15,{0,1,2},{7,8,6,1,2,0,4,5,3},{5,3,4,8,6,7,2,0,1} },{ 15,{0,2,1},{6,7,8,4,5,3,2,0,1},{7,8,6,5,3,4,0,1,2} },{ 15,{0,2,1},{8,6,7,3,4,5,1,2,0},{8,6,7,3,4,5,1,2,0} },{ 15,{0,2,1},{7,8,6,5,3,4,0,1,2},{6,7,8,4,5,3,2,0,1} },{ 15,{1,0,2},{6,7,8,3,4,5,0,1,2},{0,1,2,6,7,8,3,4,5} },{ 15,{1,0,2},{8,6,7,5,3,4,2,0,1},{1,2,0,7,8,6,4,5,3} },{ 15,{1,0,2},{7,8,6,4,5,3,1,2,0},{2,0,1,8,6,7,5,3,4} },{ 15,{1,2,0},{6,7,8,1,2,0,5,3,4},{0,1,2,5,3,4,7,8,6} },{ 15,{1,2,0},{8,6,7,0,1,2,4,5,3},{1,2,0,3,4,5,8,6,7} },{ 15,{1,2,0},{7,8,6,2,0,1,3,4,5},{2,0,1,4,5,3,6,7,8} },{ 15,{2,0,1},{6,7,8,2,0,1,4,5,3},{7,8,6,2,0,1,3,4,5} },{ 15,{2,0,1},{8,6,7,1,2,0,3,4,5},{8,6,7,0,1,2,4,5,3} },{ 15,{2,0,1},{7,8,6,0,1,2,5,3,4},{6,7,8,1,2,0,5,3,4} },{ 15,{2,1,0},{6,7,8,5,3,4,1,2,0},{3,4,5,2,0,1,7,8,6} },{ 15,{2,1,0},{8,6,7,4,5,3,0,1,2},{4,5,3,0,1,2,8,6,7} },{ 15,{2,1,0},{7,8,6,3,4,5,2,0,1},{5,3,4,1,2,0,6,7,8} },{ 16,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 16,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 16,{1,0,2},{3,4,5,0,1,2,6,7,8},{6,7,8,3,4,5,0,1,2} },{ 16,{1,0,2},{5,3,4,2,0,1,8,6,7},{7,8,6,4,5,3,1,2,0} },{ 16,{1,0,2},{4,5,3,1,2,0,7,8,6},{8,6,7,5,3,4,2,0,1} },{ 17,{0,2,1},{5,4,3,2,1,0,8,7,6},{5,4,3,2,1,0,8,7,6} },{ 18,{2,1,0},{8,7,6,5,4,3,2,1,0},{5,3,4,1,2,0,8,7,6} },{ 20,{0,2,1},{2,1,0,8,7,6,5,4,3},{2,1,0,8,7,6,5,4,3} },{ 22,{2,1,0},{3,4,5,0,1,2,8,7,6},{1,0,2,6,7,8,3,4,5} },{ 24,{2,1,0},{3,5,4,0,2,1,8,7,6},{1,0,2,6,8,7,3,5,4} },{ 25,{0,2,1},{0,2,1,7,8,6,5,3,4},{0,2,1,7,8,6,5,3,4} },{ 26,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 26,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 26,{1,2,0},{0,1,2,3,4,5,8,6,7},{6,7,8,0,1,2,3,4,5} },{ 26,{1,2,0},{2,0,1,5,3,4,7,8,6},{7,8,6,1,2,0,4,5,3} },{ 26,{1,2,0},{1,2,0,4,5,3,6,7,8},{8,6,7,2,0,1,5,3,4} },{ 26,{2,0,1},{0,1,2,3,4,5,7,8,6},{3,4,5,6,7,8,0,1,2} },{ 26,{2,0,1},{2,0,1,5,3,4,6,7,8},{4,5,3,7,8,6,1,2,0} },{ 26,{2,0,1},{1,2,0,4,5,3,8,6,7},{5,3,4,8,6,7,2,0,1} },{ 26,{0,2,1},{3,5,4,0,2,1,6,8,7},{3,5,4,0,2,1,6,8,7} },{ 26,{0,2,1},{4,3,5,1,0,2,7,6,8},{4,3,5,1,0,2,7,6,8} },{ 26,{0,2,1},{5,4,3,2,1,0,8,7,6},{5,4,3,2,1,0,8,7,6} },{ 26,{1,0,2},{3,5,4,0,2,1,8,7,6},{6,8,7,3,5,4,0,2,1} },{ 26,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,6,8,4,3,5,1,0,2} },{ 26,{1,0,2},{5,4,3,2,1,0,7,6,8},{8,7,6,5,4,3,2,1,0} },{ 26,{2,1,0},{3,5,4,0,2,1,7,6,8},{0,2,1,6,8,7,3,5,4} },{ 26,{2,1,0},{4,3,5,1,0,2,8,7,6},{1,0,2,7,6,8,4,3,5} },{ 26,{2,1,0},{5,4,3,2,1,0,6,8,7},{2,1,0,8,7,6,5,4,3} },{ 27,{2,1,0},{3,4,5,0,1,2,7,6,8},{0,2,1,6,7,8,3,4,5} },{ 