Identifier
-
Mp00112:
Set partitions
—complement⟶
Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
St000297: Binary words ⟶ ℤ
Values
{{1,2}} => {{1,2}} => [[1,2]] => 0 => 0
{{1},{2}} => {{1},{2}} => [[1],[2]] => 1 => 1
{{1,2,3}} => {{1,2,3}} => [[1,2,3]] => 00 => 0
{{1,2},{3}} => {{1},{2,3}} => [[1,3],[2]] => 10 => 1
{{1,3},{2}} => {{1,3},{2}} => [[1,3],[2]] => 10 => 1
{{1},{2,3}} => {{1,2},{3}} => [[1,2],[3]] => 01 => 0
{{1},{2},{3}} => {{1},{2},{3}} => [[1],[2],[3]] => 11 => 2
{{1,2,3,4}} => {{1,2,3,4}} => [[1,2,3,4]] => 000 => 0
{{1,2,3},{4}} => {{1},{2,3,4}} => [[1,3,4],[2]] => 100 => 1
{{1,2,4},{3}} => {{1,3,4},{2}} => [[1,3,4],[2]] => 100 => 1
{{1,2},{3,4}} => {{1,2},{3,4}} => [[1,2],[3,4]] => 010 => 0
{{1,2},{3},{4}} => {{1},{2},{3,4}} => [[1,4],[2],[3]] => 110 => 2
{{1,3,4},{2}} => {{1,2,4},{3}} => [[1,2,4],[3]] => 010 => 0
{{1,3},{2,4}} => {{1,3},{2,4}} => [[1,3],[2,4]] => 101 => 1
{{1,3},{2},{4}} => {{1},{2,4},{3}} => [[1,4],[2],[3]] => 110 => 2
{{1,4},{2,3}} => {{1,4},{2,3}} => [[1,3],[2,4]] => 101 => 1
{{1},{2,3,4}} => {{1,2,3},{4}} => [[1,2,3],[4]] => 001 => 0
{{1},{2,3},{4}} => {{1},{2,3},{4}} => [[1,3],[2],[4]] => 101 => 1
{{1,4},{2},{3}} => {{1,4},{2},{3}} => [[1,4],[2],[3]] => 110 => 2
{{1},{2,4},{3}} => {{1,3},{2},{4}} => [[1,3],[2],[4]] => 101 => 1
{{1},{2},{3,4}} => {{1,2},{3},{4}} => [[1,2],[3],[4]] => 011 => 0
{{1},{2},{3},{4}} => {{1},{2},{3},{4}} => [[1],[2],[3],[4]] => 111 => 3
{{1,2,3,4,5}} => {{1,2,3,4,5}} => [[1,2,3,4,5]] => 0000 => 0
{{1,2,3,4},{5}} => {{1},{2,3,4,5}} => [[1,3,4,5],[2]] => 1000 => 1
{{1,2,3,5},{4}} => {{1,3,4,5},{2}} => [[1,3,4,5],[2]] => 1000 => 1
{{1,2,3},{4,5}} => {{1,2},{3,4,5}} => [[1,2,5],[3,4]] => 0100 => 0
{{1,2,3},{4},{5}} => {{1},{2},{3,4,5}} => [[1,4,5],[2],[3]] => 1100 => 2
{{1,2,4,5},{3}} => {{1,2,4,5},{3}} => [[1,2,4,5],[3]] => 0100 => 0
{{1,2,4},{3,5}} => {{1,3},{2,4,5}} => [[1,3,5],[2,4]] => 1010 => 1
{{1,2,4},{3},{5}} => {{1},{2,4,5},{3}} => [[1,4,5],[2],[3]] => 1100 => 2
{{1,2,5},{3,4}} => {{1,4,5},{2,3}} => [[1,3,5],[2,4]] => 1010 => 1
{{1,2},{3,4,5}} => {{1,2,3},{4,5}} => [[1,2,3],[4,5]] => 0010 => 0
{{1,2},{3,4},{5}} => {{1},{2,3},{4,5}} => [[1,3],[2,5],[4]] => 1010 => 1
{{1,2,5},{3},{4}} => {{1,4,5},{2},{3}} => [[1,4,5],[2],[3]] => 1100 => 2
{{1,2},{3,5},{4}} => {{1,3},{2},{4,5}} => [[1,3],[2,5],[4]] => 1010 => 1
{{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => [[1,2],[3,5],[4]] => 0110 => 0
{{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}} => [[1,5],[2],[3],[4]] => 1110 => 3
{{1,3,4,5},{2}} => {{1,2,3,5},{4}} => [[1,2,3,5],[4]] => 0010 => 0
{{1,3,4},{2,5}} => {{1,4},{2,3,5}} => [[1,3,5],[2,4]] => 1010 => 1
{{1,3,4},{2},{5}} => {{1},{2,3,5},{4}} => [[1,3,5],[2],[4]] => 1010 => 1
{{1,3,5},{2,4}} => {{1,3,5},{2,4}} => [[1,3,5],[2,4]] => 1010 => 1
{{1,3},{2,4,5}} => {{1,2,4},{3,5}} => [[1,2,4],[3,5]] => 0101 => 0
{{1,3},{2,4},{5}} => {{1},{2,4},{3,5}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => [[1,3,5],[2],[4]] => 1010 => 1
{{1,3},{2,5},{4}} => {{1,4},{2},{3,5}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1,3},{2},{4,5}} => {{1,2},{3,5},{4}} => [[1,2],[3,5],[4]] => 0110 => 0
{{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}} => [[1,5],[2],[3],[4]] => 1110 => 3
{{1,4,5},{2,3}} => {{1,2,5},{3,4}} => [[1,2,5],[3,4]] => 0100 => 0
{{1,4},{2,3,5}} => {{1,3,4},{2,5}} => [[1,3,4],[2,5]] => 1001 => 1
{{1,4},{2,3},{5}} => {{1},{2,5},{3,4}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1,5},{2,3,4}} => {{1,5},{2,3,4}} => [[1,3,4],[2,5]] => 1001 => 1
{{1},{2,3,4,5}} => {{1,2,3,4},{5}} => [[1,2,3,4],[5]] => 0001 => 0
{{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => [[1,3,4],[2],[5]] => 1001 => 1
{{1,5},{2,3},{4}} => {{1,5},{2},{3,4}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1},{2,3,5},{4}} => {{1,3,4},{2},{5}} => [[1,3,4],[2],[5]] => 1001 => 1
{{1},{2,3},{4,5}} => {{1,2},{3,4},{5}} => [[1,2],[3,4],[5]] => 0101 => 0
{{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}} => [[1,4],[2],[3],[5]] => 1101 => 2
{{1,4,5},{2},{3}} => {{1,2,5},{3},{4}} => [[1,2,5],[3],[4]] => 0110 => 0
{{1,4},{2,5},{3}} => {{1,4},{2,5},{3}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1,4},{2},{3,5}} => {{1,3},{2,5},{4}} => [[1,3],[2,5],[4]] => 1010 => 1
{{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}} => [[1,5],[2],[3],[4]] => 1110 => 3
{{1,5},{2,4},{3}} => {{1,5},{2,4},{3}} => [[1,4],[2,5],[3]] => 1101 => 2
{{1},{2,4,5},{3}} => {{1,2,4},{3},{5}} => [[1,2,4],[3],[5]] => 0101 => 0
{{1},{2,4},{3,5}} => {{1,3},{2,4},{5}} => [[1,3],[2,4],[5]] => 1011 => 1
{{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => [[1,4],[2],[3],[5]] => 1101 => 2
{{1,5},{2},{3,4}} => {{1,5},{2,3},{4}} => [[1,3],[2,5],[4]] => 1010 => 1
{{1},{2,5},{3,4}} => {{1,4},{2,3},{5}} => [[1,3],[2,4],[5]] => 1011 => 1
{{1},{2},{3,4,5}} => {{1,2,3},{4},{5}} => [[1,2,3],[4],[5]] => 0011 => 0
{{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}} => [[1,3],[2],[4],[5]] => 1011 => 1
{{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => [[1,5],[2],[3],[4]] => 1110 => 3
{{1},{2,5},{3},{4}} => {{1,4},{2},{3},{5}} => [[1,4],[2],[3],[5]] => 1101 => 2
{{1},{2},{3,5},{4}} => {{1,3},{2},{4},{5}} => [[1,3],[2],[4],[5]] => 1011 => 1
{{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}} => [[1,2],[3],[4],[5]] => 0111 => 0
{{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => [[1],[2],[3],[4],[5]] => 1111 => 4
{{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => [[1,2,3,4,5,6]] => 00000 => 0
{{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}} => [[1,3,4,5,6],[2]] => 10000 => 1
{{1,2,3,4,6},{5}} => {{1,3,4,5,6},{2}} => [[1,3,4,5,6],[2]] => 10000 => 1
{{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}} => [[1,2,5,6],[3,4]] => 01000 => 0
{{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}} => [[1,4,5,6],[2],[3]] => 11000 => 2
{{1,2,3,5,6},{4}} => {{1,2,4,5,6},{3}} => [[1,2,4,5,6],[3]] => 01000 => 0
{{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}} => [[1,3,5,6],[2,4]] => 10100 => 1
{{1,2,3,5},{4},{6}} => {{1},{2,4,5,6},{3}} => [[1,4,5,6],[2],[3]] => 11000 => 2
{{1,2,3,6},{4,5}} => {{1,4,5,6},{2,3}} => [[1,3,5,6],[2,4]] => 10100 => 1
{{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => [[1,2,3],[4,5,6]] => 00100 => 0
{{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,2,3,6},{4},{5}} => {{1,4,5,6},{2},{3}} => [[1,4,5,6],[2],[3]] => 11000 => 2
{{1,2,3},{4,6},{5}} => {{1,3},{2},{4,5,6}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}} => [[1,2,6],[3,5],[4]] => 01100 => 0
{{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}} => [[1,5,6],[2],[3],[4]] => 11100 => 3
{{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}} => [[1,2,3,5,6],[4]] => 00100 => 0
{{1,2,4,5},{3,6}} => {{1,4},{2,3,5,6}} => [[1,3,5,6],[2,4]] => 10100 => 1
{{1,2,4,5},{3},{6}} => {{1},{2,3,5,6},{4}} => [[1,3,5,6],[2],[4]] => 10100 => 1
{{1,2,4,6},{3,5}} => {{1,3,5,6},{2,4}} => [[1,3,5,6],[2,4]] => 10100 => 1
{{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}} => [[1,2,4],[3,5,6]] => 01010 => 0
{{1,2,4},{3,5},{6}} => {{1},{2,4},{3,5,6}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2,4,6},{3},{5}} => {{1,3,5,6},{2},{4}} => [[1,3,5,6],[2],[4]] => 10100 => 1
{{1,2,4},{3,6},{5}} => {{1,4},{2},{3,5,6}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2,4},{3},{5,6}} => {{1,2},{3,5,6},{4}} => [[1,2,6],[3,5],[4]] => 01100 => 0
{{1,2,4},{3},{5},{6}} => {{1},{2},{3,5,6},{4}} => [[1,5,6],[2],[3],[4]] => 11100 => 3
{{1,2,5,6},{3,4}} => {{1,2,5,6},{3,4}} => [[1,2,5,6],[3,4]] => 01000 => 0
{{1,2,5},{3,4,6}} => {{1,3,4},{2,5,6}} => [[1,3,4],[2,5,6]] => 10010 => 1
>>> Load all 1630 entries. <<<{{1,2,5},{3,4},{6}} => {{1},{2,5,6},{3,4}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2,6},{3,4,5}} => {{1,5,6},{2,3,4}} => [[1,3,4],[2,5,6]] => 10010 => 1
{{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}} => [[1,2,3,4],[5,6]] => 00010 => 0
{{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}} => [[1,3,4],[2,6],[5]] => 10010 => 1
{{1,2,6},{3,4},{5}} => {{1,5,6},{2},{3,4}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2},{3,4,6},{5}} => {{1,3,4},{2},{5,6}} => [[1,3,4],[2,6],[5]] => 10010 => 1
{{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => [[1,2],[3,4],[5,6]] => 01010 => 0
{{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => [[1,2,5,6],[3],[4]] => 01100 => 0
{{1,2,5},{3,6},{4}} => {{1,4},{2,5,6},{3}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2,5},{3},{4,6}} => {{1,3},{2,5,6},{4}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,2,5},{3},{4},{6}} => {{1},{2,5,6},{3},{4}} => [[1,5,6],[2],[3],[4]] => 11100 => 3
{{1,2,6},{3,5},{4}} => {{1,5,6},{2,4},{3}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,2},{3,5,6},{4}} => {{1,2,4},{3},{5,6}} => [[1,2,4],[3,6],[5]] => 01010 => 0
{{1,2},{3,5},{4,6}} => {{1,3},{2,4},{5,6}} => [[1,3],[2,4],[5,6]] => 10110 => 1
{{1,2},{3,5},{4},{6}} => {{1},{2,4},{3},{5,6}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,2,6},{3},{4,5}} => {{1,5,6},{2,3},{4}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => [[1,3],[2,4],[5,6]] => 10110 => 1
{{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}} => [[1,2,3],[4,6],[5]] => 00110 => 0
{{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1,2,6},{3},{4},{5}} => {{1,5,6},{2},{3},{4}} => [[1,5,6],[2],[3],[4]] => 11100 => 3
{{1,2},{3,6},{4},{5}} => {{1,4},{2},{3},{5,6}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,2},{3},{4,6},{5}} => {{1,3},{2},{4},{5,6}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => [[1,2],[3,6],[4],[5]] => 01110 => 0
{{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}} => [[1,6],[2],[3],[4],[5]] => 11110 => 4
{{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}} => [[1,2,3,4,6],[5]] => 00010 => 0
{{1,3,4,5},{2,6}} => {{1,5},{2,3,4,6}} => [[1,3,4,6],[2,5]] => 10010 => 1
{{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}} => [[1,3,4,6],[2],[5]] => 10010 => 1
{{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}} => [[1,3,4,6],[2,5]] => 10010 => 1
{{1,3,4},{2,5,6}} => {{1,2,5},{3,4,6}} => [[1,2,5],[3,4,6]] => 01001 => 0
{{1,3,4},{2,5},{6}} => {{1},{2,5},{3,4,6}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => [[1,3,4,6],[2],[5]] => 10010 => 1
{{1,3,4},{2,6},{5}} => {{1,5},{2},{3,4,6}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3,4},{2},{5,6}} => {{1,2},{3,4,6},{5}} => [[1,2,6],[3,4],[5]] => 01010 => 0
{{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}} => [[1,4,6],[2],[3],[5]] => 11010 => 2
{{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}} => [[1,2,4,6],[3,5]] => 01010 => 0
{{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}} => [[1,3,5],[2,4,6]] => 10101 => 1
{{1,3,5},{2,4},{6}} => {{1},{2,4,6},{3,5}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3,6},{2,4,5}} => {{1,4,6},{2,3,5}} => [[1,3,5],[2,4,6]] => 10101 => 1
{{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}} => [[1,2,3,5],[4,6]] => 00101 => 0
{{1,3},{2,4,5},{6}} => {{1},{2,3,5},{4,6}} => [[1,3,5],[2,6],[4]] => 10101 => 1
{{1,3,6},{2,4},{5}} => {{1,4,6},{2},{3,5}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3},{2,4,6},{5}} => {{1,3,5},{2},{4,6}} => [[1,3,5],[2,6],[4]] => 10101 => 1
{{1,3},{2,4},{5,6}} => {{1,2},{3,5},{4,6}} => [[1,2],[3,5],[4,6]] => 01101 => 0
{{1,3},{2,4},{5},{6}} => {{1},{2},{3,5},{4,6}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,3,5,6},{2},{4}} => {{1,2,4,6},{3},{5}} => [[1,2,4,6],[3],[5]] => 01010 => 0
{{1,3,5},{2,6},{4}} => {{1,5},{2,4,6},{3}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3,5},{2},{4,6}} => {{1,3},{2,4,6},{5}} => [[1,3,6],[2,4],[5]] => 10110 => 1
{{1,3,5},{2},{4},{6}} => {{1},{2,4,6},{3},{5}} => [[1,4,6],[2],[3],[5]] => 11010 => 2
{{1,3,6},{2,5},{4}} => {{1,4,6},{2,5},{3}} => [[1,4,6],[2,5],[3]] => 11010 => 2
{{1,3},{2,5,6},{4}} => {{1,2,5},{3},{4,6}} => [[1,2,5],[3,6],[4]] => 01101 => 0
{{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}} => [[1,3],[2,5],[4,6]] => 10101 => 1
{{1,3},{2,5},{4},{6}} => {{1},{2,5},{3},{4,6}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,3,6},{2},{4,5}} => {{1,4,6},{2,3},{5}} => [[1,3,6],[2,4],[5]] => 10110 => 1
{{1,3},{2,6},{4,5}} => {{1,5},{2,3},{4,6}} => [[1,3],[2,5],[4,6]] => 10101 => 1
{{1,3},{2},{4,5,6}} => {{1,2,3},{4,6},{5}} => [[1,2,3],[4,6],[5]] => 00110 => 0
{{1,3},{2},{4,5},{6}} => {{1},{2,3},{4,6},{5}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1,3,6},{2},{4},{5}} => {{1,4,6},{2},{3},{5}} => [[1,4,6],[2],[3],[5]] => 11010 => 2
{{1,3},{2,6},{4},{5}} => {{1,5},{2},{3},{4,6}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1,3},{2},{4},{5,6}} => {{1,2},{3},{4,6},{5}} => [[1,2],[3,6],[4],[5]] => 01110 => 0
{{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}} => [[1,6],[2],[3],[4],[5]] => 11110 => 4
{{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}} => [[1,2,3,6],[4,5]] => 00100 => 0
{{1,4,5},{2,3,6}} => {{1,4,5},{2,3,6}} => [[1,3,5],[2,4,6]] => 10101 => 1
{{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,4,6},{2,3,5}} => {{1,3,6},{2,4,5}} => [[1,3,5],[2,4,6]] => 10101 => 1
{{1,4},{2,3,5,6}} => {{1,2,4,5},{3,6}} => [[1,2,4,5],[3,6]] => 01001 => 0
{{1,4},{2,3,5},{6}} => {{1},{2,4,5},{3,6}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1,4,6},{2,3},{5}} => {{1,3,6},{2},{4,5}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,4},{2,3,6},{5}} => {{1,4,5},{2},{3,6}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => [[1,2],[3,5],[4,6]] => 01101 => 0
{{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}} => [[1,2,5],[3,4,6]] => 01001 => 0
{{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}} => [[1,3,4,5],[2,6]] => 10001 => 1
{{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => [[1,3,4,5],[2,6]] => 10001 => 1
{{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}} => [[1,2,3,4,5],[6]] => 00001 => 0
{{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => [[1,3,4,5],[2],[6]] => 10001 => 1
{{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1},{2,3,4,6},{5}} => {{1,3,4,5},{2},{6}} => [[1,3,4,5],[2],[6]] => 10001 => 1
{{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}} => [[1,2,5],[3,4],[6]] => 01001 => 0
{{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}} => [[1,4,5],[2],[3],[6]] => 11001 => 2
{{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}} => [[1,2,6],[3,5],[4]] => 01100 => 0
{{1,5},{2,3,6},{4}} => {{1,4,5},{2,6},{3}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1,5},{2,3},{4,6}} => {{1,3},{2,6},{4,5}} => [[1,3],[2,5],[4,6]] => 10101 => 1
{{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,6},{2,3,5},{4}} => {{1,6},{2,4,5},{3}} => [[1,4,5],[2,6],[3]] => 11001 => 2
{{1},{2,3,5,6},{4}} => {{1,2,4,5},{3},{6}} => [[1,2,4,5],[3],[6]] => 01001 => 0
{{1},{2,3,5},{4,6}} => {{1,3},{2,4,5},{6}} => [[1,3,5],[2,4],[6]] => 10101 => 1
{{1},{2,3,5},{4},{6}} => {{1},{2,4,5},{3},{6}} => [[1,4,5],[2],[3],[6]] => 11001 => 2
{{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => [[1,3],[2,5],[4,6]] => 10101 => 1
{{1},{2,3,6},{4,5}} => {{1,4,5},{2,3},{6}} => [[1,3,5],[2,4],[6]] => 10101 => 1
{{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}} => [[1,2,3],[4,5],[6]] => 00101 => 0
{{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => [[1,3],[2,5],[4],[6]] => 10101 => 1
{{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1},{2,3,6},{4},{5}} => {{1,4,5},{2},{3},{6}} => [[1,4,5],[2],[3],[6]] => 11001 => 2
{{1},{2,3},{4,6},{5}} => {{1,3},{2},{4,5},{6}} => [[1,3],[2,5],[4],[6]] => 10101 => 1
{{1},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}} => [[1,2],[3,5],[4],[6]] => 01101 => 0
{{1},{2,3},{4},{5},{6}} => {{1},{2},{3},{4,5},{6}} => [[1,5],[2],[3],[4],[6]] => 11101 => 3
{{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}} => [[1,2,3,6],[4],[5]] => 00110 => 0
{{1,4,5},{2,6},{3}} => {{1,5},{2,3,6},{4}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,4,5},{2},{3,6}} => {{1,4},{2,3,6},{5}} => [[1,3,6],[2,4],[5]] => 10110 => 1
{{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}} => [[1,3,6],[2],[4],[5]] => 10110 => 1
{{1,4,6},{2,5},{3}} => {{1,3,6},{2,5},{4}} => [[1,3,6],[2,5],[4]] => 10100 => 1
{{1,4},{2,5,6},{3}} => {{1,2,5},{3,6},{4}} => [[1,2,5],[3,6],[4]] => 01101 => 0
{{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1,4},{2,5},{3},{6}} => {{1},{2,5},{3,6},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,4,6},{2},{3,5}} => {{1,3,6},{2,4},{5}} => [[1,3,6],[2,4],[5]] => 10110 => 1
{{1,4},{2,6},{3,5}} => {{1,5},{2,4},{3,6}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1,4},{2},{3,5,6}} => {{1,2,4},{3,6},{5}} => [[1,2,4],[3,6],[5]] => 01010 => 0
{{1,4},{2},{3,5},{6}} => {{1},{2,4},{3,6},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,4,6},{2},{3},{5}} => {{1,3,6},{2},{4},{5}} => [[1,3,6],[2],[4],[5]] => 10110 => 1
