MinLex 416 Subgroups

Programs which generate, solve, and analyze Sudoku puzzles

MinLex 416 Subgroups

Postby Sojourner9 » Wed Jul 03, 2024 10:24 am

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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Code: Select all
//
//  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 },
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    {148, 123456789, 457189263, 689273541,   2, 25 },
    {149, 123456789, 457189263, 689327154,   2, 38 },
    {150, 123456789, 457189263, 689327415,   1,  0 },
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    {161, 123456789, 457189263, 689732145,   1,  0 },
    {162, 123456789, 457189263, 689732154,   1,  0 },
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    {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 },
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    {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 },
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    {291, 123456789, 457189623, 896327145,   1,  0 },
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    {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 },
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    {320, 123456789, 457189632, 689732154,   1,  0 },
    {321, 123456789, 457189632, 689732514,   1,  0 },
    {322, 123456789, 457189632, 689732541,   1,  0 },
    {323, 123456789, 457189632, 698237145,   1,  0 },
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    {331, 123456789, 457189632, 698732145,   1,  0 },
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    {333, 123456789, 457189632, 869273145,   1,  0 },
    {334, 123456789, 457189632, 869372145,   2,  7 },
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    {337, 123456789, 457189632, 896327145,   1,  0 },
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    {339, 123456789, 457189632, 896327451,   1,  0 },
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    {341, 123456789, 457189632, 896372145,   1,  0 },
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    {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 },
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    {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

Postby champagne » Wed Jul 03, 2024 1:14 pm

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
Hidden Text: Show
Code: Select all
   "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",


and the list of all auto morphism shown as
band index 0-415; rows order; column order; digits order
Hidden Text: Show
Code: Select all
{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
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Re: MinLex 416 Subgroups

Postby coloin » Wed Jul 03, 2024 1:38 pm

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...................................................... ## 01
123456789456789123789123465...................................................... ## 02
123456789456789123789123564...................................................... ## 03
123456789456789123789132465...................................................... ## 04
123456789456789123789132546...................................................... ## 05
123456789456789123789132564...................................................... ## 06
123456789456789123789231564...................................................... ## 07
123456789456789123789231645...................................................... ## 08
123456789456789123798132546...................................................... ## 09
123456789456789123798213564...................................................... ## 10
123456789456789123798213654...................................................... ## 11
123456789456789123798231564...................................................... ## 12
123456789456789123798231645...................................................... ## 13
123456789456789123897231564...................................................... ## 14
123456789456789132789123546...................................................... ## 15
123456789456789132789213456...................................................... ## 16
123456789456789132789213645...................................................... ## 17
123456789456789132789213654...................................................... ## 18
123456789456789132789231546...................................................... ## 19
123456789456789231789123645...................................................... ## 20
123456789456789231789312456...................................................... ## 21
123456789457189236689273145...................................................... ## 22
123456789457189236689273154...................................................... ## 23
123456789457189236689273514...................................................... ## 24
123456789457189236689372145...................................................... ## 25
123456789457189236689372154...................................................... ## 26
123456789457189236698237514...................................................... ## 27
123456789457189236698723145...................................................... ## 28
123456789457189236698732145...................................................... ## 29
123456789457189236869372145...................................................... ## 30
123456789457189263689273154...................................................... ## 31
123456789457189263689723154...................................................... ## 32
123456789457189263689732154...................................................... ## 33
123456789457189263968327145...................................................... ## 34
123456789457189263968327514...................................................... ## 35
123456789457189263968372145...................................................... ## 36
123456789457189263986327145...................................................... ## 37
123456789457189263986327154...................................................... ## 38
123456789457189623689723145...................................................... ## 39
123456789457189623689723154...................................................... ## 40
123456789457189623689723514...................................................... ## 41
123456789457189632698732514...................................................... ## 42
123456789457189632896372154...................................................... ## 43
123456789457289631896137254...................................................... ## 44
coloin
 
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Location: Devon

Re: MinLex 416 Subgroups

Postby Sojourner9 » Wed Jul 03, 2024 9:44 pm

So this is the minLex for the 44, I will update this in index416ML.
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Re: MinLex 416 Subgroups

Postby Sojourner9 » Mon Jul 08, 2024 8:49 pm

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

Postby champagne » Tue Jul 09, 2024 10:53 am

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
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Location: France Brittany

Re: MinLex 416 Subgroups

Postby champagne » Tue Jul 09, 2024 12:13 pm

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
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