28,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 28,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 28,{2,1,0},{0,2,1,8,7,6,5,4,3},{6,8,7,3,5,4,0,2,1} },{ 28,{2,1,0},{1,0,2,6,8,7,3,5,4},{7,6,8,4,3,5,1,0,2} },{ 28,{2,1,0},{2,1,0,7,6,8,4,3,5},{8,7,6,5,4,3,2,1,0} },{ 28,{0,1,2},{3,4,5,6,7,8,1,2,0},{8,6,7,0,1,2,3,4,5} },{ 28,{0,1,2},{5,3,4,8,6,7,0,1,2},{6,7,8,1,2,0,4,5,3} },{ 28,{0,1,2},{4,5,3,7,8,6,2,0,1},{7,8,6,2,0,1,5,3,4} },{ 28,{2,1,0},{3,5,4,0,2,1,8,7,6},{1,0,2,6,8,7,3,5,4} },{ 28,{2,1,0},{4,3,5,1,0,2,6,8,7},{2,1,0,7,6,8,4,3,5} },{ 28,{2,1,0},{5,4,3,2,1,0,7,6,8},{0,2,1,8,7,6,5,4,3} },{ 28,{0,1,2},{6,7,8,1,2,0,4,5,3},{5,3,4,8,6,7,0,1,2} },{ 28,{0,1,2},{8,6,7,0,1,2,3,4,5},{3,4,5,6,7,8,1,2,0} },{ 28,{0,1,2},{7,8,6,2,0,1,5,3,4},{4,5,3,7,8,6,2,0,1} },{ 28,{2,1,0},{6,8,7,3,5,4,0,2,1},{4,3,5,1,0,2,6,8,7} },{ 28,{2,1,0},{7,6,8,4,3,5,1,0,2},{5,4,3,2,1,0,7,6,8} },{ 28,{2,1,0},{8,7,6,5,4,3,2,1,0},{3,5,4,0,2,1,8,7,6} },{ 29,{0,1,2},{2,0,1,5,3,4,8,6,7},{1,2,0,4,5,3,7,8,6} },{ 29,{0,1,2},{1,2,0,4,5,3,7,8,6},{2,0,1,5,3,4,8,6,7} },{ 29,{0,2,1},{0,2,1,6,8,7,3,5,4},{0,2,1,6,8,7,3,5,4} },{ 29,{0,2,1},{1,0,2,7,6,8,4,3,5},{1,0,2,7,6,8,4,3,5} },{ 29,{0,2,1},{2,1,0,8,7,6,5,4,3},{2,1,0,8,7,6,5,4,3} },{ 29,{2,0,1},{3,4,5,6,7,8,0,1,2},{1,2,0,3,4,5,6,7,8} },{ 29,{2,0,1},{5,3,4,8,6,7,2,0,1},{2,0,1,4,5,3,7,8,6} },{ 29,{2,0,1},{4,5,3,7,8,6,1,2,0},{0,1,2,5,3,4,8,6,7} },{ 29,{2,1,0},{3,5,4,0,2,1,6,8,7},{2,1,0,6,8,7,3,5,4} },{ 29,{2,1,0},{4,3,5,1,0,2,7,6,8},{0,2,1,7,6,8,4,3,5} },{ 29,{2,1,0},{5,4,3,2,1,0,8,7,6},{1,0,2,8,7,6,5,4,3} },{ 29,{1,0,2},{6,8,7,3,5,4,0,2,1},{1,0,2,6,8,7,3,5,4} },{ 29,{1,0,2},{7,6,8,4,3,5,1,0,2},{2,1,0,7,6,8,4,3,5} },{ 29,{1,0,2},{8,7,6,5,4,3,2,1,0},{0,2,1,8,7,6,5,4,3} },{ 29,{1,2,0},{6,7,8,0,1,2,3,4,5},{2,0,1,3,4,5,6,7,8} },{ 29,{1,2,0},{8,6,7,2,0,1,5,3,4},{0,1,2,4,5,3,7,8,6} },{ 29,{1,2,0},{7,8,6,1,2,0,4,5,3},{1,2,0,5,3,4,8,6,7} },{ 30,{0,2,1},{1,0,2,8,6,7,4,5,3},{1,0,2,8,6,7,4,5,3} },{ 30,{1,0,2},{5,4,3,2,1,0,7,6,8},{8,7,6,5,4,3,2,1,0} },{ 30,{1,2,0},{4,5,3,8,7,6,1,0,2},{3,5,4,7,6,8,2,0,1} },{ 30,{2,0,1},{7,6,8,2,0,1,5,4,3},{7,8,6,0,2,1,4,3,5} },{ 30,{2,1,0},{6,7,8,3,5,4,0,1,2},{5,3,4,1,2,0,6,8,7} },{ 31,{2,1,0},{6,7,8,3,4,5,0,1,2},{0,3,4,1,2,6,5,7,8} },{ 35,{2,1,0},{5,4,3,2,1,0,7,6,8},{6,2,1,8,7,5,0,4,3} },{ 40,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 44,{2,1,0},{5,4,3,2,1,0,6,7,8},{6,1,2,8,7,5,0,4,3} },{ 52,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 53,{2,1,0},{0,1,2,8,6,7,4,5,3},{5,7,8,3,4,0,6,1,2} },{ 66,{2,1,0},{0,1,2,8,7,6,5,4,3},{5,8,7,3,4,0,6,2,1} },{ 