{{1,4},{2,6},{3},{5}} => {{1,5},{2},{3,6},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,4},{2},{3,6},{5}} => {{1,4},{2},{3,6},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,4},{2},{3},{5,6}} => {{1,2},{3,6},{4},{5}} => [[1,2],[3,6],[4],[5]] => 01110 => 0
{{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}} => [[1,6],[2],[3],[4],[5]] => 11110 => 4
{{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}} => [[1,2,6],[3,5],[4]] => 01100 => 0
{{1,5},{2,4,6},{3}} => {{1,3,5},{2,6},{4}} => [[1,3,5],[2,6],[4]] => 10101 => 1
{{1,5},{2,4},{3,6}} => {{1,4},{2,6},{3,5}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}} => [[1,3,5],[2,6],[4]] => 10101 => 1
{{1},{2,4,5,6},{3}} => {{1,2,3,5},{4},{6}} => [[1,2,3,5],[4],[6]] => 00101 => 0
{{1},{2,4,5},{3,6}} => {{1,4},{2,3,5},{6}} => [[1,3,5],[2,4],[6]] => 10101 => 1
{{1},{2,4,5},{3},{6}} => {{1},{2,3,5},{4},{6}} => [[1,3,5],[2],[4],[6]] => 10101 => 1
{{1,6},{2,4},{3,5}} => {{1,6},{2,4},{3,5}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1},{2,4,6},{3,5}} => {{1,3,5},{2,4},{6}} => [[1,3,5],[2,4],[6]] => 10101 => 1
{{1},{2,4},{3,5,6}} => {{1,2,4},{3,5},{6}} => [[1,2,4],[3,5],[6]] => 01011 => 0
{{1},{2,4},{3,5},{6}} => {{1},{2,4},{3,5},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1},{2,4,6},{3},{5}} => {{1,3,5},{2},{4},{6}} => [[1,3,5],[2],[4],[6]] => 10101 => 1
{{1},{2,4},{3,6},{5}} => {{1,4},{2},{3,5},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1},{2,4},{3},{5,6}} => {{1,2},{3,5},{4},{6}} => [[1,2],[3,5],[4],[6]] => 01101 => 0
{{1},{2,4},{3},{5},{6}} => {{1},{2},{3,5},{4},{6}} => [[1,5],[2],[3],[4],[6]] => 11101 => 3
{{1,5,6},{2},{3,4}} => {{1,2,6},{3,4},{5}} => [[1,2,6],[3,4],[5]] => 01010 => 0
{{1,5},{2,6},{3,4}} => {{1,5},{2,6},{3,4}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1,5},{2},{3,4,6}} => {{1,3,4},{2,6},{5}} => [[1,3,4],[2,6],[5]] => 10010 => 1
{{1,5},{2},{3,4},{6}} => {{1},{2,6},{3,4},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => [[1,4],[2,5],[3,6]] => 11011 => 2
{{1},{2,5,6},{3,4}} => {{1,2,5},{3,4},{6}} => [[1,2,5],[3,4],[6]] => 01001 => 0
{{1},{2,5},{3,4,6}} => {{1,3,4},{2,5},{6}} => [[1,3,4],[2,5],[6]] => 10011 => 1
{{1},{2,5},{3,4},{6}} => {{1},{2,5},{3,4},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1,6},{2},{3,4,5}} => {{1,6},{2,3,4},{5}} => [[1,3,4],[2,6],[5]] => 10010 => 1
{{1},{2,6},{3,4,5}} => {{1,5},{2,3,4},{6}} => [[1,3,4],[2,5],[6]] => 10011 => 1
{{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}} => [[1,2,3,4],[5],[6]] => 00011 => 0
{{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}} => [[1,3,4],[2],[5],[6]] => 10011 => 1
{{1,6},{2},{3,4},{5}} => {{1,6},{2},{3,4},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1},{2,6},{3,4},{5}} => {{1,5},{2},{3,4},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1},{2},{3,4,6},{5}} => {{1,3,4},{2},{5},{6}} => [[1,3,4],[2],[5],[6]] => 10011 => 1
{{1},{2},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}} => [[1,2],[3,4],[5],[6]] => 01011 => 0
{{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => [[1,4],[2],[3],[5],[6]] => 11011 => 2
{{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}} => [[1,2,6],[3],[4],[5]] => 01110 => 0
{{1,5},{2,6},{3},{4}} => {{1,5},{2,6},{3},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1,5},{2},{3,6},{4}} => {{1,4},{2,6},{3},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1,5},{2},{3},{4,6}} => {{1,3},{2,6},{4},{5}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}} => [[1,6],[2],[3],[4],[5]] => 11110 => 4
{{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}} => [[1,5],[2,6],[3],[4]] => 11101 => 3
{{1},{2,5,6},{3},{4}} => {{1,2,5},{3},{4},{6}} => [[1,2,5],[3],[4],[6]] => 01101 => 0
{{1},{2,5},{3,6},{4}} => {{1,4},{2,5},{3},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1},{2,5},{3},{4,6}} => {{1,3},{2,5},{4},{6}} => [[1,3],[2,5],[4],[6]] => 10101 => 1
{{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => [[1,5],[2],[3],[4],[6]] => 11101 => 3
{{1,6},{2},{3,5},{4}} => {{1,6},{2,4},{3},{5}} => [[1,4],[2,6],[3],[5]] => 11010 => 2
{{1},{2,6},{3,5},{4}} => {{1,5},{2,4},{3},{6}} => [[1,4],[2,5],[3],[6]] => 11011 => 2
{{1},{2},{3,5,6},{4}} => {{1,2,4},{3},{5},{6}} => [[1,2,4],[3],[5],[6]] => 01011 => 0
{{1},{2},{3,5},{4,6}} => {{1,3},{2,4},{5},{6}} => [[1,3],[2,4],[5],[6]] => 10111 => 1
{{1},{2},{3,5},{4},{6}} => {{1},{2,4},{3},{5},{6}} => [[1,4],[2],[3],[5],[6]] => 11011 => 2
{{1,6},{2},{3},{4,5}} => {{1,6},{2,3},{4},{5}} => [[1,3],[2,6],[4],[5]] => 10110 => 1
{{1},{2,6},{3},{4,5}} => {{1,5},{2,3},{4},{6}} => [[1,3],[2,5],[4],[6]] => 10101 => 1
{{1},{2},{3,6},{4,5}} => {{1,4},{2,3},{5},{6}} => [[1,3],[2,4],[5],[6]] => 10111 => 1
{{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}} => [[1,2,3],[4],[5],[6]] => 00111 => 0
{{1},{2},{3},{4,5},{6}} => {{1},{2,3},{4},{5},{6}} => [[1,3],[2],[4],[5],[6]] => 10111 => 1
{{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => [[1,6],[2],[3],[4],[5]] => 11110 => 4
{{1},{2,6},{3},{4},{5}} => {{1,5},{2},{3},{4},{6}} => [[1,5],[2],[3],[4],[6]] => 11101 => 3
{{1},{2},{3,6},{4},{5}} => {{1,4},{2},{3},{5},{6}} => [[1,4],[2],[3],[5],[6]] => 11011 => 2
{{1},{2},{3},{4,6},{5}} => {{1,3},{2},{4},{5},{6}} => [[1,3],[2],[4],[5],[6]] => 10111 => 1
{{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}} => [[1,2],[3],[4],[5],[6]] => 01111 => 0
{{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => [[1],[2],[3],[4],[5],[6]] => 11111 => 5
{{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => [[1,2,3,4,5,6,7]] => 000000 => 0
{{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}} => [[1,3,4,5,6,7],[2]] => 100000 => 1
{{1,2,3,4,5,7},{6}} => {{1,3,4,5,6,7},{2}} => [[1,3,4,5,6,7],[2]] => 100000 => 1
{{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}} => [[1,2,5,6,7],[3,4]] => 010000 => 0
{{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}} => [[1,4,5,6,7],[2],[3]] => 110000 => 2
{{1,2,3,4,6,7},{5}} => {{1,2,4,5,6,7},{3}} => [[1,2,4,5,6,7],[3]] => 010000 => 0
{{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}} => [[1,3,5,6,7],[2,4]] => 101000 => 1
{{1,2,3,4,6},{5},{7}} => {{1},{2,4,5,6,7},{3}} => [[1,4,5,6,7],[2],[3]] => 110000 => 2
{{1,2,3,4,7},{5,6}} => {{1,4,5,6,7},{2,3}} => [[1,3,5,6,7],[2,4]] => 101000 => 1
{{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}} => [[1,2,3,7],[4,5,6]] => 001000 => 0
{{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,3,4,7},{5},{6}} => {{1,4,5,6,7},{2},{3}} => [[1,4,5,6,7],[2],[3]] => 110000 => 2
{{1,2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6,7}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}} => [[1,2,6,7],[3,5],[4]] => 011000 => 0
{{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}} => [[1,5,6,7],[2],[3],[4]] => 111000 => 3
{{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}} => [[1,2,3,5,6,7],[4]] => 001000 => 0
{{1,2,3,5,6},{4,7}} => {{1,4},{2,3,5,6,7}} => [[1,3,5,6,7],[2,4]] => 101000 => 1
{{1,2,3,5,6},{4},{7}} => {{1},{2,3,5,6,7},{4}} => [[1,3,5,6,7],[2],[4]] => 101000 => 1
{{1,2,3,5,7},{4,6}} => {{1,3,5,6,7},{2,4}} => [[1,3,5,6,7],[2,4]] => 101000 => 1
{{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}} => [[1,2,4,7],[3,5,6]] => 010100 => 0
{{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3,5,7},{4},{6}} => {{1,3,5,6,7},{2},{4}} => [[1,3,5,6,7],[2],[4]] => 101000 => 1
{{1,2,3,5},{4,7},{6}} => {{1,4},{2},{3,5,6,7}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3,5},{4},{6,7}} => {{1,2},{3,5,6,7},{4}} => [[1,2,6,7],[3,5],[4]] => 011000 => 0
{{1,2,3,5},{4},{6},{7}} => {{1},{2},{3,5,6,7},{4}} => [[1,5,6,7],[2],[3],[4]] => 111000 => 3
{{1,2,3,6,7},{4,5}} => {{1,2,5,6,7},{3,4}} => [[1,2,5,6,7],[3,4]] => 010000 => 0
{{1,2,3,6},{4,5,7}} => {{1,3,4},{2,5,6,7}} => [[1,3,4,7],[2,5,6]] => 100100 => 1
{{1,2,3,6},{4,5},{7}} => {{1},{2,5,6,7},{3,4}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3,7},{4,5,6}} => {{1,5,6,7},{2,3,4}} => [[1,3,4,7],[2,5,6]] => 100100 => 1
{{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}} => [[1,2,3,4],[5,6,7]] => 000100 => 0
{{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}} => [[1,3,4],[2,6,7],[5]] => 100100 => 1
{{1,2,3,7},{4,5},{6}} => {{1,5,6,7},{2},{3,4}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3},{4,5,7},{6}} => {{1,3,4},{2},{5,6,7}} => [[1,3,4],[2,6,7],[5]] => 100100 => 1
{{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}} => [[1,2,7],[3,4],[5,6]] => 010100 => 0
{{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,3,6,7},{4},{5}} => {{1,2,5,6,7},{3},{4}} => [[1,2,5,6,7],[3],[4]] => 011000 => 0
{{1,2,3,6},{4,7},{5}} => {{1,4},{2,5,6,7},{3}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3,6},{4},{5,7}} => {{1,3},{2,5,6,7},{4}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,3,6},{4},{5},{7}} => {{1},{2,5,6,7},{3},{4}} => [[1,5,6,7],[2],[3],[4]] => 111000 => 3
{{1,2,3,7},{4,6},{5}} => {{1,5,6,7},{2,4},{3}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6,7}} => [[1,2,4],[3,6,7],[5]] => 010100 => 0
{{1,2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6,7}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,3,7},{4},{5,6}} => {{1,5,6,7},{2,3},{4}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6,7}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => [[1,2,3],[4,6,7],[5]] => 001100 => 0
{{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2,3,7},{4},{5},{6}} => {{1,5,6,7},{2},{3},{4}} => [[1,5,6,7],[2],[3],[4]] => 111000 => 3
{{1,2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6,7}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}} => [[1,6,7],[2],[3],[4],[5]] => 111100 => 4
{{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}} => [[1,2,3,4,6,7],[5]] => 000100 => 0
{{1,2,4,5,6},{3,7}} => {{1,5},{2,3,4,6,7}} => [[1,3,4,6,7],[2,5]] => 100100 => 1
{{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}} => [[1,3,4,6,7],[2],[5]] => 100100 => 1
{{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}} => [[1,3,4,6,7],[2,5]] => 100100 => 1
{{1,2,4,5},{3,6,7}} => {{1,2,5},{3,4,6,7}} => [[1,2,5,7],[3,4,6]] => 010010 => 0
{{1,2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6,7}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4,5,7},{3},{6}} => {{1,3,4,6,7},{2},{5}} => [[1,3,4,6,7],[2],[5]] => 100100 => 1
{{1,2,4,5},{3,7},{6}} => {{1,5},{2},{3,4,6,7}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4,5},{3},{6,7}} => {{1,2},{3,4,6,7},{5}} => [[1,2,6,7],[3,4],[5]] => 010100 => 0
{{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6,7},{5}} => [[1,4,6,7],[2],[3],[5]] => 110100 => 2
{{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}} => [[1,2,4,6,7],[3,5]] => 010100 => 0
{{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,2,4,6},{3,5},{7}} => {{1},{2,4,6,7},{3,5}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4,7},{3,5,6}} => {{1,4,6,7},{2,3,5}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}} => [[1,2,3,5],[4,6,7]] => 001010 => 0
{{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}} => [[1,3,5],[2,6,7],[4]] => 101010 => 1
{{1,2,4,7},{3,5},{6}} => {{1,4,6,7},{2},{3,5}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4},{3,5,7},{6}} => {{1,3,5},{2},{4,6,7}} => [[1,3,5],[2,6,7],[4]] => 101010 => 1
{{1,2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6,7}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}} => [[1,2,4,6,7],[3],[5]] => 010100 => 0
{{1,2,4,6},{3,7},{5}} => {{1,5},{2,4,6,7},{3}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4,6},{3},{5,7}} => {{1,3},{2,4,6,7},{5}} => [[1,3,6,7],[2,4],[5]] => 101100 => 1
{{1,2,4,6},{3},{5},{7}} => {{1},{2,4,6,7},{3},{5}} => [[1,4,6,7],[2],[3],[5]] => 110100 => 2
{{1,2,4,7},{3,6},{5}} => {{1,4,6,7},{2,5},{3}} => [[1,4,6,7],[2,5],[3]] => 110100 => 2
{{1,2,4},{3,6,7},{5}} => {{1,2,5},{3},{4,6,7}} => [[1,2,5],[3,6,7],[4]] => 011010 => 0
{{1,2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6,7}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,2,4},{3,6},{5},{7}} => {{1},{2,5},{3},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,4,7},{3},{5,6}} => {{1,4,6,7},{2,3},{5}} => [[1,3,6,7],[2,4],[5]] => 101100 => 1
{{1,2,4},{3,7},{5,6}} => {{1,5},{2,3},{4,6,7}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,2,4},{3},{5,6,7}} => {{1,2,3},{4,6,7},{5}} => [[1,2,3],[4,6,7],[5]] => 001100 => 0
{{1,2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6,7},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2,4,7},{3},{5},{6}} => {{1,4,6,7},{2},{3},{5}} => [[1,4,6,7],[2],[3],[5]] => 110100 => 2
{{1,2,4},{3,7},{5},{6}} => {{1,5},{2},{3},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6,7},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6,7},{5}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6,7},{5}} => [[1,6,7],[2],[3],[4],[5]] => 111100 => 4
{{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}} => [[1,2,3,6,7],[4,5]] => 001000 => 0
{{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,2,5,6},{3,4},{7}} => {{1},{2,3,6,7},{4,5}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,5,7},{3,4,6}} => {{1,3,6,7},{2,4,5}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,2,5},{3,4,6,7}} => {{1,2,4,5},{3,6,7}} => [[1,2,4,5],[3,6,7]] => 010010 => 0
{{1,2,5},{3,4,6},{7}} => {{1},{2,4,5},{3,6,7}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2,5,7},{3,4},{6}} => {{1,3,6,7},{2},{4,5}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,5},{3,4,7},{6}} => {{1,4,5},{2},{3,6,7}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2,5},{3,4},{6,7}} => {{1,2},{3,6,7},{4,5}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,2,5},{3,4},{6},{7}} => {{1},{2},{3,6,7},{4,5}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}} => [[1,2,5,7],[3,4,6]] => 010010 => 0
{{1,2,6},{3,4,5,7}} => {{1,3,4,5},{2,6,7}} => [[1,3,4,5],[2,6,7]] => 100010 => 1
{{1,2,6},{3,4,5},{7}} => {{1},{2,6,7},{3,4,5}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2,7},{3,4,5,6}} => {{1,6,7},{2,3,4,5}} => [[1,3,4,5],[2,6,7]] => 100010 => 1
{{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}} => [[1,2,3,4,5],[6,7]] => 000010 => 0
{{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}} => [[1,3,4,5],[2,7],[6]] => 100010 => 1
{{1,2,7},{3,4,5},{6}} => {{1,6,7},{2},{3,4,5}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2},{3,4,5,7},{6}} => {{1,3,4,5},{2},{6,7}} => [[1,3,4,5],[2,7],[6]] => 100010 => 1
{{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => [[1,2,5],[3,4],[6,7]] => 010010 => 0
{{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,2,6,7},{3,4},{5}} => {{1,2,6,7},{3},{4,5}} => [[1,2,6,7],[3,5],[4]] => 011000 => 0
{{1,2,6},{3,4,7},{5}} => {{1,4,5},{2,6,7},{3}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2,6},{3,4},{5,7}} => {{1,3},{2,6,7},{4,5}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,2,6},{3,4},{5},{7}} => {{1},{2,6,7},{3},{4,5}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,7},{3,4,6},{5}} => {{1,6,7},{2,4,5},{3}} => [[1,4,5],[2,6,7],[3]] => 110010 => 2
{{1,2},{3,4,6,7},{5}} => {{1,2,4,5},{3},{6,7}} => [[1,2,4,5],[3,7],[6]] => 010010 => 0
{{1,2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6,7}} => [[1,3,5],[2,4],[6,7]] => 101010 => 1
{{1,2},{3,4,6},{5},{7}} => {{1},{2,4,5},{3},{6,7}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,2,7},{3,4},{5,6}} => {{1,6,7},{2,3},{4,5}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,2},{3,4,7},{5,6}} => {{1,4,5},{2,3},{6,7}} => [[1,3,5],[2,4],[6,7]] => 101010 => 1
{{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}} => [[1,2,3],[4,5],[6,7]] => 001010 => 0
{{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,2,7},{3,4},{5},{6}} => {{1,6,7},{2},{3},{4,5}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2},{3,4,7},{5},{6}} => {{1,4,5},{2},{3},{6,7}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => [[1,2],[3,5],[4,7],[6]] => 011010 => 0
{{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}} => [[1,2,3,6,7],[4],[5]] => 001100 => 0
{{1,2,5,6},{3,7},{4}} => {{1,5},{2,3,6,7},{4}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,5,6},{3},{4,7}} => {{1,4},{2,3,6,7},{5}} => [[1,3,6,7],[2,4],[5]] => 101100 => 1
{{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6,7},{4},{5}} => [[1,3,6,7],[2],[4],[5]] => 101100 => 1
{{1,2,5,7},{3,6},{4}} => {{1,3,6,7},{2,5},{4}} => [[1,3,6,7],[2,5],[4]] => 101000 => 1
{{1,2,5},{3,6,7},{4}} => {{1,2,5},{3,6,7},{4}} => [[1,2,5],[3,6,7],[4]] => 011010 => 0
{{1,2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2,5},{3,6},{4},{7}} => {{1},{2,5},{3,6,7},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,5,7},{3},{4,6}} => {{1,3,6,7},{2,4},{5}} => [[1,3,6,7],[2,4],[5]] => 101100 => 1
{{1,2,5},{3,7},{4,6}} => {{1,5},{2,4},{3,6,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2,5},{3},{4,6,7}} => {{1,2,4},{3,6,7},{5}} => [[1,2,4],[3,6,7],[5]] => 010100 => 0
{{1,2,5},{3},{4,6},{7}} => {{1},{2,4},{3,6,7},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,5,7},{3},{4},{6}} => {{1,3,6,7},{2},{4},{5}} => [[1,3,6,7],[2],[4],[5]] => 101100 => 1
{{1,2,5},{3,7},{4},{6}} => {{1,5},{2},{3,6,7},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,5},{3},{4,7},{6}} => {{1,4},{2},{3,6,7},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,5},{3},{4},{6,7}} => {{1,2},{3,6,7},{4},{5}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,2,5},{3},{4},{6},{7}} => {{1},{2},{3,6,7},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => 111100 => 4
{{1,2,6,7},{3,5},{4}} => {{1,2,6,7},{3,5},{4}} => [[1,2,6,7],[3,5],[4]] => 011000 => 0
{{1,2,6},{3,5,7},{4}} => {{1,3,5},{2,6,7},{4}} => [[1,3,5],[2,6,7],[4]] => 101010 => 1
{{1,2,6},{3,5},{4,7}} => {{1,4},{2,6,7},{3,5}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2,6},{3,5},{4},{7}} => {{1},{2,6,7},{3,5},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,7},{3,5,6},{4}} => {{1,6,7},{2,3,5},{4}} => [[1,3,5],[2,6,7],[4]] => 101010 => 1
{{1,2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6,7}} => [[1,2,3,5],[4,7],[6]] => 001010 => 0
{{1,2},{3,5,6},{4,7}} => {{1,4},{2,3,5},{6,7}} => [[1,3,5],[2,4],[6,7]] => 101010 => 1
{{1,2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6,7}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1,2,7},{3,5},{4,6}} => {{1,6,7},{2,4},{3,5}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2},{3,5,7},{4,6}} => {{1,3,5},{2,4},{6,7}} => [[1,3,5],[2,4],[6,7]] => 101010 => 1
{{1,2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6,7}} => [[1,2,4],[3,5],[6,7]] => 010110 => 0
{{1,2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2,7},{3,5},{4},{6}} => {{1,6,7},{2},{3,5},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2},{3,5,7},{4},{6}} => {{1,3,5},{2},{4},{6,7}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1,2},{3,5},{4,7},{6}} => {{1,4},{2},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => [[1,2],[3,5],[4,7],[6]] => 011010 => 0
{{1,2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,2,6,7},{3},{4,5}} => {{1,2,6,7},{3,4},{5}} => [[1,2,6,7],[3,4],[5]] => 010100 => 0
{{1,2,6},{3,7},{4,5}} => {{1,5},{2,6,7},{3,4}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2,6},{3},{4,5,7}} => {{1,3,4},{2,6,7},{5}} => [[1,3,4],[2,6,7],[5]] => 100100 => 1
{{1,2,6},{3},{4,5},{7}} => {{1},{2,6,7},{3,4},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,7},{3,6},{4,5}} => {{1,6,7},{2,5},{3,4}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6,7}} => [[1,2,5],[3,4],[6,7]] => 010010 => 0
{{1,2},{3,6},{4,5,7}} => {{1,3,4},{2,5},{6,7}} => [[1,3,4],[2,5],[6,7]] => 100110 => 1
{{1,2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2,7},{3},{4,5,6}} => {{1,6,7},{2,3,4},{5}} => [[1,3,4],[2,6,7],[5]] => 100100 => 1
{{1,2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6,7}} => [[1,3,4],[2,5],[6,7]] => 100110 => 1
{{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}} => [[1,2,3,4],[5,7],[6]] => 000110 => 0
{{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1,2,7},{3},{4,5},{6}} => {{1,6,7},{2},{3,4},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2},{3},{4,5,7},{6}} => {{1,3,4},{2},{5},{6,7}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => [[1,2],[3,4],[5,7],[6]] => 010110 => 0
{{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => [[1,2,6,7],[3],[4],[5]] => 011100 => 0
{{1,2,6},{3,7},{4},{5}} => {{1,5},{2,6,7},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2,6},{3},{4,7},{5}} => {{1,4},{2,6,7},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2,6},{3},{4},{5,7}} => {{1,3},{2,6,7},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2,6},{3},{4},{5},{7}} => {{1},{2,6,7},{3},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => 111100 => 4
{{1,2,7},{3,6},{4},{5}} => {{1,6,7},{2,5},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6,7}} => [[1,2,5],[3,7],[4],[6]] => 011010 => 0
{{1,2},{3,6},{4,7},{5}} => {{1,4},{2,5},{3},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2},{3,6},{4},{5,7}} => {{1,3},{2,5},{4},{6,7}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,2,7},{3},{4,6},{5}} => {{1,6,7},{2,4},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6,7}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6,7}} => [[1,2,4],[3,7],[5],[6]] => 010110 => 0
{{1,2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6,7}} => [[1,3],[2,4],[5,7],[6]] => 101110 => 1
{{1,2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,2,7},{3},{4},{5,6}} => {{1,6,7},{2,3},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6,7}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6,7}} => [[1,3],[2,4],[5,7],[6]] => 101110 => 1
{{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}} => [[1,2,3],[4,7],[5],[6]] => 001110 => 0
{{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,2,7},{3},{4},{5},{6}} => {{1,6,7},{2},{3},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => 111100 => 4
{{1,2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6,7}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => [[1,2],[3,7],[4],[5],[6]] => 011110 => 0
{{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}} => [[1,2,3,4,5,7],[6]] => 000010 => 0
{{1,3,4,5,6},{2,7}} => {{1,6},{2,3,4,5,7}} => [[1,3,4,5,7],[2,6]] => 100010 => 1
{{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}} => [[1,3,4,5,7],[2],[6]] => 100010 => 1
{{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}} => [[1,3,4,5,7],[2,6]] => 100010 => 1
{{1,3,4,5},{2,6,7}} => {{1,2,6},{3,4,5,7}} => [[1,2,5,7],[3,4,6]] => 010010 => 0
{{1,3,4,5},{2,6},{7}} => {{1},{2,6},{3,4,5,7}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}} => [[1,3,4,5,7],[2],[6]] => 100010 => 1
{{1,3,4,5},{2,7},{6}} => {{1,6},{2},{3,4,5,7}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4,5},{2},{6,7}} => {{1,2},{3,4,5,7},{6}} => [[1,2,5,7],[3,4],[6]] => 010010 => 0
{{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}} => [[1,4,5,7],[2],[3],[6]] => 110010 => 2
{{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}} => [[1,2,4,5,7],[3,6]] => 010010 => 0
{{1,3,4,6},{2,5,7}} => {{1,3,6},{2,4,5,7}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4,7},{2,5,6}} => {{1,4,5,7},{2,3,6}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,3,4},{2,5,6,7}} => {{1,2,3,6},{4,5,7}} => [[1,2,3,6],[4,5,7]] => 001001 => 0
{{1,3,4},{2,5,6},{7}} => {{1},{2,3,6},{4,5,7}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,3,4,7},{2,5},{6}} => {{1,4,5,7},{2},{3,6}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4},{2,5,7},{6}} => {{1,3,6},{2},{4,5,7}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,3,4},{2,5},{6,7}} => {{1,2},{3,6},{4,5,7}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,3,4},{2,5},{6},{7}} => {{1},{2},{3,6},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,4,6,7},{2},{5}} => {{1,2,4,5,7},{3},{6}} => [[1,2,4,5,7],[3],[6]] => 010010 => 0
{{1,3,4,6},{2,7},{5}} => {{1,6},{2,4,5,7},{3}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4,6},{2},{5,7}} => {{1,3},{2,4,5,7},{6}} => [[1,3,5,7],[2,4],[6]] => 101010 => 1
{{1,3,4,6},{2},{5},{7}} => {{1},{2,4,5,7},{3},{6}} => [[1,4,5,7],[2],[3],[6]] => 110010 => 2
{{1,3,4,7},{2,6},{5}} => {{1,4,5,7},{2,6},{3}} => [[1,4,5,7],[2,6],[3]] => 110010 => 2
{{1,3,4},{2,6,7},{5}} => {{1,2,6},{3},{4,5,7}} => [[1,2,6],[3,5,7],[4]] => 011001 => 0
{{1,3,4},{2,6},{5,7}} => {{1,3},{2,6},{4,5,7}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,3,4},{2,6},{5},{7}} => {{1},{2,6},{3},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,4,7},{2},{5,6}} => {{1,4,5,7},{2,3},{6}} => [[1,3,5,7],[2,4],[6]] => 101010 => 1
{{1,3,4},{2,7},{5,6}} => {{1,6},{2,3},{4,5,7}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,3,4},{2},{5,6,7}} => {{1,2,3},{4,5,7},{6}} => [[1,2,3],[4,5,7],[6]] => 001010 => 0
{{1,3,4},{2},{5,6},{7}} => {{1},{2,3},{4,5,7},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,3,4,7},{2},{5},{6}} => {{1,4,5,7},{2},{3},{6}} => [[1,4,5,7],[2],[3],[6]] => 110010 => 2
{{1,3,4},{2,7},{5},{6}} => {{1,6},{2},{3},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,4},{2},{5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,3,4},{2},{5},{6,7}} => {{1,2},{3},{4,5,7},{6}} => [[1,2,7],[3,5],[4],[6]] => 011010 => 0
{{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}} => [[1,5,7],[2],[3],[4],[6]] => 111010 => 3
{{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}} => [[1,2,3,5,7],[4,6]] => 001010 => 0
{{1,3,5,6},{2,4,7}} => {{1,4,6},{2,3,5,7}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}} => [[1,3,5,7],[2,6],[4]] => 101010 => 1
{{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}} => [[1,3,5,7],[2,4,6]] => 101010 => 1
{{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}} => [[1,2,4,6],[3,5,7]] => 010101 => 0
{{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3,5,7},{2,4},{6}} => {{1,3,5,7},{2},{4,6}} => [[1,3,5,7],[2,6],[4]] => 101010 => 1
{{1,3,5},{2,4,7},{6}} => {{1,4,6},{2},{3,5,7}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3,5},{2,4},{6,7}} => {{1,2},{3,5,7},{4,6}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,3,5},{2,4},{6},{7}} => {{1},{2},{3,5,7},{4,6}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,6,7},{2,4,5}} => {{1,2,5,7},{3,4,6}} => [[1,2,5,7],[3,4,6]] => 010010 => 0
{{1,3,6},{2,4,5,7}} => {{1,3,4,6},{2,5,7}} => [[1,3,4,6],[2,5,7]] => 100101 => 1
{{1,3,6},{2,4,5},{7}} => {{1},{2,5,7},{3,4,6}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3,7},{2,4,5,6}} => {{1,5,7},{2,3,4,6}} => [[1,3,4,6],[2,5,7]] => 100101 => 1
{{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}} => [[1,2,3,4,6],[5,7]] => 000101 => 0
{{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}} => [[1,3,4,6],[2,7],[5]] => 100101 => 1
{{1,3,7},{2,4,5},{6}} => {{1,5,7},{2},{3,4,6}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3},{2,4,5,7},{6}} => {{1,3,4,6},{2},{5,7}} => [[1,3,4,6],[2,7],[5]] => 100101 => 1
{{1,3},{2,4,5},{6,7}} => {{1,2},{3,4,6},{5,7}} => [[1,2,6],[3,4],[5,7]] => 010101 => 0
{{1,3},{2,4,5},{6},{7}} => {{1},{2},{3,4,6},{5,7}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,3,6,7},{2,4},{5}} => {{1,2,5,7},{3},{4,6}} => [[1,2,5,7],[3,6],[4]] => 011010 => 0
{{1,3,6},{2,4,7},{5}} => {{1,4,6},{2,5,7},{3}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3,6},{2,4},{5,7}} => {{1,3},{2,5,7},{4,6}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,3,6},{2,4},{5},{7}} => {{1},{2,5,7},{3},{4,6}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,7},{2,4,6},{5}} => {{1,5,7},{2,4,6},{3}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,3},{2,4,6,7},{5}} => {{1,2,4,6},{3},{5,7}} => [[1,2,4,6],[3,7],[5]] => 010101 => 0
{{1,3},{2,4,6},{5,7}} => {{1,3},{2,4,6},{5,7}} => [[1,3,6],[2,4],[5,7]] => 101101 => 1
{{1,3},{2,4,6},{5},{7}} => {{1},{2,4,6},{3},{5,7}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,3,7},{2,4},{5,6}} => {{1,5,7},{2,3},{4,6}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,3},{2,4,7},{5,6}} => {{1,4,6},{2,3},{5,7}} => [[1,3,6],[2,4],[5,7]] => 101101 => 1
{{1,3},{2,4},{5,6,7}} => {{1,2,3},{4,6},{5,7}} => [[1,2,3],[4,6],[5,7]] => 001101 => 0
{{1,3},{2,4},{5,6},{7}} => {{1},{2,3},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,3,7},{2,4},{5},{6}} => {{1,5,7},{2},{3},{4,6}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3},{2,4,7},{5},{6}} => {{1,4,6},{2},{3},{5,7}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,3},{2,4},{5,7},{6}} => {{1,3},{2},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,3},{2,4},{5},{6,7}} => {{1,2},{3},{4,6},{5,7}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,3},{2,4},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,3,5,6,7},{2},{4}} => {{1,2,3,5,7},{4},{6}} => [[1,2,3,5,7],[4],[6]] => 001010 => 0
{{1,3,5,6},{2,7},{4}} => {{1,6},{2,3,5,7},{4}} => [[1,3,5,7],[2,6],[4]] => 101010 => 1
{{1,3,5,6},{2},{4,7}} => {{1,4},{2,3,5,7},{6}} => [[1,3,5,7],[2,4],[6]] => 101010 => 1
{{1,3,5,6},{2},{4},{7}} => {{1},{2,3,5,7},{4},{6}} => [[1,3,5,7],[2],[4],[6]] => 101010 => 1
{{1,3,5,7},{2,6},{4}} => {{1,3,5,7},{2,6},{4}} => [[1,3,5,7],[2,6],[4]] => 101010 => 1
{{1,3,5},{2,6,7},{4}} => {{1,2,6},{3,5,7},{4}} => [[1,2,6],[3,5,7],[4]] => 011001 => 0
{{1,3,5},{2,6},{4,7}} => {{1,4},{2,6},{3,5,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3,5},{2,6},{4},{7}} => {{1},{2,6},{3,5,7},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,5,7},{2},{4,6}} => {{1,3,5,7},{2,4},{6}} => [[1,3,5,7],[2,4],[6]] => 101010 => 1
{{1,3,5},{2,7},{4,6}} => {{1,6},{2,4},{3,5,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3,5},{2},{4,6,7}} => {{1,2,4},{3,5,7},{6}} => [[1,2,4],[3,5,7],[6]] => 010110 => 0
{{1,3,5},{2},{4,6},{7}} => {{1},{2,4},{3,5,7},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => [[1,3,5,7],[2],[4],[6]] => 101010 => 1
{{1,3,5},{2,7},{4},{6}} => {{1,6},{2},{3,5,7},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,5},{2},{4,7},{6}} => {{1,4},{2},{3,5,7},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3,5},{2},{4},{6,7}} => {{1,2},{3,5,7},{4},{6}} => [[1,2,7],[3,5],[4],[6]] => 011010 => 0
{{1,3,5},{2},{4},{6},{7}} => {{1},{2},{3,5,7},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => 111010 => 3
{{1,3,6,7},{2,5},{4}} => {{1,2,5,7},{3,6},{4}} => [[1,2,5,7],[3,6],[4]] => 011010 => 0
{{1,3,6},{2,5,7},{4}} => {{1,3,6},{2,5,7},{4}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,3,6},{2,5},{4,7}} => {{1,4},{2,5,7},{3,6}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3,6},{2,5},{4},{7}} => {{1},{2,5,7},{3,6},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,7},{2,5,6},{4}} => {{1,5,7},{2,3,6},{4}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,3},{2,5,6,7},{4}} => {{1,2,3,6},{4},{5,7}} => [[1,2,3,6],[4,7],[5]] => 001101 => 0
{{1,3},{2,5,6},{4,7}} => {{1,4},{2,3,6},{5,7}} => [[1,3,6],[2,4],[5,7]] => 101101 => 1
{{1,3},{2,5,6},{4},{7}} => {{1},{2,3,6},{4},{5,7}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1,3,7},{2,5},{4,6}} => {{1,5,7},{2,4},{3,6}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3},{2,5,7},{4,6}} => {{1,3,6},{2,4},{5,7}} => [[1,3,6],[2,4],[5,7]] => 101101 => 1
{{1,3},{2,5},{4,6,7}} => {{1,2,4},{3,6},{5,7}} => [[1,2,4],[3,6],[5,7]] => 010101 => 0
{{1,3},{2,5},{4,6},{7}} => {{1},{2,4},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3,7},{2,5},{4},{6}} => {{1,5,7},{2},{3,6},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3},{2,5,7},{4},{6}} => {{1,3,6},{2},{4},{5,7}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1,3},{2,5},{4,7},{6}} => {{1,4},{2},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3},{2,5},{4},{6,7}} => {{1,2},{3,6},{4},{5,7}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,3},{2,5},{4},{6},{7}} => {{1},{2},{3,6},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,3,6,7},{2},{4,5}} => {{1,2,5,7},{3,4},{6}} => [[1,2,5,7],[3,4],[6]] => 010010 => 0
{{1,3,6},{2,7},{4,5}} => {{1,6},{2,5,7},{3,4}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3,6},{2},{4,5,7}} => {{1,3,4},{2,5,7},{6}} => [[1,3,4],[2,5,7],[6]] => 100110 => 1
{{1,3,6},{2},{4,5},{7}} => {{1},{2,5,7},{3,4},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3,7},{2,6},{4,5}} => {{1,5,7},{2,6},{3,4}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,3},{2,6,7},{4,5}} => {{1,2,6},{3,4},{5,7}} => [[1,2,6],[3,4],[5,7]] => 010101 => 0
{{1,3},{2,6},{4,5,7}} => {{1,3,4},{2,6},{5,7}} => [[1,3,4],[2,6],[5,7]] => 100101 => 1
{{1,3},{2,6},{4,5},{7}} => {{1},{2,6},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3,7},{2},{4,5,6}} => {{1,5,7},{2,3,4},{6}} => [[1,3,4],[2,5,7],[6]] => 100110 => 1
{{1,3},{2,7},{4,5,6}} => {{1,6},{2,3,4},{5,7}} => [[1,3,4],[2,6],[5,7]] => 100101 => 1
{{1,3},{2},{4,5,6,7}} => {{1,2,3,4},{5,7},{6}} => [[1,2,3,4],[5,7],[6]] => 000110 => 0
{{1,3},{2},{4,5,6},{7}} => {{1},{2,3,4},{5,7},{6}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1,3,7},{2},{4,5},{6}} => {{1,5,7},{2},{3,4},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3},{2,7},{4,5},{6}} => {{1,6},{2},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3},{2},{4,5,7},{6}} => {{1,3,4},{2},{5,7},{6}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1,3},{2},{4,5},{6,7}} => {{1,2},{3,4},{5,7},{6}} => [[1,2],[3,4],[5,7],[6]] => 010110 => 0
{{1,3},{2},{4,5},{6},{7}} => {{1},{2},{3,4},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,3,6,7},{2},{4},{5}} => {{1,2,5,7},{3},{4},{6}} => [[1,2,5,7],[3],[4],[6]] => 011010 => 0