70,{2,1,0},{6,7,8,3,5,4,0,1,2},{0,3,4,1,2,6,5,8,7} },{ 74,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 83,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 96,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 97,{0,2,1},{0,2,1,7,8,6,5,3,4},{0,2,1,7,8,6,5,3,4} },{ 100,{2,1,0},{7,6,8,3,4,5,1,0,2},{0,4,3,2,1,6,5,7,8} },{ 103,{2,1,0},{1,0,2,8,6,7,4,5,3},{5,7,8,4,3,0,6,1,2} },{ 103,{0,2,1},{5,3,4,1,2,0,6,8,7},{5,3,4,1,2,0,6,8,7} },{ 103,{1,2,0},{3,5,4,7,6,8,2,0,1},{0,4,3,7,8,5,6,2,1} },{ 103,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 103,{2,0,1},{7,8,6,0,2,1,4,3,5},{0,8,7,2,1,5,6,3,4} },{ 113,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 119,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 121,{0,2,1},{0,1,2,7,8,6,5,3,4},{0,1,2,7,8,6,5,3,4} },{ 123,{0,2,1},{5,4,3,2,1,0,6,8,7},{5,4,3,2,1,0,6,8,7} },{ 128,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 132,{1,2,0},{2,0,1,4,5,3,8,6,7},{5,7,8,1,2,6,0,3,4} },{ 132,{2,0,1},{1,2,0,5,3,4,7,8,6},{6,3,4,7,8,0,5,1,2} },{ 132,{0,2,1},{6,8,7,4,3,5,0,2,1},{6,8,7,4,3,5,0,2,1} },{ 132,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 132,{2,1,0},{7,6,8,3,5,4,1,0,2},{0,4,3,2,1,6,5,8,7} },{ 136,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 138,{1,0,2},{8,7,6,5,4,3,2,1,0},{5,2,1,8,7,0,6,4,3} },{ 141,{2,1,0},{5,4,3,2,1,0,8,7,6},{6,2,1,8,7,5,0,4,3} },{ 143,{2,1,0},{6,8,7,3,5,4,0,2,1},{0,3,4,1,2,6,5,8,7} },{ 147,{2,1,0},{0,1,2,7,6,8,4,3,5},{5,7,8,3,4,0,6,1,2} },{ 148,{2,1,0},{5,4,3,2,1,0,6,7,8},{6,1,2,8,7,5,0,4,3} },{ 166,{2,1,0},{6,8,7,3,4,5,0,2,1},{0,3,4,1,2,6,5,7,8} },{ 174,{2,1,0},{0,1,2,7,8,6,5,3,4},{5,8,7,3,4,0,6,2,1} },{ 189,{2,1,0},{1,0,2,7,6,8,4,3,5},{5,7,8,4,3,0,6,1,2} },{ 209,{2,1,0},{1,0,2,7,8,6,5,3,4},{5,8,7,4,3,0,6,2,1} },{ 212,{2,1,0},{8,6,7,3,4,5,1,2,0},{0,4,3,2,1,6,5,7,8} },{ 213,{2,1,0},{4,5,3,2,0,1,6,7,8},{6,1,2,7,8,5,0,3,4} },{ 218,{2,1,0},{5,4,3,2,1,0,7,6,8},{6,2,1,8,7,5,0,4,3} },{ 223,{2,1,0},{0,1,2,8,7,6,5,4,3},{5,7,8,3,4,0,6,1,2} },{ 223,{0,1,2},{5,4,3,8,7,6,0,1,2},{6,7,8,2,1,0,5,4,3} },{ 223,{2,1,0},{5,4,3,2,1,0,6,7,8},{6,1,2,8,7,5,0,4,3} },{ 223,{0,1,2},{6,7,8,2,1,0,5,4,3},{5,4,3,8,7,6,0,1,2} },{ 223,{2,1,0},{6,7,8,3,4,5,0,1,2},{0,4,3,2,1,6,5,7,8} },{ 234,{0,1,2},{5,4,3,8,7,6,0,1,2},{6,7,8,2,1,0,5,4,3} },{ 234,{0,1,2},{6,7,8,2,1,0,5,4,3},{5,4,3,8,7,6,0,1,2} },{ 236,{2,1,0},{0,1,2,8,6,7,4,5,3},{5,8,7,3,4,0,6,2,1} },{ 239,{0,2,1},{0,2,1,7,8,6,5,3,4},{0,2,1,7,8,6,5,3,4} },{ 239,{0,1,2},{5,4,3,8,7,6,0,1,2},{6,7,8,2,1,0,5,4,3} },{ 239,{0,2,1},{5,3,4,1,2,0,6,8,7},{5,3,4,1,2,0,6,8,7} },{ 239,{0,1,2},{6,7,8,2,1,0,5,4,3},{5,4,3,8,7,6,0,1,2} },{ 239,{0,2,1},{6,8,7,4,3,5,0,2,1},{6,8,7,4,3,5,0,2,1} },{ 240,{2,1,0},{5,4,3,2,1,0,6,8,7},{6,2,1,8,7,5,0,4,3} },{ 244,{0,2,1},{6,7,8,4,3,5,0,1,2},{6,7,8,4,3,5,0,1,2} },{ 246,{2,1,0},{5,4,3,2,1,0,6,7,8},{6,1,2,8,7,5,0,4,3} },{ 249,{0,2,1},{6,8,7,4,3,5,0,2,1},{6,8,7,4,3,5,0,2,1} },{ 250,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 251,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 252,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 253,{2,1,0},{0,1,2,6,7,8,3,4,5},{5,7,8,3,4,0,6,1,2} },{ 253,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 253,{2,0,1},{3,4,5,6,7,8,0,1,2},{5,1,2,3,4,6,0,7,8} },{ 253,{0,2,1},{6,7,8,3,4,5,0,1,2},{6,7,8,3,4,5,0,1,2} },{ 253,{1,2,0},{6,7,8,0,1,2,3,4,5},{6,1,2,3,4,0,5,7,8} },{ 254,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 255,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 258,{0,2,1},{6,8,7,3,4,5,0,2,1},{6,8,7,3,4,5,0,2,1} },{ 272,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 273,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 274,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 275,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 276,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 278,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 279,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 280,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 283,{0,2,1},{5,3,4,1,2,0,6,8,7},{5,3,4,1,2,0,6,8,7} },{ 284,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 285,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 286,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 287,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 288,{0,2,1},{0,1,2,7,8,6,5,3,4},{0,1,2,7,8,6,5,3,4} },{ 288,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 288,{1,2,0},{3,4,5,7,8,6,2,0,1},{0,3,4,7,8,5,6,1,2} },{ 288,{2,0,1},{7,8,6,0,1,2,5,3,4},{0,7,8,1,2,5,6,3,4} },{ 288,{2,1,0},{7,8,6,3,4,5,2,0,1},{0,3,4,1,2,6,5,7,8} },{ 289,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 297,{2,1,0},{8,7,6,3,5,4,2,1,0},{0,4,3,2,1,6,5,8,7} },{ 301,{1,2,0},{2,0,1,4,5,3,6,7,8},{5,7,8,1,2,6,0,3,4} },{ 301,{2,0,1},{1,2,0,5,3,4,6,7,8},{6,3,4,7,8,0,5,1,2} },{ 301,{0,2,1},{5,3,4,1,2,0,6,7,8},{5,3,4,1,2,0,6,7,8} },{ 301,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 301,{2,1,0},{4,5,3,2,0,1,6,7,8},{6,1,2,7,8,5,0,3,4} },{ 302,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 303,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 