{{1,3,6},{2,7},{4},{5}} => {{1,6},{2,5,7},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3,6},{2},{4,7},{5}} => {{1,4},{2,5,7},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3,6},{2},{4},{5,7}} => {{1,3},{2,5,7},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,3,6},{2},{4},{5},{7}} => {{1},{2,5,7},{3},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => 111010 => 3
{{1,3,7},{2,6},{4},{5}} => {{1,5,7},{2,6},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => 111010 => 3
{{1,3},{2,6,7},{4},{5}} => {{1,2,6},{3},{4},{5,7}} => [[1,2,6],[3,7],[4],[5]] => 011101 => 0
{{1,3},{2,6},{4,7},{5}} => {{1,4},{2,6},{3},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3},{2,6},{4},{5,7}} => {{1,3},{2,6},{4},{5,7}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,3},{2,6},{4},{5},{7}} => {{1},{2,6},{3},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,3,7},{2},{4,6},{5}} => {{1,5,7},{2,4},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,3},{2,7},{4,6},{5}} => {{1,6},{2,4},{3},{5,7}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,3},{2},{4,6,7},{5}} => {{1,2,4},{3},{5,7},{6}} => [[1,2,4],[3,7],[5],[6]] => 010110 => 0
{{1,3},{2},{4,6},{5,7}} => {{1,3},{2,4},{5,7},{6}} => [[1,3],[2,4],[5,7],[6]] => 101110 => 1
{{1,3},{2},{4,6},{5},{7}} => {{1},{2,4},{3},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,3,7},{2},{4},{5,6}} => {{1,5,7},{2,3},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,3},{2,7},{4},{5,6}} => {{1,6},{2,3},{4},{5,7}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,3},{2},{4,7},{5,6}} => {{1,4},{2,3},{5,7},{6}} => [[1,3],[2,4],[5,7],[6]] => 101110 => 1
{{1,3},{2},{4},{5,6,7}} => {{1,2,3},{4},{5,7},{6}} => [[1,2,3],[4,7],[5],[6]] => 001110 => 0
{{1,3},{2},{4},{5,6},{7}} => {{1},{2,3},{4},{5,7},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,3,7},{2},{4},{5},{6}} => {{1,5,7},{2},{3},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => 111010 => 3
{{1,3},{2,7},{4},{5},{6}} => {{1,6},{2},{3},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,3},{2},{4,7},{5},{6}} => {{1,4},{2},{3},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,3},{2},{4},{5},{6,7}} => {{1,2},{3},{4},{5,7},{6}} => [[1,2],[3,7],[4],[5],[6]] => 011110 => 0
{{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}} => [[1,2,3,4,7],[5,6]] => 000100 => 0
{{1,4,5,6},{2,3,7}} => {{1,5,6},{2,3,4,7}} => [[1,3,4,7],[2,5,6]] => 100100 => 1
{{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}} => [[1,3,4,7],[2,6],[5]] => 100100 => 1
{{1,4,5,7},{2,3,6}} => {{1,3,4,7},{2,5,6}} => [[1,3,4,7],[2,5,6]] => 100100 => 1
{{1,4,5},{2,3,6,7}} => {{1,2,5,6},{3,4,7}} => [[1,2,5,6],[3,4,7]] => 010001 => 0
{{1,4,5},{2,3,6},{7}} => {{1},{2,5,6},{3,4,7}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4,5,7},{2,3},{6}} => {{1,3,4,7},{2},{5,6}} => [[1,3,4,7],[2,6],[5]] => 100100 => 1
{{1,4,5},{2,3,7},{6}} => {{1,5,6},{2},{3,4,7}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4,5},{2,3},{6,7}} => {{1,2},{3,4,7},{5,6}} => [[1,2,7],[3,4],[5,6]] => 010100 => 0
{{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,6,7},{2,3,5}} => {{1,2,4,7},{3,5,6}} => [[1,2,4,7],[3,5,6]] => 010100 => 0
{{1,4,6},{2,3,5,7}} => {{1,3,5,6},{2,4,7}} => [[1,3,5,6],[2,4,7]] => 101001 => 1
{{1,4,6},{2,3,5},{7}} => {{1},{2,4,7},{3,5,6}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4,7},{2,3,5,6}} => {{1,4,7},{2,3,5,6}} => [[1,3,5,6],[2,4,7]] => 101001 => 1
{{1,4},{2,3,5,6,7}} => {{1,2,3,5,6},{4,7}} => [[1,2,3,5,6],[4,7]] => 001001 => 0
{{1,4},{2,3,5,6},{7}} => {{1},{2,3,5,6},{4,7}} => [[1,3,5,6],[2,7],[4]] => 101001 => 1
{{1,4,7},{2,3,5},{6}} => {{1,4,7},{2},{3,5,6}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4},{2,3,5,7},{6}} => {{1,3,5,6},{2},{4,7}} => [[1,3,5,6],[2,7],[4]] => 101001 => 1
{{1,4},{2,3,5},{6,7}} => {{1,2},{3,5,6},{4,7}} => [[1,2,6],[3,5],[4,7]] => 011001 => 0
{{1,4},{2,3,5},{6},{7}} => {{1},{2},{3,5,6},{4,7}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,4,6,7},{2,3},{5}} => {{1,2,4,7},{3},{5,6}} => [[1,2,4,7],[3,6],[5]] => 010100 => 0
{{1,4,6},{2,3,7},{5}} => {{1,5,6},{2,4,7},{3}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4,6},{2,3},{5,7}} => {{1,3},{2,4,7},{5,6}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,4,6},{2,3},{5},{7}} => {{1},{2,4,7},{3},{5,6}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,7},{2,3,6},{5}} => {{1,4,7},{2,5,6},{3}} => [[1,4,6],[2,5,7],[3]] => 110101 => 2
{{1,4},{2,3,6,7},{5}} => {{1,2,5,6},{3},{4,7}} => [[1,2,5,6],[3,7],[4]] => 011001 => 0
{{1,4},{2,3,6},{5,7}} => {{1,3},{2,5,6},{4,7}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,4},{2,3,6},{5},{7}} => {{1},{2,5,6},{3},{4,7}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,4,7},{2,3},{5,6}} => {{1,4,7},{2,3},{5,6}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,4},{2,3,7},{5,6}} => {{1,5,6},{2,3},{4,7}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,4},{2,3},{5,6,7}} => {{1,2,3},{4,7},{5,6}} => [[1,2,3],[4,6],[5,7]] => 001101 => 0
{{1,4},{2,3},{5,6},{7}} => {{1},{2,3},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,4,7},{2,3},{5},{6}} => {{1,4,7},{2},{3},{5,6}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4},{2,3,7},{5},{6}} => {{1,5,6},{2},{3},{4,7}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,4},{2,3},{5,7},{6}} => {{1,3},{2},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,4},{2,3},{5},{6,7}} => {{1,2},{3},{4,7},{5,6}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}} => [[1,2,3,7],[4,5,6]] => 001000 => 0
{{1,5,6},{2,3,4,7}} => {{1,4,5,6},{2,3,7}} => [[1,3,5,6],[2,4,7]] => 101001 => 1
{{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}} => [[1,3,5,6],[2,4,7]] => 101001 => 1
{{1,5},{2,3,4,6,7}} => {{1,2,4,5,6},{3,7}} => [[1,2,4,5,6],[3,7]] => 010001 => 0
{{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1,5,7},{2,3,4},{6}} => {{1,3,7},{2},{4,5,6}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,5},{2,3,4,7},{6}} => {{1,4,5,6},{2},{3,7}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1,5},{2,3,4},{6,7}} => {{1,2},{3,7},{4,5,6}} => [[1,2,6],[3,5],[4,7]] => 011001 => 0
{{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}} => [[1,2,5,6],[3,4,7]] => 010001 => 0
{{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}} => [[1,3,4,5,6],[2,7]] => 100001 => 1
{{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => [[1,3,4,5,6],[2,7]] => 100001 => 1
{{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}} => [[1,2,3,4,5,6],[7]] => 000001 => 0
{{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => [[1,3,4,5,6],[2],[7]] => 100001 => 1
{{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1},{2,3,4,5,7},{6}} => {{1,3,4,5,6},{2},{7}} => [[1,3,4,5,6],[2],[7]] => 100001 => 1
{{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}} => [[1,2,5,6],[3,4],[7]] => 010001 => 0
{{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}} => [[1,4,5,6],[2],[3],[7]] => 110001 => 2
{{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}} => [[1,2,6],[3,5,7],[4]] => 011001 => 0
{{1,6},{2,3,4,7},{5}} => {{1,4,5,6},{2,7},{3}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1,6},{2,3,4},{5,7}} => {{1,3},{2,7},{4,5,6}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,7},{2,3,4,6},{5}} => {{1,7},{2,4,5,6},{3}} => [[1,4,5,6],[2,7],[3]] => 110001 => 2
{{1},{2,3,4,6,7},{5}} => {{1,2,4,5,6},{3},{7}} => [[1,2,4,5,6],[3],[7]] => 010001 => 0
{{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}} => [[1,3,5,6],[2,4],[7]] => 101001 => 1
{{1},{2,3,4,6},{5},{7}} => {{1},{2,4,5,6},{3},{7}} => [[1,4,5,6],[2],[3],[7]] => 110001 => 2
{{1,7},{2,3,4},{5,6}} => {{1,7},{2,3},{4,5,6}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1},{2,3,4,7},{5,6}} => {{1,4,5,6},{2,3},{7}} => [[1,3,5,6],[2,4],[7]] => 101001 => 1
{{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}} => [[1,2,3],[4,5,6],[7]] => 001001 => 0
{{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1},{2,3,4,7},{5},{6}} => {{1,4,5,6},{2},{3},{7}} => [[1,4,5,6],[2],[3],[7]] => 110001 => 2
{{1},{2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}} => [[1,2,6],[3,5],[4],[7]] => 011001 => 0
{{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}} => [[1,5,6],[2],[3],[4],[7]] => 111001 => 3
{{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}} => [[1,2,3,7],[4,6],[5]] => 001100 => 0
{{1,5,6},{2,3,7},{4}} => {{1,5,6},{2,3,7},{4}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,5,6},{2,3},{4,7}} => {{1,4},{2,3,7},{5,6}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5,7},{2,3,6},{4}} => {{1,3,7},{2,5,6},{4}} => [[1,3,6],[2,5,7],[4]] => 101001 => 1
{{1,5},{2,3,6,7},{4}} => {{1,2,5,6},{3,7},{4}} => [[1,2,5,6],[3,7],[4]] => 011001 => 0
{{1,5},{2,3,6},{4,7}} => {{1,4},{2,5,6},{3,7}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,5},{2,3,6},{4},{7}} => {{1},{2,5,6},{3,7},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,5,7},{2,3},{4,6}} => {{1,3,7},{2,4},{5,6}} => [[1,3,7],[2,4],[5,6]] => 101100 => 1
{{1,5},{2,3,7},{4,6}} => {{1,5,6},{2,4},{3,7}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,5},{2,3},{4,6,7}} => {{1,2,4},{3,7},{5,6}} => [[1,2,4],[3,6],[5,7]] => 010101 => 0
{{1,5},{2,3},{4,6},{7}} => {{1},{2,4},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,5,7},{2,3},{4},{6}} => {{1,3,7},{2},{4},{5,6}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5},{2,3,7},{4},{6}} => {{1,5,6},{2},{3,7},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,5},{2,3},{4,7},{6}} => {{1,4},{2},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,5},{2,3},{4},{6,7}} => {{1,2},{3,7},{4},{5,6}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,6,7},{2,3,5},{4}} => {{1,2,7},{3,5,6},{4}} => [[1,2,6],[3,5,7],[4]] => 011001 => 0
{{1,6},{2,3,5,7},{4}} => {{1,3,5,6},{2,7},{4}} => [[1,3,5,6],[2,7],[4]] => 101001 => 1
{{1,6},{2,3,5},{4,7}} => {{1,4},{2,7},{3,5,6}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,6},{2,3,5},{4},{7}} => {{1},{2,7},{3,5,6},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5,6},{4}} => [[1,3,5,6],[2,7],[4]] => 101001 => 1
{{1},{2,3,5,6,7},{4}} => {{1,2,3,5,6},{4},{7}} => [[1,2,3,5,6],[4],[7]] => 001001 => 0
{{1},{2,3,5,6},{4,7}} => {{1,4},{2,3,5,6},{7}} => [[1,3,5,6],[2,4],[7]] => 101001 => 1
{{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}} => [[1,3,5,6],[2],[4],[7]] => 101001 => 1
{{1,7},{2,3,5},{4,6}} => {{1,7},{2,4},{3,5,6}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1},{2,3,5,7},{4,6}} => {{1,3,5,6},{2,4},{7}} => [[1,3,5,6],[2,4],[7]] => 101001 => 1
{{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}} => [[1,2,4],[3,5,6],[7]] => 010101 => 0
{{1},{2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1,7},{2,3,5},{4},{6}} => {{1,7},{2},{3,5,6},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1},{2,3,5,7},{4},{6}} => {{1,3,5,6},{2},{4},{7}} => [[1,3,5,6],[2],[4],[7]] => 101001 => 1
{{1},{2,3,5},{4,7},{6}} => {{1,4},{2},{3,5,6},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,3,5},{4},{6,7}} => {{1,2},{3,5,6},{4},{7}} => [[1,2,6],[3,5],[4],[7]] => 011001 => 0
{{1},{2,3,5},{4},{6},{7}} => {{1},{2},{3,5,6},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => 111001 => 3
{{1,6,7},{2,3},{4,5}} => {{1,2,7},{3,4},{5,6}} => [[1,2,7],[3,4],[5,6]] => 010100 => 0
{{1,6},{2,3,7},{4,5}} => {{1,5,6},{2,7},{3,4}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,6},{2,3},{4,5,7}} => {{1,3,4},{2,7},{5,6}} => [[1,3,4],[2,6],[5,7]] => 100101 => 1
{{1,6},{2,3},{4,5},{7}} => {{1},{2,7},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,7},{2,3,6},{4,5}} => {{1,7},{2,5,6},{3,4}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1},{2,3,6,7},{4,5}} => {{1,2,5,6},{3,4},{7}} => [[1,2,5,6],[3,4],[7]] => 010001 => 0
{{1},{2,3,6},{4,5,7}} => {{1,3,4},{2,5,6},{7}} => [[1,3,4],[2,5,6],[7]] => 100101 => 1
{{1},{2,3,6},{4,5},{7}} => {{1},{2,5,6},{3,4},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1,7},{2,3},{4,5,6}} => {{1,7},{2,3,4},{5,6}} => [[1,3,4],[2,6],[5,7]] => 100101 => 1
{{1},{2,3,7},{4,5,6}} => {{1,5,6},{2,3,4},{7}} => [[1,3,4],[2,5,6],[7]] => 100101 => 1
{{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}} => [[1,2,3,4],[5,6],[7]] => 000101 => 0
{{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => [[1,3,4],[2,6],[5],[7]] => 100101 => 1
{{1,7},{2,3},{4,5},{6}} => {{1,7},{2},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1},{2,3,7},{4,5},{6}} => {{1,5,6},{2},{3,4},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,3},{4,5,7},{6}} => {{1,3,4},{2},{5,6},{7}} => [[1,3,4],[2,6],[5],[7]] => 100101 => 1
{{1},{2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6},{7}} => [[1,2],[3,4],[5,6],[7]] => 010101 => 0
{{1},{2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,6},{2,3,7},{4},{5}} => {{1,5,6},{2,7},{3},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1,6},{2,3},{4,7},{5}} => {{1,4},{2,7},{3},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,6},{2,3},{4},{5,7}} => {{1,3},{2,7},{4},{5,6}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,7},{2,3,6},{4},{5}} => {{1,7},{2,5,6},{3},{4}} => [[1,5,6],[2,7],[3],[4]] => 111001 => 3
{{1},{2,3,6,7},{4},{5}} => {{1,2,5,6},{3},{4},{7}} => [[1,2,5,6],[3],[4],[7]] => 011001 => 0
{{1},{2,3,6},{4,7},{5}} => {{1,4},{2,5,6},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,3,6},{4},{5,7}} => {{1,3},{2,5,6},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,3,6},{4},{5},{7}} => {{1},{2,5,6},{3},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => 111001 => 3
{{1,7},{2,3},{4,6},{5}} => {{1,7},{2,4},{3},{5,6}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1},{2,3,7},{4,6},{5}} => {{1,5,6},{2,4},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6},{7}} => [[1,2,4],[3,6],[5],[7]] => 010101 => 0
{{1},{2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6},{7}} => [[1,3],[2,4],[5,6],[7]] => 101101 => 1
{{1},{2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1,7},{2,3},{4},{5,6}} => {{1,7},{2,3},{4},{5,6}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1},{2,3,7},{4},{5,6}} => {{1,5,6},{2,3},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6},{7}} => [[1,3],[2,4],[5,6],[7]] => 101101 => 1
{{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}} => [[1,2,3],[4,6],[5],[7]] => 001101 => 0
{{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1},{2,3,7},{4},{5},{6}} => {{1,5,6},{2},{3},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => 111001 => 3
{{1},{2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1},{2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1},{2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6},{7}} => [[1,2],[3,6],[4],[5],[7]] => 011101 => 0
{{1},{2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => [[1,6],[2],[3],[4],[5],[7]] => 111101 => 4
{{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}} => [[1,2,3,4,7],[5],[6]] => 000110 => 0
{{1,4,5,6},{2,7},{3}} => {{1,6},{2,3,4,7},{5}} => [[1,3,4,7],[2,6],[5]] => 100100 => 1
{{1,4,5,6},{2},{3,7}} => {{1,5},{2,3,4,7},{6}} => [[1,3,4,7],[2,5],[6]] => 100110 => 1
{{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}} => [[1,3,4,7],[2],[5],[6]] => 100110 => 1
{{1,4,5,7},{2,6},{3}} => {{1,3,4,7},{2,6},{5}} => [[1,3,4,7],[2,6],[5]] => 100100 => 1
{{1,4,5},{2,6,7},{3}} => {{1,2,6},{3,4,7},{5}} => [[1,2,6],[3,4,7],[5]] => 010101 => 0
{{1,4,5},{2,6},{3,7}} => {{1,5},{2,6},{3,4,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4,5},{2,6},{3},{7}} => {{1},{2,6},{3,4,7},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,5,7},{2},{3,6}} => {{1,3,4,7},{2,5},{6}} => [[1,3,4,7],[2,5],[6]] => 100110 => 1
{{1,4,5},{2,7},{3,6}} => {{1,6},{2,5},{3,4,7}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4,5},{2},{3,6,7}} => {{1,2,5},{3,4,7},{6}} => [[1,2,5],[3,4,7],[6]] => 010010 => 0
{{1,4,5},{2},{3,6},{7}} => {{1},{2,5},{3,4,7},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4,5,7},{2},{3},{6}} => {{1,3,4,7},{2},{5},{6}} => [[1,3,4,7],[2],[5],[6]] => 100110 => 1
{{1,4,5},{2,7},{3},{6}} => {{1,6},{2},{3,4,7},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,5},{2},{3,7},{6}} => {{1,5},{2},{3,4,7},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4,5},{2},{3},{6,7}} => {{1,2},{3,4,7},{5},{6}} => [[1,2,7],[3,4],[5],[6]] => 010110 => 0
{{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => 110110 => 2
{{1,4,6,7},{2,5},{3}} => {{1,2,4,7},{3,6},{5}} => [[1,2,4,7],[3,6],[5]] => 010100 => 0
{{1,4,6},{2,5,7},{3}} => {{1,3,6},{2,4,7},{5}} => [[1,3,6],[2,4,7],[5]] => 101101 => 1
{{1,4,6},{2,5},{3,7}} => {{1,5},{2,4,7},{3,6}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4,6},{2,5},{3},{7}} => {{1},{2,4,7},{3,6},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,7},{2,5,6},{3}} => {{1,4,7},{2,3,6},{5}} => [[1,3,6],[2,4,7],[5]] => 101101 => 1
{{1,4},{2,5,6,7},{3}} => {{1,2,3,6},{4,7},{5}} => [[1,2,3,6],[4,7],[5]] => 001101 => 0