304,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 305,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 306,{0,2,1},{0,1,2,8,7,6,5,4,3},{0,1,2,8,7,6,5,4,3} },{ 306,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 306,{1,2,0},{3,4,5,8,7,6,2,1,0},{0,4,3,8,7,5,6,1,2} },{ 306,{2,0,1},{8,7,6,0,1,2,5,4,3},{0,7,8,2,1,5,6,4,3} },{ 306,{2,1,0},{8,7,6,3,4,5,2,1,0},{0,4,3,2,1,6,5,7,8} },{ 307,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 308,{1,0,2},{3,4,5,0,1,2,6,7,8},{0,7,8,3,4,6,5,1,2} },{ 309,{2,1,0},{5,4,3,2,1,0,6,8,7},{6,2,1,8,7,5,0,4,3} },{ 313,{2,1,0},{5,4,3,2,1,0,6,7,8},{6,1,2,8,7,5,0,4,3} },{ 333,{0,2,1},{5,3,4,1,2,0,6,8,7},{5,3,4,1,2,0,6,8,7} },{ 345,{0,2,1},{0,2,1,8,7,6,5,4,3},{0,2,1,8,7,6,5,4,3} },{ 347,{0,2,1},{2,1,0,8,7,6,5,4,3},{2,1,0,8,7,6,5,4,3} },{ 347,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,6,4,0,2,5,1,8,7} },{ 347,{1,2,0},{1,2,0,4,5,3,7,8,6},{8,5,7,2,0,6,1,3,4} },{ 347,{2,0,1},{2,0,1,5,3,4,8,6,7},{4,6,3,7,8,1,5,2,0} },{ 347,{2,1,0},{1,0,2,7,6,8,4,3,5},{7,5,8,4,3,1,6,0,2} },{ 347,{0,1,2},{4,5,3,7,8,6,1,2,0},{8,6,7,2,0,1,5,3,4} },{ 347,{0,2,1},{3,5,4,0,2,1,6,8,7},{3,5,4,0,2,1,6,8,7} },{ 347,{1,0,2},{4,3,5,1,0,2,7,6,8},{7,1,8,4,3,6,5,0,2} },{ 347,{1,2,0},{5,3,4,8,6,7,2,0,1},{4,1,3,7,8,5,6,2,0} },{ 347,{2,0,1},{3,4,5,6,7,8,0,1,2},{0,5,2,3,4,6,1,7,8} },{ 347,{2,1,0},{5,4,3,2,1,0,8,7,6},{2,6,0,8,7,5,1,4,3} },{ 347,{0,1,2},{8,6,7,2,0,1,5,3,4},{4,5,3,7,8,6,1,2,0} },{ 347,{0,2,1},{7,6,8,4,3,5,1,0,2},{7,6,8,4,3,5,1,0,2} },{ 347,{1,0,2},{8,7,6,5,4,3,2,1,0},{2,5,0,8,7,1,6,4,3} },{ 347,{1,2,0},{6,7,8,0,1,2,3,4,5},{0,6,2,3,4,1,5,7,8} },{ 347,{2,0,1},{7,8,6,1,2,0,4,5,3},{8,1,7,2,0,5,6,3,4} },{ 347,{2,1,0},{6,8,7,3,5,4,0,2,1},{3,1,4,0,2,6,5,8,7} },{ 348,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,6,4,0,2,5,1,8,7} },{ 349,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,6,4,0,2,5,1,8,7} },{ 351,{2,1,0},{1,0,2,7,8,6,5,3,4},{8,5,7,4,3,1,6,2,0} },{ 352,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,6,4,0,2,5,1,8,7} },{ 353,{1,0,2},{0,2,1,6,8,7,3,5,4},{3,6,4,0,2,5,1,8,7} },{ 358,{0,2,1},{0,1,2,7,8,6,5,3,4},{0,1,2,7,8,6,5,3,4} },{ 358,{0,1,2},{4,5,3,7,8,6,1,2,0},{8,6,7,2,0,1,5,3,4} },{ 358,{0,2,1},{4,5,3,2,0,1,6,7,8},{4,5,3,2,0,1,6,7,8} },{ 358,{0,1,2},{8,6,7,2,0,1,5,3,4},{4,5,3,7,8,6,1,2,0} },{ 358,{0,2,1},{8,6,7,3,4,5,1,2,0},{8,6,7,3,4,5,1,2,0} },{ 359,{2,1,0},{5,4,3,2,1,0,6,8,7},{2,6,0,8,7,5,1,4,3} },{ 374,{0,2,1},{4,5,3,2,0,1,6,7,8},{4,5,3,2,0,1,6,7,8} },{ 376,{2,1,0},{4,5,3,2,0,1,6,8,7},{2,6,0,7,8,5,1,3,4} },{ 379,{1,2,0},{1,2,0,4,5,3,6,7,8},{8,5,7,2,0,6,1,3,4} },{ 379,{2,0,1},{2,0,1,5,3,4,6,7,8},{4,6,3,7,8,1,5,2,0} },{ 379,{0,2,1},{3,5,4,0,2,1,6,8,7},{3,5,4,0,2,1,6,8,7} },{ 379,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 379,{2,1,0},{5,4,3,2,1,0,6,8,7},{2,6,0,8,7,5,1,4,3} },{ 382,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 383,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 388,{1,2,0},{4,3,5,7,8,6,2,1,0},{4,1,3,8,7,5,6,0,2} },{ 388,{2,0,1},{8,7,6,1,0,2,5,3,4},{7,1,8,2,0,5,6,4,3} },{ 389,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 390,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 391,{0,2,1},{4,5,3,2,0,1,6,7,8},{4,5,3,2,0,1,6,7,8} },{ 392,{2,1,0},{4,5,3,2,0,1,6,8,7},{2,6,0,7,8,5,1,3,4} },{ 393,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 394,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 395,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 396,{1,0,2},{4,3,5,1,0,2,6,8,7},{7,1,8,4,3,6,5,0,2} },{ 397,{2,1,0},{7,8,6,3,4,5,2,0,1},{3,4,2,0,1,6,5,7,8} },{ 399,{1,0,2},{8,7,6,5,4,3,2,1,0},{1,0,5,8,7,2,6,4,3} },{ 400,{0,2,1},{7,8,6,4,3,5,2,0,1},{7,8,6,4,3,5,2,0,1} },{ 403,{1,2,0},{0,1,2,4,5,3,6,7,8},{7,8,5,0,1,6,2,3,4} },{ 403,{2,0,1},{0,1,2,5,3,4,6,7,8},{3,4,6,7,8,2,5,0,1} },{ 403,{0,2,1},{8,7,6,4,3,5,2,1,0},{8,7,6,4,3,5,2,1,0} },{ 403,{1,0,2},{8,7,6,5,4,3,2,1,0},{1,0,5,8,7,2,6,4,3} },{ 403,{2,1,0},{8,7,6,3,5,4,2,1,0},{4,3,2,1,0,6,5,8,7} },{ 406,{0,2,1},{8,7,6,3,4,5,2,1,0},{8,7,6,3,4,5,2,1,0} },{ 407,{1,0,2},{8,7,6,5,4,3,2,1,0},{1,0,5,8,7,2,6,4,3} },{ 410,{2,1,0},{7,8,6,3,4,5,2,0,1},{4,3,2,1,0,6,5,7,8} },{ 411,{2,1,0},{8,7,6,3,4,5,2,1,0},{3,4,2,0,1,6,5,7,8} },{ 412,{0,1,2},{1,0,2,4,3,5,6,8,7},{1,0,2,4,3,5,6,8,7} },{ 412,{0,2,1},{0,1,2,7,8,6,5,3,4},{0,1,2,7,8,6,5,3,4} },{ 412,{0,2,1},{1,0,2,8,7,6,5,4,3},{1,0,2,8,7,6,5,4,3} },{ 412,{1,0,2},{0,1,2,7,8,6,5,3,4},{3,4,6,0,1,5,2,7,8} },{ 412,{1,0,2},{1,0,2,8,7,6,5,4,3},{4,3,6,1,0,5,2,8,7} },{ 412,{1,2,0},{0,1,2,3,4,5,6,7,8},{7,8,5,0,1,6,2,3,4} },{ 412,{1,2,0},{1,0,2,4,3,5,6,8,7},{8,7,5,1,0,6,2,4,3} },{ 412,{2,0,1},{0,1,2,3,4,5,6,7,8},{3,4,6,7,8,2,5,0,1} },{ 412,{2,0,1},{1,0,2,4,3,5,6,8,7},{4,3,6,8,7,2,5,1,0} },{ 412,{2,1,0},{0,1,2,7,8,6,5,3,4},{7,8,5,3,4,2,6,0,1} },{ 412,{2,1,0},{1,0,2,8,7,6,5,4,3},{8,7,5,4,3,2,6,1,0} },{ 412,{0,1,2},{3,4,5,7,8,6,2,0,1},{7,8,6,0,1,2,5,3,4} },{ 412,{0,1,2},{4,3,5,8,7,6,2,1,0},{8,7,6,1,0,2,5,4,3} },{ 412,{0,2,1},{3,4,5,0,1,2,6,7,8},{3,4,5,0,1,2,6,7,8} },{ 412,{0,2,1},{4,3,5,1,0,2,6,8,7},{4,3,5,1,0,2,6,8,7} },{ 412,{1,0,2},{3,4,5,0,1,2,6,7,8},{7,8,2,3,4,6,5,0,1} },{ 412,{1,0,2},{4,3,5,1,0,2,6,8,7},{8,7,2,4,3,6,5,1,0} },{ 