{{1,4},{2,5,6},{3,7}} => {{1,5},{2,3,6},{4,7}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,4},{2,5,6},{3},{7}} => {{1},{2,3,6},{4,7},{5}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1,4,7},{2,5},{3,6}} => {{1,4,7},{2,5},{3,6}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4},{2,5,7},{3,6}} => {{1,3,6},{2,5},{4,7}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,4},{2,5},{3,6,7}} => {{1,2,5},{3,6},{4,7}} => [[1,2,5],[3,6],[4,7]] => 011011 => 0
{{1,4},{2,5},{3,6},{7}} => {{1},{2,5},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4,7},{2,5},{3},{6}} => {{1,4,7},{2},{3,6},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4},{2,5,7},{3},{6}} => {{1,3,6},{2},{4,7},{5}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1,4},{2,5},{3,7},{6}} => {{1,5},{2},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4},{2,5},{3},{6,7}} => {{1,2},{3,6},{4,7},{5}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,4},{2,5},{3},{6},{7}} => {{1},{2},{3,6},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,4,6,7},{2},{3,5}} => {{1,2,4,7},{3,5},{6}} => [[1,2,4,7],[3,5],[6]] => 010110 => 0
{{1,4,6},{2,7},{3,5}} => {{1,6},{2,4,7},{3,5}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4,6},{2},{3,5,7}} => {{1,3,5},{2,4,7},{6}} => [[1,3,5],[2,4,7],[6]] => 101010 => 1
{{1,4,6},{2},{3,5},{7}} => {{1},{2,4,7},{3,5},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4,7},{2,6},{3,5}} => {{1,4,7},{2,6},{3,5}} => [[1,4,7],[2,5],[3,6]] => 110110 => 2
{{1,4},{2,6,7},{3,5}} => {{1,2,6},{3,5},{4,7}} => [[1,2,6],[3,5],[4,7]] => 011001 => 0
{{1,4},{2,6},{3,5,7}} => {{1,3,5},{2,6},{4,7}} => [[1,3,5],[2,6],[4,7]] => 101011 => 1
{{1,4},{2,6},{3,5},{7}} => {{1},{2,6},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4,7},{2},{3,5,6}} => {{1,4,7},{2,3,5},{6}} => [[1,3,5],[2,4,7],[6]] => 101010 => 1
{{1,4},{2,7},{3,5,6}} => {{1,6},{2,3,5},{4,7}} => [[1,3,5],[2,6],[4,7]] => 101011 => 1
{{1,4},{2},{3,5,6,7}} => {{1,2,3,5},{4,7},{6}} => [[1,2,3,5],[4,7],[6]] => 001010 => 0
{{1,4},{2},{3,5,6},{7}} => {{1},{2,3,5},{4,7},{6}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1,4,7},{2},{3,5},{6}} => {{1,4,7},{2},{3,5},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4},{2,7},{3,5},{6}} => {{1,6},{2},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4},{2},{3,5,7},{6}} => {{1,3,5},{2},{4,7},{6}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1,4},{2},{3,5},{6,7}} => {{1,2},{3,5},{4,7},{6}} => [[1,2],[3,5],[4,7],[6]] => 011010 => 0
{{1,4},{2},{3,5},{6},{7}} => {{1},{2},{3,5},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,4,6,7},{2},{3},{5}} => {{1,2,4,7},{3},{5},{6}} => [[1,2,4,7],[3],[5],[6]] => 010110 => 0
{{1,4,6},{2,7},{3},{5}} => {{1,6},{2,4,7},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4,6},{2},{3,7},{5}} => {{1,5},{2,4,7},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4,6},{2},{3},{5,7}} => {{1,3},{2,4,7},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => 101110 => 1
{{1,4,6},{2},{3},{5},{7}} => {{1},{2,4,7},{3},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => 110110 => 2
{{1,4,7},{2,6},{3},{5}} => {{1,4,7},{2,6},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => 110100 => 2
{{1,4},{2,6,7},{3},{5}} => {{1,2,6},{3},{4,7},{5}} => [[1,2,6],[3,7],[4],[5]] => 011101 => 0
{{1,4},{2,6},{3,7},{5}} => {{1,5},{2,6},{3},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4},{2,6},{3},{5,7}} => {{1,3},{2,6},{4,7},{5}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,4},{2,6},{3},{5},{7}} => {{1},{2,6},{3},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,4,7},{2},{3,6},{5}} => {{1,4,7},{2,5},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => 110110 => 2
{{1,4},{2,7},{3,6},{5}} => {{1,6},{2,5},{3},{4,7}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,4},{2},{3,6,7},{5}} => {{1,2,5},{3},{4,7},{6}} => [[1,2,5],[3,7],[4],[6]] => 011010 => 0
{{1,4},{2},{3,6},{5,7}} => {{1,3},{2,5},{4,7},{6}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,4},{2},{3,6},{5},{7}} => {{1},{2,5},{3},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,4,7},{2},{3},{5,6}} => {{1,4,7},{2,3},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => 101110 => 1
{{1,4},{2,7},{3},{5,6}} => {{1,6},{2,3},{4,7},{5}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,4},{2},{3,7},{5,6}} => {{1,5},{2,3},{4,7},{6}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,4},{2},{3},{5,6,7}} => {{1,2,3},{4,7},{5},{6}} => [[1,2,3],[4,7],[5],[6]] => 001110 => 0
{{1,4},{2},{3},{5,6},{7}} => {{1},{2,3},{4,7},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => 110110 => 2
{{1,4},{2,7},{3},{5},{6}} => {{1,6},{2},{3},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,4},{2},{3,7},{5},{6}} => {{1,5},{2},{3},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,4},{2},{3},{5,7},{6}} => {{1,3},{2},{4,7},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,4},{2},{3},{5},{6,7}} => {{1,2},{3},{4,7},{5},{6}} => [[1,2],[3,7],[4],[5],[6]] => 011110 => 0
{{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}} => [[1,2,3,7],[4,6],[5]] => 001100 => 0
{{1,5,6},{2,4,7},{3}} => {{1,4,6},{2,3,7},{5}} => [[1,3,6],[2,4,7],[5]] => 101101 => 1
{{1,5,6},{2,4},{3,7}} => {{1,5},{2,3,7},{4,6}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5,7},{2,4,6},{3}} => {{1,3,7},{2,4,6},{5}} => [[1,3,6],[2,4,7],[5]] => 101101 => 1
{{1,5},{2,4,6,7},{3}} => {{1,2,4,6},{3,7},{5}} => [[1,2,4,6],[3,7],[5]] => 010101 => 0
{{1,5},{2,4,6},{3,7}} => {{1,5},{2,4,6},{3,7}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,5},{2,4,6},{3},{7}} => {{1},{2,4,6},{3,7},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,5,7},{2,4},{3,6}} => {{1,3,7},{2,5},{4,6}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,5},{2,4,7},{3,6}} => {{1,4,6},{2,5},{3,7}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,5},{2,4},{3,6,7}} => {{1,2,5},{3,7},{4,6}} => [[1,2,5],[3,6],[4,7]] => 011011 => 0
{{1,5},{2,4},{3,6},{7}} => {{1},{2,5},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5,7},{2,4},{3},{6}} => {{1,3,7},{2},{4,6},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5},{2,4,7},{3},{6}} => {{1,4,6},{2},{3,7},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,5},{2,4},{3,7},{6}} => {{1,5},{2},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5},{2,4},{3},{6,7}} => {{1,2},{3,7},{4,6},{5}} => [[1,2],[3,6],[4,7],[5]] => 011101 => 0
{{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}} => [[1,2,6],[3,4,7],[5]] => 010101 => 0
{{1,6},{2,4,5,7},{3}} => {{1,3,4,6},{2,7},{5}} => [[1,3,4,6],[2,7],[5]] => 100101 => 1
{{1,6},{2,4,5},{3,7}} => {{1,5},{2,7},{3,4,6}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}} => [[1,3,4,6],[2,7],[5]] => 100101 => 1
{{1},{2,4,5,6,7},{3}} => {{1,2,3,4,6},{5},{7}} => [[1,2,3,4,6],[5],[7]] => 000101 => 0
{{1},{2,4,5,6},{3,7}} => {{1,5},{2,3,4,6},{7}} => [[1,3,4,6],[2,5],[7]] => 100101 => 1
{{1},{2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5},{7}} => [[1,3,4,6],[2],[5],[7]] => 100101 => 1
{{1,7},{2,4,5},{3,6}} => {{1,7},{2,5},{3,4,6}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1},{2,4,5,7},{3,6}} => {{1,3,4,6},{2,5},{7}} => [[1,3,4,6],[2,5],[7]] => 100101 => 1
{{1},{2,4,5},{3,6,7}} => {{1,2,5},{3,4,6},{7}} => [[1,2,5],[3,4,6],[7]] => 010011 => 0
{{1},{2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1},{2,4,5,7},{3},{6}} => {{1,3,4,6},{2},{5},{7}} => [[1,3,4,6],[2],[5],[7]] => 100101 => 1
{{1},{2,4,5},{3,7},{6}} => {{1,5},{2},{3,4,6},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5},{7}} => [[1,2,6],[3,4],[5],[7]] => 010101 => 0
{{1},{2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => 110101 => 2
{{1,6,7},{2,4},{3,5}} => {{1,2,7},{3,5},{4,6}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,6},{2,4,7},{3,5}} => {{1,4,6},{2,7},{3,5}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1,6},{2,4},{3,5,7}} => {{1,3,5},{2,7},{4,6}} => [[1,3,5],[2,6],[4,7]] => 101011 => 1
{{1,6},{2,4},{3,5},{7}} => {{1},{2,7},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,7},{2,4,6},{3,5}} => {{1,7},{2,4,6},{3,5}} => [[1,4,6],[2,5],[3,7]] => 110101 => 2
{{1},{2,4,6,7},{3,5}} => {{1,2,4,6},{3,5},{7}} => [[1,2,4,6],[3,5],[7]] => 010101 => 0
{{1},{2,4,6},{3,5,7}} => {{1,3,5},{2,4,6},{7}} => [[1,3,5],[2,4,6],[7]] => 101011 => 1
{{1},{2,4,6},{3,5},{7}} => {{1},{2,4,6},{3,5},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1,7},{2,4},{3,5,6}} => {{1,7},{2,3,5},{4,6}} => [[1,3,5],[2,6],[4,7]] => 101011 => 1
{{1},{2,4,7},{3,5,6}} => {{1,4,6},{2,3,5},{7}} => [[1,3,5],[2,4,6],[7]] => 101011 => 1
{{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}} => [[1,2,3,5],[4,6],[7]] => 001011 => 0
{{1},{2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6},{7}} => [[1,3,5],[2,6],[4],[7]] => 101011 => 1
{{1,7},{2,4},{3,5},{6}} => {{1,7},{2},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,4,7},{3,5},{6}} => {{1,4,6},{2},{3,5},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,4},{3,5,7},{6}} => {{1,3,5},{2},{4,6},{7}} => [[1,3,5],[2,6],[4],[7]] => 101011 => 1
{{1},{2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6},{7}} => [[1,2],[3,5],[4,6],[7]] => 011011 => 0
{{1},{2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,6},{2,4,7},{3},{5}} => {{1,4,6},{2,7},{3},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1,6},{2,4},{3,7},{5}} => {{1,5},{2,7},{3},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,6},{2,4},{3},{5,7}} => {{1,3},{2,7},{4,6},{5}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,7},{2,4,6},{3},{5}} => {{1,7},{2,4,6},{3},{5}} => [[1,4,6],[2,7],[3],[5]] => 110101 => 2
{{1},{2,4,6,7},{3},{5}} => {{1,2,4,6},{3},{5},{7}} => [[1,2,4,6],[3],[5],[7]] => 010101 => 0
{{1},{2,4,6},{3,7},{5}} => {{1,5},{2,4,6},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,4,6},{3},{5,7}} => {{1,3},{2,4,6},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => 101101 => 1
{{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => 110101 => 2
{{1,7},{2,4},{3,6},{5}} => {{1,7},{2,5},{3},{4,6}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,4,7},{3,6},{5}} => {{1,4,6},{2,5},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => 110101 => 2
{{1},{2,4},{3,6,7},{5}} => {{1,2,5},{3},{4,6},{7}} => [[1,2,5],[3,6],[4],[7]] => 011011 => 0
{{1},{2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6},{7}} => [[1,3],[2,5],[4,6],[7]] => 101011 => 1
{{1},{2,4},{3,6},{5},{7}} => {{1},{2,5},{3},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,7},{2,4},{3},{5,6}} => {{1,7},{2,3},{4,6},{5}} => [[1,3],[2,6],[4,7],[5]] => 101101 => 1
{{1},{2,4,7},{3},{5,6}} => {{1,4,6},{2,3},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => 101101 => 1
{{1},{2,4},{3,7},{5,6}} => {{1,5},{2,3},{4,6},{7}} => [[1,3],[2,5],[4,6],[7]] => 101011 => 1
{{1},{2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5},{7}} => [[1,2,3],[4,6],[5],[7]] => 001101 => 0
{{1},{2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1},{2,4,7},{3},{5},{6}} => {{1,4,6},{2},{3},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => 110101 => 2
{{1},{2,4},{3,7},{5},{6}} => {{1,5},{2},{3},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1},{2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5},{7}} => [[1,2],[3,6],[4],[5],[7]] => 011101 => 0
{{1},{2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => 111101 => 4
{{1,5,6,7},{2},{3,4}} => {{1,2,3,7},{4,5},{6}} => [[1,2,3,7],[4,5],[6]] => 001010 => 0
{{1,5,6},{2,7},{3,4}} => {{1,6},{2,3,7},{4,5}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,5,6},{2},{3,4,7}} => {{1,4,5},{2,3,7},{6}} => [[1,3,5],[2,4,7],[6]] => 101010 => 1
{{1,5,6},{2},{3,4},{7}} => {{1},{2,3,7},{4,5},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,5,7},{2,6},{3,4}} => {{1,3,7},{2,6},{4,5}} => [[1,3,7],[2,5],[4,6]] => 101010 => 1
{{1,5},{2,6,7},{3,4}} => {{1,2,6},{3,7},{4,5}} => [[1,2,6],[3,5],[4,7]] => 011001 => 0
{{1,5},{2,6},{3,4,7}} => {{1,4,5},{2,6},{3,7}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1,5},{2,6},{3,4},{7}} => {{1},{2,6},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5,7},{2},{3,4,6}} => {{1,3,7},{2,4,5},{6}} => [[1,3,5],[2,4,7],[6]] => 101010 => 1
{{1,5},{2,7},{3,4,6}} => {{1,6},{2,4,5},{3,7}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1,5},{2},{3,4,6,7}} => {{1,2,4,5},{3,7},{6}} => [[1,2,4,5],[3,7],[6]] => 010010 => 0
{{1,5},{2},{3,4,6},{7}} => {{1},{2,4,5},{3,7},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,5,7},{2},{3,4},{6}} => {{1,3,7},{2},{4,5},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,5},{2,7},{3,4},{6}} => {{1,6},{2},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5},{2},{3,4,7},{6}} => {{1,4,5},{2},{3,7},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,5},{2},{3,4},{6,7}} => {{1,2},{3,7},{4,5},{6}} => [[1,2],[3,5],[4,7],[6]] => 011010 => 0
{{1,5},{2},{3,4},{6},{7}} => {{1},{2},{3,7},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}} => [[1,2,7],[3,5],[4,6]] => 011010 => 0
{{1,6},{2,5,7},{3,4}} => {{1,3,6},{2,7},{4,5}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1,6},{2,5},{3,4,7}} => {{1,4,5},{2,7},{3,6}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}} => [[1,3,6],[2,5],[4,7]] => 101001 => 1
{{1},{2,5,6,7},{3,4}} => {{1,2,3,6},{4,5},{7}} => [[1,2,3,6],[4,5],[7]] => 001001 => 0
{{1},{2,5,6},{3,4,7}} => {{1,4,5},{2,3,6},{7}} => [[1,3,5],[2,4,6],[7]] => 101011 => 1
{{1},{2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1,7},{2,5},{3,4,6}} => {{1,7},{2,4,5},{3,6}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1},{2,5,7},{3,4,6}} => {{1,3,6},{2,4,5},{7}} => [[1,3,5],[2,4,6],[7]] => 101011 => 1
{{1},{2,5},{3,4,6,7}} => {{1,2,4,5},{3,6},{7}} => [[1,2,4,5],[3,6],[7]] => 010011 => 0
{{1},{2,5},{3,4,6},{7}} => {{1},{2,4,5},{3,6},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,5,7},{3,4},{6}} => {{1,3,6},{2},{4,5},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,5},{3,4,7},{6}} => {{1,4,5},{2},{3,6},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1},{2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5},{7}} => [[1,2],[3,5],[4,6],[7]] => 011011 => 0
{{1},{2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,6,7},{2},{3,4,5}} => {{1,2,7},{3,4,5},{6}} => [[1,2,5],[3,4,7],[6]] => 010010 => 0
{{1,6},{2,7},{3,4,5}} => {{1,6},{2,7},{3,4,5}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1,6},{2},{3,4,5,7}} => {{1,3,4,5},{2,7},{6}} => [[1,3,4,5],[2,7],[6]] => 100010 => 1
{{1,6},{2},{3,4,5},{7}} => {{1},{2,7},{3,4,5},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => [[1,4,5],[2,6],[3,7]] => 110011 => 2
{{1},{2,6,7},{3,4,5}} => {{1,2,6},{3,4,5},{7}} => [[1,2,5],[3,4,6],[7]] => 010011 => 0
{{1},{2,6},{3,4,5,7}} => {{1,3,4,5},{2,6},{7}} => [[1,3,4,5],[2,6],[7]] => 100011 => 1
{{1},{2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1,7},{2},{3,4,5,6}} => {{1,7},{2,3,4,5},{6}} => [[1,3,4,5],[2,7],[6]] => 100010 => 1
{{1},{2,7},{3,4,5,6}} => {{1,6},{2,3,4,5},{7}} => [[1,3,4,5],[2,6],[7]] => 100011 => 1
{{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}} => [[1,2,3,4,5],[6],[7]] => 000011 => 0
{{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}} => [[1,3,4,5],[2],[6],[7]] => 100011 => 1
{{1,7},{2},{3,4,5},{6}} => {{1,7},{2},{3,4,5},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1},{2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1},{2},{3,4,5,7},{6}} => {{1,3,4,5},{2},{6},{7}} => [[1,3,4,5],[2],[6],[7]] => 100011 => 1
{{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}} => [[1,2,5],[3,4],[6],[7]] => 010011 => 0
{{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => 110011 => 2
{{1,6,7},{2},{3,4},{5}} => {{1,2,7},{3},{4,5},{6}} => [[1,2,7],[3,5],[4],[6]] => 011010 => 0
{{1,6},{2,7},{3,4},{5}} => {{1,6},{2,7},{3},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,6},{2},{3,4,7},{5}} => {{1,4,5},{2,7},{3},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1,6},{2},{3,4},{5,7}} => {{1,3},{2,7},{4,5},{6}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1,6},{2},{3,4},{5},{7}} => {{1},{2,7},{3},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5},{7}} => [[1,2,6],[3,5],[4],[7]] => 011001 => 0
{{1},{2,6},{3,4,7},{5}} => {{1,4,5},{2,6},{3},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1},{2,6},{3,4},{5,7}} => {{1,3},{2,6},{4,5},{7}} => [[1,3],[2,5],[4,6],[7]] => 101011 => 1
{{1},{2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,7},{2},{3,4,6},{5}} => {{1,7},{2,4,5},{3},{6}} => [[1,4,5],[2,7],[3],[6]] => 110010 => 2
{{1},{2,7},{3,4,6},{5}} => {{1,6},{2,4,5},{3},{7}} => [[1,4,5],[2,6],[3],[7]] => 110011 => 2
{{1},{2},{3,4,6,7},{5}} => {{1,2,4,5},{3},{6},{7}} => [[1,2,4,5],[3],[6],[7]] => 010011 => 0
{{1},{2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => 101011 => 1
{{1},{2},{3,4,6},{5},{7}} => {{1},{2,4,5},{3},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => 110011 => 2