412,{1,2,0},{3,4,5,7,8,6,2,0,1},{3,4,2,7,8,5,6,0,1} },{ 412,{1,2,0},{4,3,5,8,7,6,2,1,0},{4,3,2,8,7,5,6,1,0} },{ 412,{2,0,1},{3,4,5,7,8,6,2,0,1},{0,1,5,3,4,6,2,7,8} },{ 412,{2,0,1},{4,3,5,8,7,6,2,1,0},{1,0,5,4,3,6,2,8,7} },{ 412,{2,1,0},{3,4,5,0,1,2,6,7,8},{0,1,6,7,8,5,2,3,4} },{ 412,{2,1,0},{4,3,5,1,0,2,6,8,7},{1,0,6,8,7,5,2,4,3} },{ 412,{0,1,2},{7,8,6,0,1,2,5,3,4},{3,4,5,7,8,6,2,0,1} },{ 412,{0,1,2},{8,7,6,1,0,2,5,4,3},{4,3,5,8,7,6,2,1,0} },{ 412,{0,2,1},{7,8,6,3,4,5,2,0,1},{7,8,6,3,4,5,2,0,1} },{ 412,{0,2,1},{8,7,6,4,3,5,2,1,0},{8,7,6,4,3,5,2,1,0} },{ 412,{1,0,2},{7,8,6,3,4,5,2,0,1},{0,1,5,7,8,2,6,3,4} },{ 412,{1,0,2},{8,7,6,4,3,5,2,1,0},{1,0,5,8,7,2,6,4,3} },{ 412,{1,2,0},{7,8,6,0,1,2,5,3,4},{0,1,6,3,4,2,5,7,8} },{ 412,{1,2,0},{8,7,6,1,0,2,5,4,3},{1,0,6,4,3,2,5,8,7} },{ 412,{2,0,1},{7,8,6,0,1,2,5,3,4},{7,8,2,0,1,5,6,3,4} },{ 412,{2,0,1},{8,7,6,1,0,2,5,4,3},{8,7,2,1,0,5,6,4,3} },{ 412,{2,1,0},{7,8,6,3,4,5,2,0,1},{3,4,2,0,1,6,5,7,8} },{ 412,{2,1,0},{8,7,6,4,3,5,2,1,0},{4,3,2,1,0,6,5,8,7} },{ 413,{0,1,2},{1,0,2,4,3,5,6,8,7},{1,0,2,4,3,5,6,8,7} },{ 413,{1,0,2},{3,4,5,0,1,2,6,7,8},{7,8,2,3,4,6,5,0,1} },{ 413,{1,0,2},{4,3,5,1,0,2,6,8,7},{8,7,2,4,3,6,5,1,0} },{ 414,{0,1,2},{1,0,2,4,3,5,6,8,7},{1,0,2,4,3,5,6,8,7} },{ 414,{1,0,2},{0,1,2,7,8,6,5,3,4},{3,4,6,0,1,5,2,7,8} },{ 414,{1,0,2},{1,0,2,8,7,6,5,4,3},{4,3,6,1,0,5,2,8,7} },{ 414,{1,2,0},{3,4,5,8,7,6,2,0,1},{4,3,2,7,8,5,6,0,1} },{ 414,{1,2,0},{4,3,5,7,8,6,2,1,0},{3,4,2,8,7,5,6,1,0} },{ 414,{2,1,0},{3,4,5,0,1,2,6,8,7},{1,0,6,7,8,5,2,3,4} },{ 414,{2,1,0},{4,3,5,1,0,2,6,7,8},{0,1,6,8,7,5,2,4,3} },{ 414,{0,2,1},{7,8,6,4,3,5,2,0,1},{7,8,6,4,3,5,2,0,1} },{ 414,{0,2,1},{8,7,6,3,4,5,2,1,0},{8,7,6,3,4,5,2,1,0} },{ 414,{2,0,1},{7,8,6,0,1,2,5,4,3},{7,8,2,1,0,5,6,3,4} },{ 414,{2,0,1},{8,7,6,1,0,2,5,3,4},{8,7,2,0,1,5,6,4,3} },{ 415,{0,1,2},{1,0,2,4,3,5,6,8,7},{1,0,2,4,3,5,6,8,7} },{ 415,{1,0,2},{0,1,2,7,8,6,5,3,4},{3,4,6,0,1,5,2,7,8} },{ 415,{1,0,2},{1,0,2,8,7,6,5,4,3},{4,3,6,1,0,5,2,8,7} },{ 415,{0,1,2},{3,4,5,7,8,6,2,0,1},{7,8,6,0,1,2,5,3,4} },{ 415,{0,1,2},{4,3,5,8,7,6,2,1,0},{8,7,6,1,0,2,5,4,3} },{ 415,{1,0,2},{3,4,5,0,1,2,6,7,8},{7,8,2,3,4,6,5,0,1} },{ 415,{1,0,2},{4,3,5,1,0,2,6,8,7},{8,7,2,4,3,6,5,1,0} },{ 415,{0,1,2},{7,8,6,0,1,2,5,3,4},{3,4,5,7,8,6,2,0,1} },{ 415,{0,1,2},{8,7,6,1,0,2,5,4,3},{4,3,5,8,7,6,2,1,0} },{ 415,{1,0,2},{7,8,6,3,4,5,2,0,1},{0,1,5,7,8,2,6,3,4} },{ 415,{1,0,2},{8,7,6,4,3,5,2,1,0},{1,0,5,8,7,2,6,4,3} },`
Last edited by champagne on Wed Jul 03, 2024 4:06 pm, edited 1 time in total.
champagne
2017 Supporter