{{1,7},{2},{3,4},{5,6}} => {{1,7},{2,3},{4,5},{6}} => [[1,3],[2,5],[4,7],[6]] => 101010 => 1
{{1},{2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5},{7}} => [[1,3],[2,5],[4,6],[7]] => 101011 => 1
{{1},{2},{3,4,7},{5,6}} => {{1,4,5},{2,3},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => 101011 => 1
{{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}} => [[1,2,3],[4,5],[6],[7]] => 001011 => 0
{{1},{2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => 101011 => 1
{{1,7},{2},{3,4},{5},{6}} => {{1,7},{2},{3},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1},{2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2},{3,4,7},{5},{6}} => {{1,4,5},{2},{3},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => 110011 => 2
{{1},{2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => 101011 => 1
{{1},{2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6},{7}} => [[1,2],[3,5],[4],[6],[7]] => 011011 => 0
{{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => 111011 => 3
{{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}} => [[1,2,3,7],[4],[5],[6]] => 001110 => 0
{{1,5,6},{2,7},{3},{4}} => {{1,6},{2,3,7},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5,6},{2},{3,7},{4}} => {{1,5},{2,3,7},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,5,6},{2},{3},{4,7}} => {{1,4},{2,3,7},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => 101110 => 1
{{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}} => [[1,3,7],[2],[4],[5],[6]] => 101110 => 1
{{1,5,7},{2,6},{3},{4}} => {{1,3,7},{2,6},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => 101100 => 1
{{1,5},{2,6,7},{3},{4}} => {{1,2,6},{3,7},{4},{5}} => [[1,2,6],[3,7],[4],[5]] => 011101 => 0
{{1,5},{2,6},{3,7},{4}} => {{1,5},{2,6},{3,7},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5},{2,6},{3},{4,7}} => {{1,4},{2,6},{3,7},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,5},{2,6},{3},{4},{7}} => {{1},{2,6},{3,7},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,5,7},{2},{3,6},{4}} => {{1,3,7},{2,5},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => 101010 => 1
{{1,5},{2,7},{3,6},{4}} => {{1,6},{2,5},{3,7},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,5},{2},{3,6,7},{4}} => {{1,2,5},{3,7},{4},{6}} => [[1,2,5],[3,7],[4],[6]] => 011010 => 0
{{1,5},{2},{3,6},{4,7}} => {{1,4},{2,5},{3,7},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,5},{2},{3,6},{4},{7}} => {{1},{2,5},{3,7},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,5,7},{2},{3},{4,6}} => {{1,3,7},{2,4},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => 101110 => 1
{{1,5},{2,7},{3},{4,6}} => {{1,6},{2,4},{3,7},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,5},{2},{3,7},{4,6}} => {{1,5},{2,4},{3,7},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,5},{2},{3},{4,6,7}} => {{1,2,4},{3,7},{5},{6}} => [[1,2,4],[3,7],[5],[6]] => 010110 => 0
{{1,5},{2},{3},{4,6},{7}} => {{1},{2,4},{3,7},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,5,7},{2},{3},{4},{6}} => {{1,3,7},{2},{4},{5},{6}} => [[1,3,7],[2],[4],[5],[6]] => 101110 => 1
{{1,5},{2,7},{3},{4},{6}} => {{1,6},{2},{3,7},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,5},{2},{3,7},{4},{6}} => {{1,5},{2},{3,7},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,5},{2},{3},{4,7},{6}} => {{1,4},{2},{3,7},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,5},{2},{3},{4},{6,7}} => {{1,2},{3,7},{4},{5},{6}} => [[1,2],[3,7],[4],[5],[6]] => 011110 => 0
{{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}} => [[1,2,7],[3,6],[4],[5]] => 011100 => 0
{{1,6},{2,5,7},{3},{4}} => {{1,3,6},{2,7},{4},{5}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1,6},{2,5},{3,7},{4}} => {{1,5},{2,7},{3,6},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,6},{2,5},{3},{4,7}} => {{1,4},{2,7},{3,6},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}} => [[1,3,6],[2,7],[4],[5]] => 101101 => 1
{{1},{2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5},{7}} => [[1,2,3,6],[4],[5],[7]] => 001101 => 0
{{1},{2,5,6},{3,7},{4}} => {{1,5},{2,3,6},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,5,6},{3},{4,7}} => {{1,4},{2,3,6},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => 101101 => 1
{{1},{2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5},{7}} => [[1,3,6],[2],[4],[5],[7]] => 101101 => 1
{{1,7},{2,5},{3,6},{4}} => {{1,7},{2,5},{3,6},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,5,7},{3,6},{4}} => {{1,3,6},{2,5},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => 101001 => 1
{{1},{2,5},{3,6,7},{4}} => {{1,2,5},{3,6},{4},{7}} => [[1,2,5],[3,6],[4],[7]] => 011011 => 0
{{1},{2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2,5},{3,6},{4},{7}} => {{1},{2,5},{3,6},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,7},{2,5},{3},{4,6}} => {{1,7},{2,4},{3,6},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1},{2,5,7},{3},{4,6}} => {{1,3,6},{2,4},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => 101101 => 1
{{1},{2,5},{3,7},{4,6}} => {{1,5},{2,4},{3,6},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2,5},{3},{4,6,7}} => {{1,2,4},{3,6},{5},{7}} => [[1,2,4],[3,6],[5],[7]] => 010101 => 0
{{1},{2,5},{3},{4,6},{7}} => {{1},{2,4},{3,6},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1},{2,5,7},{3},{4},{6}} => {{1,3,6},{2},{4},{5},{7}} => [[1,3,6],[2],[4],[5],[7]] => 101101 => 1
{{1},{2,5},{3,7},{4},{6}} => {{1,5},{2},{3,6},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2,5},{3},{4,7},{6}} => {{1,4},{2},{3,6},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1},{2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5},{7}} => [[1,2],[3,6],[4],[5],[7]] => 011101 => 0
{{1},{2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => 111101 => 4
{{1,6,7},{2},{3,5},{4}} => {{1,2,7},{3,5},{4},{6}} => [[1,2,7],[3,5],[4],[6]] => 011010 => 0
{{1,6},{2,7},{3,5},{4}} => {{1,6},{2,7},{3,5},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1,6},{2},{3,5,7},{4}} => {{1,3,5},{2,7},{4},{6}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1,6},{2},{3,5},{4,7}} => {{1,4},{2,7},{3,5},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,6},{2},{3,5},{4},{7}} => {{1},{2,7},{3,5},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}} => [[1,5],[2,6],[3,7],[4]] => 111011 => 3
{{1},{2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4},{7}} => [[1,2,6],[3,5],[4],[7]] => 011001 => 0
{{1},{2,6},{3,5,7},{4}} => {{1,3,5},{2,6},{4},{7}} => [[1,3,5],[2,6],[4],[7]] => 101011 => 1
{{1},{2,6},{3,5},{4,7}} => {{1,4},{2,6},{3,5},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1,7},{2},{3,5,6},{4}} => {{1,7},{2,3,5},{4},{6}} => [[1,3,5],[2,7],[4],[6]] => 101010 => 1
{{1},{2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4},{7}} => [[1,3,5],[2,6],[4],[7]] => 101011 => 1
{{1},{2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6},{7}} => [[1,2,3,5],[4],[6],[7]] => 001011 => 0
{{1},{2},{3,5,6},{4,7}} => {{1,4},{2,3,5},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => 101011 => 1
{{1},{2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6},{7}} => [[1,3,5],[2],[4],[6],[7]] => 101011 => 1
{{1,7},{2},{3,5},{4,6}} => {{1,7},{2,4},{3,5},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1},{2,7},{3,5},{4,6}} => {{1,6},{2,4},{3,5},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2},{3,5,7},{4,6}} => {{1,3,5},{2,4},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => 101011 => 1
{{1},{2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6},{7}} => [[1,2,4],[3,5],[6],[7]] => 010111 => 0
{{1},{2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1,7},{2},{3,5},{4},{6}} => {{1,7},{2},{3,5},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1},{2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2},{3,5,7},{4},{6}} => {{1,3,5},{2},{4},{6},{7}} => [[1,3,5],[2],[4],[6],[7]] => 101011 => 1
{{1},{2},{3,5},{4,7},{6}} => {{1,4},{2},{3,5},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1},{2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6},{7}} => [[1,2],[3,5],[4],[6],[7]] => 011011 => 0
{{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => 111011 => 3
{{1,6,7},{2},{3},{4,5}} => {{1,2,7},{3,4},{5},{6}} => [[1,2,7],[3,4],[5],[6]] => 010110 => 0
{{1,6},{2,7},{3},{4,5}} => {{1,6},{2,7},{3,4},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1,6},{2},{3,7},{4,5}} => {{1,5},{2,7},{3,4},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1,6},{2},{3},{4,5,7}} => {{1,3,4},{2,7},{5},{6}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1,6},{2},{3},{4,5},{7}} => {{1},{2,7},{3,4},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,7},{2,6},{3},{4,5}} => {{1,7},{2,6},{3,4},{5}} => [[1,4],[2,6],[3,7],[5]] => 110101 => 2
{{1},{2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5},{7}} => [[1,2,6],[3,4],[5],[7]] => 010101 => 0
{{1},{2,6},{3,7},{4,5}} => {{1,5},{2,6},{3,4},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2,6},{3},{4,5,7}} => {{1,3,4},{2,6},{5},{7}} => [[1,3,4],[2,6],[5],[7]] => 100101 => 1
{{1},{2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1,7},{2},{3,6},{4,5}} => {{1,7},{2,5},{3,4},{6}} => [[1,4],[2,5],[3,7],[6]] => 110110 => 2
{{1},{2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4},{7}} => [[1,4],[2,5],[3,6],[7]] => 110111 => 2
{{1},{2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6},{7}} => [[1,2,5],[3,4],[6],[7]] => 010011 => 0
{{1},{2},{3,6},{4,5,7}} => {{1,3,4},{2,5},{6},{7}} => [[1,3,4],[2,5],[6],[7]] => 100111 => 1
{{1},{2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1,7},{2},{3},{4,5,6}} => {{1,7},{2,3,4},{5},{6}} => [[1,3,4],[2,7],[5],[6]] => 100110 => 1
{{1},{2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5},{7}} => [[1,3,4],[2,6],[5],[7]] => 100101 => 1
{{1},{2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6},{7}} => [[1,3,4],[2,5],[6],[7]] => 100111 => 1
{{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}} => [[1,2,3,4],[5],[6],[7]] => 000111 => 0
{{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}} => [[1,3,4],[2],[5],[6],[7]] => 100111 => 1
{{1,7},{2},{3},{4,5},{6}} => {{1,7},{2},{3,4},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1},{2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1},{2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1},{2},{3},{4,5,7},{6}} => {{1,3,4},{2},{5},{6},{7}} => [[1,3,4],[2],[5],[6],[7]] => 100111 => 1
{{1},{2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6},{7}} => [[1,2],[3,4],[5],[6],[7]] => 010111 => 0
{{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => 110111 => 2
{{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}} => [[1,2,7],[3],[4],[5],[6]] => 011110 => 0
{{1,6},{2,7},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1,6},{2},{3,7},{4},{5}} => {{1,5},{2,7},{3},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1,6},{2},{3},{4,7},{5}} => {{1,4},{2,7},{3},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1,6},{2},{3},{4},{5,7}} => {{1,3},{2,7},{4},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => 111101 => 4
{{1},{2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5},{7}} => [[1,2,6],[3],[4],[5],[7]] => 011101 => 0
{{1},{2,6},{3,7},{4},{5}} => {{1,5},{2,6},{3},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2,6},{3},{4,7},{5}} => {{1,4},{2,6},{3},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1},{2,6},{3},{4},{5,7}} => {{1,3},{2,6},{4},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => 111101 => 4
{{1,7},{2},{3,6},{4},{5}} => {{1,7},{2,5},{3},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => 111010 => 3
{{1},{2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => 111011 => 3
{{1},{2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6},{7}} => [[1,2,5],[3],[4],[6],[7]] => 011011 => 0
{{1},{2},{3,6},{4,7},{5}} => {{1,4},{2,5},{3},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1},{2},{3,6},{4},{5,7}} => {{1,3},{2,5},{4},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => 101011 => 1
{{1},{2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => 111011 => 3
{{1,7},{2},{3},{4,6},{5}} => {{1,7},{2,4},{3},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => 110110 => 2
{{1},{2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => 110101 => 2
{{1},{2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => 110111 => 2
{{1},{2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6},{7}} => [[1,2,4],[3],[5],[6],[7]] => 010111 => 0
{{1},{2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6},{7}} => [[1,3],[2,4],[5],[6],[7]] => 101111 => 1
{{1},{2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => 110111 => 2
{{1,7},{2},{3},{4},{5,6}} => {{1,7},{2,3},{4},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => 101110 => 1
{{1},{2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => 101101 => 1
{{1},{2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => 101011 => 1
{{1},{2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6},{7}} => [[1,3],[2,4],[5],[6],[7]] => 101111 => 1
{{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}} => [[1,2,3],[4],[5],[6],[7]] => 001111 => 0
{{1},{2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => [[1,3],[2],[4],[5],[6],[7]] => 101111 => 1
{{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 5
{{1},{2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => 111101 => 4
{{1},{2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => 111011 => 3
{{1},{2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => 110111 => 2
{{1},{2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6},{7}} => [[1,3],[2],[4],[5],[6],[7]] => 101111 => 1
{{1},{2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6},{7}} => [[1,2],[3],[4],[5],[6],[7]] => 011111 => 0
{{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 6
{{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
{{1,3},{2,4},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6,8}} => [[1,2],[3,4],[5,7],[6,8]] => 0101101 => 0
{{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}} => [[1,2],[3,4],[5,7],[6,8]] => 0101101 => 0
{{1,5},{2,3},{4,6},{7,8}} => {{1,2},{3,5},{4,8},{6,7}} => [[1,2],[3,5],[4,7],[6,8]] => 0110101 => 0
{{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}} => [[1,2],[3,5],[4,7],[6,8]] => 0110101 => 0
{{1,7},{2,3},{4,5},{6,8}} => {{1,3},{2,8},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,8},{2,4},{3,5},{6,7}} => {{1,8},{2,3},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,7},{2,4},{3,5},{6,8}} => {{1,3},{2,8},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,6},{2,4},{3,5},{7,8}} => {{1,2},{3,8},{4,6},{5,7}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,5},{2,4},{3,6},{7,8}} => {{1,2},{3,6},{4,8},{5,7}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,4},{2,5},{3,6},{7,8}} => {{1,2},{3,6},{4,7},{5,8}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,3},{2,5},{4,6},{7,8}} => {{1,2},{3,5},{4,7},{6,8}} => [[1,2],[3,5],[4,7],[6,8]] => 0110101 => 0
{{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => [[1,2],[3,5],[4,6],[7,8]] => 0110110 => 0
{{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => [[1,2],[3,5],[4,6],[7,8]] => 0110110 => 0
{{1,3},{2,6},{4,5},{7,8}} => {{1,2},{3,7},{4,5},{6,8}} => [[1,2],[3,5],[4,7],[6,8]] => 0110101 => 0
{{1,4},{2,6},{3,5},{7,8}} => {{1,2},{3,7},{4,6},{5,8}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,5},{2,6},{3,4},{7,8}} => {{1,2},{3,7},{4,8},{5,6}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}} => [[1,2],[3,6],[4,7],[5,8]] => 0111011 => 0
{{1,7},{2,5},{3,4},{6,8}} => {{1,3},{2,8},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,8},{2,6},{3,4},{5,7}} => {{1,8},{2,4},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,7},{2,6},{3,4},{5,8}} => {{1,4},{2,8},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,6},{2,7},{3,4},{5,8}} => {{1,4},{2,7},{3,8},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,5},{2,7},{3,4},{6,8}} => {{1,3},{2,7},{4,8},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,4},{2,7},{3,5},{6,8}} => {{1,3},{2,7},{4,6},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,3},{2,7},{4,5},{6,8}} => {{1,3},{2,7},{4,5},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,2},{3,7},{4,5},{6,8}} => {{1,3},{2,6},{4,5},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => 1010110 => 1
{{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => 1010110 => 1