Posts: 7399
Joined: 02 August 2007
Location: France Brittany

### Re: MinLex 416 Subgroups

Sojourner9 wrote:The representation presented is human readable as the priority, while easily crunched by code.
These represent something constant in Sudoku.

I have to agree with you and also the gangsters in minlex order as defined too
Hidden Text: Show
Code: Select all
`123456789456789123789123456...................................................... ## 01123456789456789123789123465...................................................... ## 02123456789456789123789123564...................................................... ## 03123456789456789123789132465...................................................... ## 04123456789456789123789132546...................................................... ## 05123456789456789123789132564...................................................... ## 06123456789456789123789231564...................................................... ## 07123456789456789123789231645...................................................... ## 08123456789456789123798132546...................................................... ## 09123456789456789123798213564...................................................... ## 10123456789456789123798213654...................................................... ## 11123456789456789123798231564...................................................... ## 12123456789456789123798231645...................................................... ## 13123456789456789123897231564...................................................... ## 14123456789456789132789123546...................................................... ## 15123456789456789132789213456...................................................... ## 16123456789456789132789213645...................................................... ## 17123456789456789132789213654...................................................... ## 18123456789456789132789231546...................................................... ## 19123456789456789231789123645...................................................... ## 20123456789456789231789312456...................................................... ## 21123456789457189236689273145...................................................... ## 22123456789457189236689273154...................................................... ## 23123456789457189236689273514...................................................... ## 24123456789457189236689372145...................................................... ## 25123456789457189236689372154...................................................... ## 26123456789457189236698237514...................................................... ## 27123456789457189236698723145...................................................... ## 28123456789457189236698732145...................................................... ## 29123456789457189236869372145...................................................... ## 30123456789457189263689273154...................................................... ## 31123456789457189263689723154...................................................... ## 32123456789457189263689732154...................................................... ## 33123456789457189263968327145...................................................... ## 34123456789457189263968327514...................................................... ## 35123456789457189263968372145...................................................... ## 36123456789457189263986327145...................................................... ## 37123456789457189263986327154...................................................... ## 38123456789457189623689723145...................................................... ## 39123456789457189623689723154...................................................... ## 40123456789457189623689723514...................................................... ## 41123456789457189632698732514...................................................... ## 42123456789457189632896372154...................................................... ## 43123456789457289631896137254...................................................... ## 44`
coloin

Posts: 2425
Joined: 05 May 2005
Location: Devon

### Re: MinLex 416 Subgroups

So this is the minLex for the 44, I will update this in index416ML.
Sojourner9

Posts: 34
Joined: 10 March 2018

### Re: MinLex 416 Subgroups

champagne wrote:Hi,
It happens that I am just working (again) on the mapping of a band to the minlex form and reverse.
I don't want to pollute this thread, but this already exists in other forms.

Hi champagne,
Looking at your data it looks like the same thing I am reporting.
My main goal was to create something human readable but also readable by the code.
I toyed with leaving the identity off the list in each case but opted to leave it on because I should and because it shows that this is a subgroup.
All those with AMC 1 are left off your list because they are just the identity.
The fact that some have the same subgroup, by itself, is not important so much as it save duplications.
I sorted them by size and content so the identity was 0 and the 108 was 83.
Then all the 416 with AMC 1 got entry 0 and the one that was so long was pushed to the end.
But I'm not trying to judge, just pointing out some differences.

Do you have links to you work?
Sojourner9

Posts: 34
Joined: 10 March 2018

### Re: MinLex 416 Subgroups

Sojourner9 wrote:
champagne wrote:Hi,
It happens that I am just working (again) on the mapping of a band to the minlex form and reverse.
I don't want to pollute this thread, but this already exists in other forms.

Hi champagne,
Looking at your data it looks like the same thing I am reporting.
My main goal was to create something human readable but also readable by the code.
I toyed with leaving the identity off the list in each case but opted to leave it on because I should and because it shows that this is a subgroup.
All those with AMC 1 are left off your list because they are just the identity.
The fact that some have the same subgroup, by itself, is not important so much as it save duplications.
I sorted them by size and content so the identity was 0 and the 108 was 83.
Then all the 416 with AMC 1 got entry 0 and the one that was so long was pushed to the end.
But I'm not trying to judge, just pointing out some differences.

Do you have links to you work?

Hi Sojourner9,

We are not looking at these data with the same eyes, so variations in the tables are not surprising.
I use intensively all these data ( band minlex; 44 gangster list; auto morphisms;...) to produce efficient code to solve problems..
As a consequence, for example, automorphisms don't include as you noticed the base morph

Take just my tables as examples of existing uses of what gives your theoretical work.
champagne
2017 Supporter

Posts: 7399
Joined: 02 August 2007
Location: France Brittany

### Re: MinLex 416 Subgroups

Sojourner9 wrote:Do you have links to you work?

Sorry,I did not answer to this.
I'll just give links to the recent work on a virtual catalog :

http://forum.enjoysudoku.com/high-density-files-for-solution-grids-and-18-clues-puzzles-t42669.html
and
http://forum.enjoysudoku.com/solution-grids-per-gangster-t42904.html

but the use of bands and gangsters can be seen in many old threads related to the 17 clues search. as

http://forum.enjoysudoku.com/scan-solution-grids-for-17-clues-as-of-blue-t34012.html

BTW, my gangster tables don't have the same design as the table shown by coloin.
champagne
2017 Supporter

Posts: 7399
Joined: 02 August 2007
Location: France Brittany