{{1,3},{2,8},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,4},{2,8},{3,5},{6,7}} => {{1,7},{2,3},{4,6},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,5},{2,8},{3,4},{6,7}} => {{1,7},{2,3},{4,8},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,6},{2,8},{3,4},{5,7}} => {{1,7},{2,4},{3,8},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,7},{2,8},{3,4},{5,6}} => {{1,7},{2,8},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,8},{2,7},{3,5},{4,6}} => {{1,8},{2,7},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,8},{3,5},{4,7}} => {{1,7},{2,5},{3,8},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,5},{2,8},{3,6},{4,7}} => {{1,7},{2,5},{3,6},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,4},{2,8},{3,6},{5,7}} => {{1,7},{2,4},{3,6},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,3},{2,8},{4,6},{5,7}} => {{1,7},{2,4},{3,5},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,2},{3,8},{4,6},{5,7}} => {{1,6},{2,4},{3,5},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,2},{3,7},{4,6},{5,8}} => {{1,4},{2,6},{3,5},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,3},{2,7},{4,6},{5,8}} => {{1,4},{2,7},{3,5},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,4},{2,7},{3,6},{5,8}} => {{1,4},{2,7},{3,6},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,5},{2,7},{3,6},{4,8}} => {{1,5},{2,7},{3,6},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,7},{3,5},{4,8}} => {{1,5},{2,7},{3,8},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,6},{3,5},{4,8}} => {{1,5},{2,8},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,8},{2,6},{3,5},{4,7}} => {{1,8},{2,5},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,8},{2,5},{3,6},{4,7}} => {{1,8},{2,5},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,5},{3,6},{4,8}} => {{1,5},{2,8},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,5},{3,7},{4,8}} => {{1,5},{2,6},{3,8},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,3},{2,6},{4,7},{5,8}} => {{1,4},{2,5},{3,7},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,2},{3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => 1010110 => 1
{{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,4},{2,5},{3,7},{6,8}} => {{1,3},{2,6},{4,7},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,5},{2,4},{3,7},{6,8}} => {{1,3},{2,6},{4,8},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,6},{2,4},{3,7},{5,8}} => {{1,4},{2,6},{3,8},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,7},{2,4},{3,6},{5,8}} => {{1,4},{2,8},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,8},{2,4},{3,6},{5,7}} => {{1,8},{2,4},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,8},{2,3},{4,6},{5,7}} => {{1,8},{2,4},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,7},{2,3},{4,6},{5,8}} => {{1,4},{2,8},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,6},{2,3},{4,7},{5,8}} => {{1,4},{2,5},{3,8},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,5},{2,3},{4,7},{6,8}} => {{1,3},{2,5},{4,8},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,4},{2,3},{5,7},{6,8}} => {{1,3},{2,4},{5,8},{6,7}} => [[1,3],[2,4],[5,7],[6,8]] => 1011101 => 1
{{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}} => [[1,3],[2,4],[5,7],[6,8]] => 1011101 => 1
{{1,2},{3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6},{7,8}} => [[1,3],[2,4],[5,6],[7,8]] => 1011010 => 1
{{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}} => [[1,3],[2,4],[5,6],[7,8]] => 1011010 => 1
{{1,3},{2,4},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6,8}} => [[1,3],[2,4],[5,7],[6,8]] => 1011101 => 1
{{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => [[1,3],[2,4],[5,7],[6,8]] => 1011101 => 1
{{1,5},{2,3},{4,8},{6,7}} => {{1,5},{2,3},{4,8},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,6},{2,3},{4,8},{5,7}} => {{1,5},{2,4},{3,8},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,7},{2,3},{4,8},{5,6}} => {{1,5},{2,8},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,8},{2,4},{3,7},{5,6}} => {{1,8},{2,6},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,7},{2,4},{3,8},{5,6}} => {{1,6},{2,8},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,6},{2,4},{3,8},{5,7}} => {{1,6},{2,4},{3,8},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,5},{2,4},{3,8},{6,7}} => {{1,6},{2,3},{4,8},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,4},{2,5},{3,8},{6,7}} => {{1,6},{2,3},{4,7},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1
{{1,3},{2,5},{4,8},{6,7}} => {{1,5},{2,3},{4,7},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1
{{1,2},{3,5},{4,8},{6,7}} => {{1,5},{2,3},{4,6},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => 1010110 => 1
{{1,2},{3,6},{4,8},{5,7}} => {{1,5},{2,4},{3,6},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,3},{2,6},{4,8},{5,7}} => {{1,5},{2,4},{3,7},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,4},{2,6},{3,8},{5,7}} => {{1,6},{2,4},{3,7},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,5},{2,6},{3,8},{4,7}} => {{1,6},{2,5},{3,7},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,5},{3,8},{4,7}} => {{1,6},{2,5},{3,8},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,5},{3,8},{4,6}} => {{1,6},{2,8},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,8},{2,5},{3,7},{4,6}} => {{1,8},{2,6},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,8},{2,6},{3,7},{4,5}} => {{1,8},{2,6},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,6},{3,8},{4,5}} => {{1,6},{2,8},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,7},{3,8},{4,5}} => {{1,6},{2,7},{3,8},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,5},{2,7},{3,8},{4,6}} => {{1,6},{2,7},{3,5},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,4},{2,7},{3,8},{5,6}} => {{1,6},{2,7},{3,4},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,3},{2,7},{4,8},{5,6}} => {{1,5},{2,7},{3,4},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,2},{3,7},{4,8},{5,6}} => {{1,5},{2,6},{3,4},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => 1101110 => 2
{{1,3},{2,8},{4,7},{5,6}} => {{1,7},{2,5},{3,4},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => 1101101 => 2
{{1,4},{2,8},{3,7},{5,6}} => {{1,7},{2,6},{3,4},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => 1101011 => 2
{{1,5},{2,8},{3,7},{4,6}} => {{1,7},{2,6},{3,5},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,6},{2,8},{3,7},{4,5}} => {{1,7},{2,6},{3,8},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,7},{2,8},{3,6},{4,5}} => {{1,7},{2,8},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => 1110111 => 3
{{1},{2,4,6,8},{3},{5},{7}} => {{1,3,5,7},{2},{4},{6},{8}} => [[1,3,5,7],[2],[4],[6],[8]] => 1010101 => 1
{{1},{2,4,8},{3},{5,7},{6}} => {{1,5,7},{2,4},{3},{6},{8}} => [[1,4,7],[2,5],[3],[6],[8]] => 1101101 => 2
{{1},{2,6,8},{3,5},{4},{7}} => {{1,3,7},{2},{4,6},{5},{8}} => [[1,3,7],[2,6],[4],[5],[8]] => 1011001 => 1
{{1},{2,8},{3,5,7},{4},{6}} => {{1,7},{2,4,6},{3},{5},{8}} => [[1,4,6],[2,7],[3],[5],[8]] => 1101011 => 2
{{1},{2,8},{3,7},{4,6},{5}} => {{1,7},{2,6},{3,5},{4},{8}} => [[1,5],[2,6],[3,7],[4],[8]] => 1110111 => 3
{{1,2},{3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6},{7,8}} => [[1,2,4],[3,6],[5,8],[7]] => 0101010 => 0
{{1,2},{3,4},{5,6,8},{7}} => {{1,3,4},{2},{5,6},{7,8}} => [[1,3,4],[2,6],[5,8],[7]] => 1001010 => 1
{{1,2},{3,5,6},{4},{7,8}} => {{1,2},{3,4,6},{5},{7,8}} => [[1,2,6],[3,4],[5,8],[7]] => 0101010 => 0
{{1,2},{3,5,7,8},{4},{6}} => {{1,2,4,6},{3},{5},{7,8}} => [[1,2,4,6],[3,8],[5],[7]] => 0101010 => 0
{{1,2},{3,5,8},{4},{6,7}} => {{1,4,6},{2,3},{5},{7,8}} => [[1,3,6],[2,4],[5,8],[7]] => 1011010 => 1
{{1,2},{3,7,8},{4,5},{6}} => {{1,2,6},{3},{4,5},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0
{{1,2},{3,6,8},{4,5},{7}} => {{1,3,6},{2},{4,5},{7,8}} => [[1,3,6],[2,5],[4,8],[7]] => 1010010 => 1
{{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,5,6},{4},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0
{{1,2},{3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0
{{1,2},{3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4},{7,8}} => [[1,3,5],[2,6],[4,8],[7]] => 1010110 => 1
{{1,2},{3,4,8},{5,6},{7}} => {{1,5,6},{2},{3,4},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => 1101010 => 2
{{1,2},{3,8},{4,5,7},{6}} => {{1,6},{2,4,5},{3},{7,8}} => [[1,4,5],[2,6],[3,8],[7]] => 1100110 => 2
{{1,2},{3,4,8},{5,7},{6}} => {{1,5,6},{2,4},{3},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => 1101010 => 2
{{1,2},{3,4,5,8},{6},{7}} => {{1,4,5,6},{2},{3},{7,8}} => [[1,4,5,6],[2,8],[3],[7]] => 1100010 => 2
{{1,3},{2},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6,8},{7}} => [[1,3,5],[2,8],[4],[6],[7]] => 1010110 => 1
{{1,3},{2},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,8},{7}} => [[1,4],[2,5],[3,8],[6],[7]] => 1101110 => 2
{{1,3,4},{2},{5,6},{7,8}} => {{1,2},{3,4},{5,6,8},{7}} => [[1,2,8],[3,4],[5,6],[7]] => 0101010 => 0
{{1,3,4},{2},{5,7,8},{6}} => {{1,2,4},{3},{5,6,8},{7}} => [[1,2,4],[3,6,8],[5],[7]] => 0101010 => 0
{{1,3,4},{2},{5,8},{6,7}} => {{1,4},{2,3},{5,6,8},{7}} => [[1,3,8],[2,4],[5,6],[7]] => 1011010 => 1
{{1,3,5},{2},{4},{6,8},{7}} => {{1,3},{2},{4,6,8},{5},{7}} => [[1,3,8],[2,6],[4],[5],[7]] => 1011010 => 1
{{1,3,5,6},{2},{4},{7,8}} => {{1,2},{3,4,6,8},{5},{7}} => [[1,2,6,8],[3,4],[5],[7]] => 0101010 => 0
{{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,4,6,8},{3},{5},{7}} => [[1,4,6,8],[2],[3],[5],[7]] => 1101010 => 2
{{1,3,5,7,8},{2},{4},{6}} => {{1,2,4,6,8},{3},{5},{7}} => [[1,2,4,6,8],[3],[5],[7]] => 0101010 => 0
{{1,3,5,8},{2},{4},{6,7}} => {{1,4,6,8},{2,3},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => 1011010 => 1
{{1,3,4,5},{2},{6,7},{8}} => {{1},{2,3},{4,5,6,8},{7}} => [[1,3,6,8],[2,5],[4],[7]] => 1010010 => 1
{{1,3,4,5},{2},{6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}} => [[1,3,6,8],[2,5],[4],[7]] => 1010010 => 1
{{1,3,6},{2},{4,5},{7,8}} => {{1,2},{3,6,8},{4,5},{7}} => [[1,2,8],[3,5],[4,6],[7]] => 0110110 => 0
{{1,3,7,8},{2},{4,5},{6}} => {{1,2,6,8},{3},{4,5},{7}} => [[1,2,6,8],[3,5],[4],[7]] => 0110010 => 0
{{1,3,8},{2},{4,5},{6,7}} => {{1,6,8},{2,3},{4,5},{7}} => [[1,3,8],[2,5],[4,6],[7]] => 1010110 => 1
{{1,3,4,6},{2},{5},{7,8}} => {{1,2},{3,5,6,8},{4},{7}} => [[1,2,6,8],[3,5],[4],[7]] => 0110010 => 0
{{1,3,7},{2},{4,6},{5},{8}} => {{1},{2,6,8},{3,5},{4},{7}} => [[1,5,8],[2,6],[3],[4],[7]] => 1110110 => 3
{{1,3,7,8},{2},{4,6},{5}} => {{1,2,6,8},{3,5},{4},{7}} => [[1,2,6,8],[3,5],[4],[7]] => 0110010 => 0
{{1,3,8},{2},{4,6,7},{5}} => {{1,6,8},{2,3,5},{4},{7}} => [[1,3,5],[2,6,8],[4],[7]] => 1010110 => 1
{{1,3,8},{2},{4,7},{5,6}} => {{1,6,8},{2,5},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,2,3},{4,6,7},{5},{8}} => {{1},{2,3,5},{4},{6,7,8}} => [[1,3,5],[2,7,8],[4],[6]] => 1010100 => 1
{{1,2,3},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6,7,8}} => [[1,3,5],[2,7,8],[4],[6]] => 1010100 => 1
{{1,4},{2,3},{5,7,8},{6}} => {{1,2,4},{3},{5,8},{6,7}} => [[1,2,4],[3,7],[5,8],[6]] => 0101101 => 0
{{1,4},{2,3},{5,6,8},{7}} => {{1,3,4},{2},{5,8},{6,7}} => [[1,3,4],[2,7],[5,8],[6]] => 1001101 => 1
{{1,5,6},{2,3},{4},{7,8}} => {{1,2},{3,4,8},{5},{6,7}} => [[1,2,8],[3,4],[5,7],[6]] => 0101100 => 0
{{1,5,7,8},{2,3},{4},{6}} => {{1,2,4,8},{3},{5},{6,7}} => [[1,2,4,8],[3,7],[5],[6]] => 0101100 => 0
{{1,5,8},{2,3},{4},{6,7}} => {{1,4,8},{2,3},{5},{6,7}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,7,8},{2,3},{4,5},{6}} => {{1,2,8},{3},{4,5},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,6,8},{2,3},{4,5},{7}} => {{1,3,8},{2},{4,5},{6,7}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,4,6},{2,3},{5},{7,8}} => {{1,2},{3,5,8},{4},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,7,8},{2,3},{4,6},{5}} => {{1,2,8},{3,5},{4},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,8},{2,3},{4,6,7},{5}} => {{1,8},{2,3,5},{4},{6,7}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,4,8},{2,3},{5,6},{7}} => {{1,5,8},{2},{3,4},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,8},{2,3},{4,5,7},{6}} => {{1,8},{2,4,5},{3},{6,7}} => [[1,4,5],[2,7],[3,8],[6]] => 1100101 => 2
{{1,4,8},{2,3},{5,7},{6}} => {{1,5,8},{2,4},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,4,5,8},{2,3},{6},{7}} => {{1,4,5,8},{2},{3},{6,7}} => [[1,4,5,8],[2,7],[3],[6]] => 1100100 => 2
{{1,2,4},{3},{5,6},{7,8}} => {{1,2},{3,4},{5,7,8},{6}} => [[1,2,8],[3,4],[5,7],[6]] => 0101100 => 0
{{1,2,4},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,7,8},{6}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,2,4},{3},{5,6,8},{7}} => {{1,3,4},{2},{5,7,8},{6}} => [[1,3,4],[2,7,8],[5],[6]] => 1001100 => 1
{{1,5},{2,4},{3},{6,8},{7}} => {{1,3},{2},{4,8},{5,7},{6}} => [[1,3],[2,7],[4,8],[5],[6]] => 1011101 => 1
{{1,5,6},{2,4},{3},{7,8}} => {{1,2},{3,4,8},{5,7},{6}} => [[1,2,8],[3,4],[5,7],[6]] => 0101100 => 0
{{1,5,7},{2,4},{3},{6},{8}} => {{1},{2,4,8},{3},{5,7},{6}} => [[1,4,8],[2,7],[3],[5],[6]] => 1101100 => 2
{{1,5,7,8},{2,4},{3},{6}} => {{1,2,4,8},{3},{5,7},{6}} => [[1,2,4,8],[3,7],[5],[6]] => 0101100 => 0
{{1,5,8},{2,4},{3},{6,7}} => {{1,4,8},{2,3},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,6},{2,4,5},{3},{7,8}} => {{1,2},{3,8},{4,5,7},{6}} => [[1,2,7],[3,5],[4,8],[6]] => 0110101 => 0
{{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}} => [[1,2,7],[3,5,8],[4],[6]] => 0110101 => 0
{{1,8},{2,4,5},{3},{6,7}} => {{1,8},{2,3},{4,5,7},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,8},{2,6,7},{3},{4,5}} => {{1,8},{2,3,7},{4,5},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,7},{2,4,6},{3},{5},{8}} => {{1},{2,8},{3,5,7},{4},{6}} => [[1,5,7],[2,8],[3],[4],[6]] => 1110101 => 3
{{1,7,8},{2,4,6},{3},{5}} => {{1,2,8},{3,5,7},{4},{6}} => [[1,2,7],[3,5,8],[4],[6]] => 0110101 => 0
{{1,8},{2,4,6,7},{3},{5}} => {{1,8},{2,3,5,7},{4},{6}} => [[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1
{{1,8},{2,4,7},{3},{5,6}} => {{1,8},{2,5,7},{3,4},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,8},{2,3,4},{5},{6,7}} => {{1,8},{2,3},{4},{5,6,7}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,7},{2,3,4},{5,6},{8}} => {{1},{2,8},{3,4},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,7,8},{2,5},{3,4},{6}} => {{1,2,8},{3},{4,7},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,6,8},{2,5},{3,4},{7}} => {{1,3,8},{2},{4,7},{5,6}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,2,6},{3,4},{5},{7,8}} => {{1,2},{3,7,8},{4},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,7,8},{2,6},{3,4},{5}} => {{1,2,8},{3,7},{4},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,8},{2,6,7},{3,4},{5}} => {{1,8},{2,3,7},{4},{5,6}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,2,8},{3,4},{5,6},{7}} => {{1,7,8},{2},{3,4},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,8},{2,5,7},{3,4},{6}} => {{1,8},{2,4,7},{3},{5,6}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,2,8},{3,4},{5,7},{6}} => {{1,7,8},{2,4},{3},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,2,5,8},{3,4},{6},{7}} => {{1,4,7,8},{2},{3},{5,6}} => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 2
{{1,6},{2,3,5},{4},{7,8}} => {{1,2},{3,8},{4,6,7},{5}} => [[1,2,7],[3,6],[4,8],[5]] => 0111001 => 0
{{1,8},{2,3,5},{4},{6,7}} => {{1,8},{2,3},{4,6,7},{5}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,6,8},{2,3,5},{4},{7}} => {{1,3,8},{2},{4,6,7},{5}} => [[1,3,7],[2,6,8],[4],[5]] => 1011001 => 1
{{1,2,6},{3,5},{4},{7,8}} => {{1,2},{3,7,8},{4,6},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,7},{2,6},{3,5},{4},{8}} => {{1},{2,8},{3,7},{4,6},{5}} => [[1,6],[2,7],[3,8],[4],[5]] => 1111011 => 4
{{1,7,8},{2,6},{3,5},{4}} => {{1,2,8},{3,7},{4,6},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,8},{2,6,7},{3,5},{4}} => {{1,8},{2,3,7},{4,6},{5}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,2,3,6},{4},{5},{7,8}} => {{1,2},{3,6,7,8},{4},{5}} => [[1,2,7,8],[3,6],[4],[5]] => 0111000 => 0
{{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,4,6},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,2,8},{3,6},{4,5},{7}} => {{1,7,8},{2},{3,6},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,8},{2,3,7},{4,5},{6}} => {{1,8},{2,6,7},{3},{4,5}} => [[1,5,7],[2,6],[3,8],[4]] => 1110101 => 3
{{1,2,8},{3,7},{4,5},{6}} => {{1,7,8},{2,6},{3},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,2,3,8},{4,5},{6},{7}} => {{1,6,7,8},{2},{3},{4,5}} => [[1,5,7,8],[2,6],[3],[4]] => 1110100 => 3
{{1,8},{2,7},{3,4,6},{5}} => {{1,8},{2,7},{3,5,6},{4}} => [[1,5,6],[2,7],[3,8],[4]] => 1110011 => 3
{{1,2,8},{3,4,6},{5},{7}} => {{1,7,8},{2},{3,5,6},{4}} => [[1,5,6],[2,7,8],[3],[4]] => 1110010 => 3
{{1,8},{2,3,7},{4,6},{5}} => {{1,8},{2,6,7},{3,5},{4}} => [[1,5,7],[2,6],[3,8],[4]] => 1110101 => 3
{{1,2,8},{3,7},{4,6},{5}} => {{1,7,8},{2,6},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,2,3,8},{4,6},{5},{7}} => {{1,6,7,8},{2},{3,5},{4}} => [[1,5,7,8],[2,6],[3],[4]] => 1110100 => 3
{{1,8},{2,3,4,7},{5},{6}} => {{1,8},{2,5,6,7},{3},{4}} => [[1,5,6,7],[2,8],[3],[4]] => 1110001 => 3
{{1,2,8},{3,4,7},{5},{6}} => {{1,7,8},{2,5,6},{3},{4}} => [[1,5,6],[2,7,8],[3],[4]] => 1110010 => 3
{{1,2,3,8},{4,7},{5},{6}} => {{1,6,7,8},{2,5},{3},{4}} => [[1,5,7,8],[2,6],[3],[4]] => 1110100 => 3
{{1,2,3,4,8},{5},{6},{7}} => {{1,5,6,7,8},{2},{3},{4}} => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 3
{{1,5,7,8},{2,6},{3},{4}} => {{1,2,4,8},{3,7},{5},{6}} => [[1,2,4,8],[3,7],[5],[6]] => 0101100 => 0
{{1,3,4,8},{2,7},{5},{6}} => {{1,5,6,8},{2,7},{3},{4}} => [[1,5,6,8],[2,7],[3],[4]] => 1110010 => 3
{{1,2,4,8},{3,7},{5},{6}} => {{1,5,7,8},{2,6},{3},{4}} => [[1,5,7,8],[2,6],[3],[4]] => 1110100 => 3
{{1,3,5,8},{2,6},{4},{7}} => {{1,4,6,8},{2},{3,7},{5}} => [[1,4,6,8],[2,7],[3],[5]] => 1101010 => 2
{{1,2,4,8},{3,6},{5},{7}} => {{1,5,7,8},{2},{3,6},{4}} => [[1,5,7,8],[2,6],[3],[4]] => 1110100 => 3
{{1,2,6,7},{3,8},{4},{5}} => {{1,6},{2,3,7,8},{4},{5}} => [[1,3,7,8],[2,6],[4],[5]] => 1011000 => 1
{{1,3,5,7},{2,8},{4},{6}} => {{1,7},{2,4,6,8},{3},{5}} => [[1,4,6,8],[2,7],[3],[5]] => 1101010 => 2
{{1,3,5,7},{2,6},{4},{8}} => {{1},{2,4,6,8},{3,7},{5}} => [[1,4,6,8],[2,7],[3],[5]] => 1101010 => 2
{{1,3,5,7},{2,4},{6},{8}} => {{1},{2,4,6,8},{3},{5,7}} => [[1,4,6,8],[2,7],[3],[5]] => 1101010 => 2
{{1,5,7},{2,6,8},{3},{4}} => {{1,3,7},{2,4,8},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => 1011101 => 1
{{1,2,7},{3,6,8},{4},{5}} => {{1,3,6},{2,7,8},{4},{5}} => [[1,3,6],[2,7,8],[4],[5]] => 1011010 => 1
{{1,3,7},{2,5,8},{4},{6}} => {{1,4,7},{2,6,8},{3},{5}} => [[1,4,7],[2,6,8],[3],[5]] => 1101001 => 2
{{1,4,5},{2,6,8},{3},{7}} => {{1,3,7},{2},{4,5,8},{6}} => [[1,3,7],[2,5,8],[4],[6]] => 1010101 => 1
{{1,3,5},{2,6,8},{4},{7}} => {{1,3,7},{2},{4,6,8},{5}} => [[1,3,7],[2,6,8],[4],[5]] => 1011001 => 1
{{1,5,8},{2,6},{3,7},{4}} => {{1,4,8},{2,6},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,2,8},{3,6},{4,7},{5}} => {{1,7,8},{2,5},{3,6},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,5,7},{2,6},{3,8},{4}} => {{1,6},{2,4,8},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,5,6},{2,7},{3,8},{4}} => {{1,6},{2,7},{3,4,8},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,4,6},{2,7},{3,8},{5}} => {{1,6},{2,7},{3,5,8},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,3,4},{2,6},{5,8},{7}} => {{1,4},{2},{3,7},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,2,4},{3,6},{5,8},{7}} => {{1,4},{2},{3,6},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,3,5},{2,4},{6,8},{7}} => {{1,3},{2},{4,6,8},{5,7}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,4,7},{2,5},{3,6},{8}} => {{1},{2,5,8},{3,6},{4,7}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,3,7},{2,5},{4,6},{8}} => {{1},{2,6,8},{3,5},{4,7}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,3,4},{2,6},{5,7},{8}} => {{1},{2,4},{3,7},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,2,4},{3,6},{5,7},{8}} => {{1},{2,4},{3,6},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,3,5,7},{2},{4},{6,8}} => {{1,3},{2,4,6,8},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => 1011010 => 1
{{1,5,7},{2,4},{3},{6,8}} => {{1,3},{2,4,8},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,4},{2},{3,6,7},{5,8}} => {{1,4},{2,3,6},{5,8},{7}} => [[1,3,6],[2,4],[5,8],[7]] => 1011010 => 1
{{1,4},{2},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,8},{7}} => [[1,2,4],[3,6],[5,8],[7]] => 0101010 => 0
{{1,4},{2},{3,7},{5,6,8}} => {{1,3,4},{2,6},{5,8},{7}} => [[1,3,4],[2,6],[5,8],[7]] => 1001010 => 1
{{1,4},{2},{3,5,8},{6,7}} => {{1,4,6},{2,3},{5,8},{7}} => [[1,3,6],[2,4],[5,8],[7]] => 1011010 => 1
{{1,5},{2},{3,4,8},{6,7}} => {{1,5,6},{2,3},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => 1010010 => 1
{{1,2,5},{3},{4,7,8},{6}} => {{1,2,5},{3},{4,7,8},{6}} => [[1,2,5],[3,7,8],[4],[6]] => 0110100 => 0
{{1,2},{3,6,7},{4,8},{5}} => {{1,5},{2,3,6},{4},{7,8}} => [[1,3,6],[2,5],[4,8],[7]] => 1010010 => 1
{{1,6},{2,3},{4},{5,7,8}} => {{1,2,4},{3,8},{5},{6,7}} => [[1,2,4],[3,7],[5,8],[6]] => 0101101 => 0
{{1,7},{2,3},{4},{5,6,8}} => {{1,3,4},{2,8},{5},{6,7}} => [[1,3,4],[2,7],[5,8],[6]] => 1001101 => 1
{{1,2},{3,7},{4,6,8},{5}} => {{1,3,5},{2,6},{4},{7,8}} => [[1,3,5],[2,6],[4,8],[7]] => 1010110 => 1
{{1,2},{3,5,8},{4,7},{6}} => {{1,4,6},{2,5},{3},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => 1101010 => 2
{{1,3,8},{2,4,7},{5},{6}} => {{1,6,8},{2,5,7},{3},{4}} => [[1,5,7],[2,6,8],[3],[4]] => 1110101 => 3
{{1,4,8},{2,3,7},{5},{6}} => {{1,5,8},{2,6,7},{3},{4}} => [[1,5,7],[2,6,8],[3],[4]] => 1110101 => 3
{{1,3,7},{2,8},{4},{5,6}} => {{1,7},{2,6,8},{3,4},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,3,7},{2,8},{4,6},{5}} => {{1,7},{2,6,8},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,7},{2,3,8},{4},{5,6}} => {{1,6,7},{2,8},{3,4},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,7,8},{2,5},{3,6},{4}} => {{1,2,8},{3,6},{4,7},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,7},{2,4,6,8},{3},{5}} => {{1,3,5,7},{2,8},{4},{6}} => [[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1
{{1,4,6},{2,5},{3},{7,8}} => {{1,2},{3,5,8},{4,7},{6}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,5,7,8},{2},{3,6},{4}} => {{1,2,4,8},{3,6},{5},{7}} => [[1,2,4,8],[3,6],[5],[7]] => 0101010 => 0
{{1,5,8},{2,7},{3,6},{4}} => {{1,4,8},{2,7},{3,6},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,8},{2,5,7},{3,6},{4}} => {{1,8},{2,4,7},{3,6},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,5,8},{2,6,7},{3},{4}} => {{1,4,8},{2,3,7},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => 1011101 => 1
{{1,3,5},{2,6},{4},{7,8}} => {{1,2},{3,7},{4,6,8},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,5},{2,3,6},{4},{7,8}} => {{1,2},{3,6,7},{4,8},{5}} => [[1,2,7],[3,6],[4,8],[5]] => 0111001 => 0
{{1,5,7},{2,4},{3,8},{6}} => {{1,6},{2,4,8},{3},{5,7}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,6,8},{2,5,7},{3},{4}} => {{1,3,8},{2,4,7},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => 1011101 => 1
{{1,6,8},{2,7},{3,5},{4}} => {{1,3,8},{2,7},{4,6},{5}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,6,7},{2,8},{3,4},{5}} => {{1,7},{2,3,8},{4},{5,6}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,7},{2,6,8},{3,4},{5}} => {{1,3,7},{2,8},{4},{5,6}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,4,8},{2,7},{3,6},{5}} => {{1,5,8},{2,7},{3,6},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,4,6},{2,8},{3,7},{5}} => {{1,7},{2,6},{3,5,8},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,8},{2,4,7},{3,6},{5}} => {{1,8},{2,5,7},{3,6},{4}} => [[1,5,7],[2,6],[3,8],[4]] => 1110101 => 3
{{1,3,8},{2,7},{4,6},{5}} => {{1,6,8},{2,7},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,7},{2,4,6},{3,8},{5}} => {{1,6},{2,8},{3,5,7},{4}} => [[1,5,7],[2,6],[3,8],[4]] => 1110101 => 3
{{1,3,5},{2},{4,6,8},{7}} => {{1,3,5},{2},{4,6,8},{7}} => [[1,3,5],[2,6,8],[4],[7]] => 1010110 => 1
{{1,3},{2,4,6,8},{5},{7}} => {{1,3,5,7},{2},{4},{6,8}} => [[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1
{{1},{2,4,6,8},{3},{5,7}} => {{1,3,5,7},{2,4},{6},{8}} => [[1,3,5,7],[2,4],[6],[8]] => 1010101 => 1
{{1,3},{2},{4,6,8},{5,7}} => {{1,3,5},{2,4},{6,8},{7}} => [[1,3,5],[2,4],[6,8],[7]] => 1010110 => 1
{{1,3,6},{2},{4,8},{5,7}} => {{1,5},{2,4},{3,6,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,3,6},{2},{4,7},{5,8}} => {{1,4},{2,5},{3,6,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,3,5},{2},{4,7},{6,8}} => {{1,3},{2,5},{4,6,8},{7}} => [[1,3,8],[2,5],[4,6],[7]] => 1010110 => 1
{{1,3,5,7},{2},{4,6},{8}} => {{1},{2,4,6,8},{3,5},{7}} => [[1,4,6,8],[2,5],[3],[7]] => 1101010 => 2
{{1,3,7},{2},{4,6,8},{5}} => {{1,3,5},{2,6,8},{4},{7}} => [[1,3,5],[2,6,8],[4],[7]] => 1010110 => 1
{{1,3,7},{2},{4,6},{5,8}} => {{1,4},{2,6,8},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,3,5,7},{2},{4,8},{6}} => {{1,5},{2,4,6,8},{3},{7}} => [[1,4,6,8],[2,5],[3],[7]] => 1101010 => 2
{{1,3},{2,4,8},{5,7},{6}} => {{1,5,7},{2,4},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1},{2,4,8},{3,5,7},{6}} => {{1,5,7},{2,4,6},{3},{8}} => [[1,4,6],[2,5,7],[3],[8]] => 1101011 => 2
{{1,4},{2,8},{3,5,7},{6}} => {{1,7},{2,4,6},{3},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,4},{2,5,7},{3,8},{6}} => {{1,6},{2,4,7},{3},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,3},{2,5,7},{4,8},{6}} => {{1,5},{2,4,7},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,3},{2,7},{4,6,8},{5}} => {{1,3,5},{2,7},{4},{6,8}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,3,7},{2,4,6},{5},{8}} => {{1},{2,6,8},{3,5,7},{4}} => [[1,5,7],[2,6,8],[3],[4]] => 1110101 => 3
{{1,7},{2,4,6},{3},{5,8}} => {{1,4},{2,8},{3,5,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5,7},{2,4,8},{3},{6}} => {{1,5,7},{2,4,8},{3},{6}} => [[1,4,7],[2,5,8],[3],[6]] => 1101101 => 2
{{1},{2,8},{3,5,7},{4,6}} => {{1,7},{2,4,6},{3,5},{8}} => [[1,4,6],[2,5],[3,7],[8]] => 1101011 => 2
{{1,7},{2,4,6},{3,5},{8}} => {{1},{2,8},{3,5,7},{4,6}} => [[1,5,7],[2,6],[3,8],[4]] => 1110101 => 3
{{1,4,7},{2,6},{3,5},{8}} => {{1},{2,5,8},{3,7},{4,6}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1},{2,5,8},{3,7},{4,6}} => {{1,4,7},{2,6},{3,5},{8}} => [[1,4,7],[2,5],[3,6],[8]] => 1101101 => 2
{{1},{2,5,8},{3,6},{4,7}} => {{1,4,7},{2,5},{3,6},{8}} => [[1,4,7],[2,5],[3,6],[8]] => 1101101 => 2
{{1},{2,4,8},{3,6},{5,7}} => {{1,5,7},{2,4},{3,6},{8}} => [[1,4,7],[2,5],[3,6],[8]] => 1101101 => 2
{{1},{2,4,6,8},{3,5},{7}} => {{1,3,5,7},{2},{4,6},{8}} => [[1,3,5,7],[2,6],[4],[8]] => 1010101 => 1
{{1,4},{2,6,8},{3,5},{7}} => {{1,3,7},{2},{4,6},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,4},{2,5},{3,6,8},{7}} => {{1,3,6},{2},{4,7},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,3},{2,5},{4,6,8},{7}} => {{1,3,5},{2},{4,7},{6,8}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,5},{2,4,6,8},{3},{7}} => {{1,3,5,7},{2},{4,8},{6}} => [[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1
{{1,5},{2,4},{3,6,8},{7}} => {{1,3,6},{2},{4,8},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1},{2,6,8},{3,5,7},{4}} => {{1,3,7},{2,4,6},{5},{8}} => [[1,3,6],[2,4,7],[5],[8]] => 1011011 => 1
{{1,6},{2,8},{3,5,7},{4}} => {{1,7},{2,4,6},{3,8},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,6},{2,4,8},{3},{5,7}} => {{1,5,7},{2,4},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,6},{2,4,7},{3},{5,8}} => {{1,4},{2,5,7},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5},{2,4,7},{3},{6,8}} => {{1,3},{2,5,7},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,5,7},{2,4,6},{3},{8}} => {{1},{2,4,8},{3,5,7},{6}} => [[1,4,7],[2,5,8],[3],[6]] => 1101101 => 2
{{1,5,7},{2,4},{3,6},{8}} => {{1},{2,4,8},{3,6},{5,7}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1},{2,6,8},{3,5},{4,7}} => {{1,3,7},{2,5},{4,6},{8}} => [[1,3,7],[2,5],[4,6],[8]] => 1010101 => 1
{{1},{2,4,6,8},{3,7},{5}} => {{1,3,5,7},{2,6},{4},{8}} => [[1,3,5,7],[2,6],[4],[8]] => 1010101 => 1
{{1,6},{2,7},{3,5,8},{4}} => {{1,4,6},{2,7},{3,8},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,3,5},{2,7},{4},{6,8}} => {{1,3},{2,7},{4,6,8},{5}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,7},{2,6,8},{3,5},{4}} => {{1,3,7},{2,8},{4,6},{5}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,7},{2,6},{3,5,8},{4}} => {{1,4,6},{2,8},{3,7},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,5,6},{2,3},{4,8},{7}} => {{1,5},{2},{3,4,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,2,4},{3,8},{5},{6,7}} => {{1,6},{2,3},{4},{5,7,8}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,3,4},{2,8},{5},{6,7}} => {{1,7},{2,3},{4},{5,6,8}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,4,6},{2,3},{5,8},{7}} => {{1,4},{2},{3,5,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,4},{2,3,6},{5,8},{7}} => {{1,4},{2},{3,6,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,3,8},{2,5,6},{4},{7}} => {{1,6,8},{2},{3,4,7},{5}} => [[1,4,7],[2,6,8],[3],[5]] => 1101001 => 2
{{1,5,7},{2,3,8},{4},{6}} => {{1,6,7},{2,4,8},{3},{5}} => [[1,4,7],[2,6,8],[3],[5]] => 1101001 => 2
{{1,6},{2,5,7,8},{3},{4}} => {{1,2,4,7},{3,8},{5},{6}} => [[1,2,4,7],[3,8],[5],[6]] => 0101101 => 0
{{1,6,7},{2,5,8},{3},{4}} => {{1,4,7},{2,3,8},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => 1011101 => 1
{{1,7},{2,5,6,8},{3},{4}} => {{1,3,4,7},{2,8},{5},{6}} => [[1,3,4,7],[2,8],[5],[6]] => 1001101 => 1
{{1,7},{2,6,8},{3},{4,5}} => {{1,3,7},{2,8},{4,5},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,8},{2,6},{3},{4,5,7}} => {{1,8},{2,4,5},{3,7},{6}} => [[1,4,5],[2,7],[3,8],[6]] => 1100101 => 2
{{1,8},{2,5,6},{3},{4,7}} => {{1,8},{2,5},{3,4,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,8},{2,5},{3},{4,6,7}} => {{1,8},{2,3,5},{4,7},{6}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,7,8},{2,5},{3},{4,6}} => {{1,2,8},{3,5},{4,7},{6}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,8},{2,4},{3,6,7},{5}} => {{1,8},{2,3,6},{4},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,7},{2,3,5,8},{4},{6}} => {{1,4,6,7},{2,8},{3},{5}} => [[1,4,6,7],[2,8],[3],[5]] => 1101001 => 2
{{1,7},{2},{3,6},{4,5,8}} => {{1,4,5},{2,8},{3,6},{7}} => [[1,4,5],[2,6],[3,8],[7]] => 1100110 => 2
{{1,7},{2},{3,5,6},{4,8}} => {{1,5},{2,8},{3,4,6},{7}} => [[1,4,6],[2,5],[3,8],[7]] => 1101010 => 2
{{1,6,7},{2},{3,5},{4,8}} => {{1,5},{2,3,8},{4,6},{7}} => [[1,3,8],[2,5],[4,6],[7]] => 1010110 => 1
{{1,6},{2},{3,5},{4,7,8}} => {{1,2,5},{3,8},{4,6},{7}} => [[1,2,5],[3,6],[4,8],[7]] => 0110110 => 0
{{1,5},{2},{3,7,8},{4,6}} => {{1,2,6},{3,5},{4,8},{7}} => [[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0
{{1,5},{2},{3,8},{4,6,7}} => {{1,6},{2,3,5},{4,8},{7}} => [[1,3,5],[2,6],[4,8],[7]] => 1010110 => 1
{{1,5,6},{2},{3,8},{4,7}} => {{1,6},{2,5},{3,4,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,6},{2},{3,8},{4,5,7}} => {{1,6},{2,4,5},{3,8},{7}} => [[1,4,5],[2,6],[3,8],[7]] => 1100110 => 2
{{1,6,8},{2},{3,7},{4,5}} => {{1,3,8},{2,6},{4,5},{7}} => [[1,3,8],[2,5],[4,6],[7]] => 1010110 => 1
{{1,5,6,8},{2},{3,7},{4}} => {{1,3,4,8},{2,6},{5},{7}} => [[1,3,4,8],[2,6],[5],[7]] => 1001010 => 1
{{1,5,8},{2},{3,6,7},{4}} => {{1,4,8},{2,3,6},{5},{7}} => [[1,3,6],[2,4,8],[5],[7]] => 1011010 => 1
{{1,3,6,8},{2},{4},{5,7}} => {{1,3,6,8},{2,4},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => 1011010 => 1
{{1,4,6,8},{2},{3,5},{7}} => {{1,3,5,8},{2},{4,6},{7}} => [[1,3,5,8],[2,6],[4],[7]] => 1010110 => 1
{{1,5,7},{2,3},{4,8},{6}} => {{1,5},{2,4,8},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,4,8},{2},{3,6},{5,7}} => {{1,5,8},{2,4},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,3,8},{2},{4,6},{5,7}} => {{1,6,8},{2,4},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,4,7,8},{2},{3,6},{5}} => {{1,2,5,8},{3,6},{4},{7}} => [[1,2,5,8],[3,6],[4],[7]] => 0110110 => 0
{{1,4,6,7},{2},{3,5},{8}} => {{1},{2,3,5,8},{4,6},{7}} => [[1,3,5,8],[2,6],[4],[7]] => 1010110 => 1
{{1,4,8},{2},{3,7},{5,6}} => {{1,5,8},{2,6},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5,8},{2},{3,7},{4,6}} => {{1,4,8},{2,6},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5,8},{2},{3,6},{4,7}} => {{1,4,8},{2,5},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,4,7},{2,3},{5,8},{6}} => {{1,4},{2,5,8},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,3},{2,5,8},{4,7},{6}} => {{1,4,7},{2,5},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5},{2,4,7,8},{3},{6}} => {{1,2,5,7},{3},{4,8},{6}} => [[1,2,5,7],[3,8],[4],[6]] => 0110101 => 0
{{1,3},{2,4,6,7},{5},{8}} => {{1},{2,3,5,7},{4},{6,8}} => [[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1
{{1,3},{2,4,8},{5,6},{7}} => {{1,5,7},{2},{3,4},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,3},{2,5,8},{4,6},{7}} => {{1,4,7},{2},{3,5},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,6},{2,3,4},{5,8},{7}} => {{1,4},{2},{3,8},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,6},{2,4},{3,5,8},{7}} => {{1,4,6},{2},{3,8},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,4},{2,6},{3,5,8},{7}} => {{1,4,6},{2},{3,7},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,4},{2,5,6},{3,7},{8}} => {{1},{2,6},{3,4,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,4},{2,6,7},{3,8},{5}} => {{1,6},{2,3,7},{4},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,2,5},{3,6},{4},{7,8}} => {{1,2},{3,6},{4,7,8},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,2,4},{3,7},{5,6},{8}} => {{1},{2,6},{3,4},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,3,4},{2,7},{5,6},{8}} => {{1},{2,7},{3,4},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,6,7},{2,8},{3},{4,5}} => {{1,7},{2,3,8},{4,5},{6}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,5,6},{2,3},{4,7},{8}} => {{1},{2,5},{3,4,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,4,6},{2,3},{5,7},{8}} => {{1},{2,4},{3,5,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,4},{2,3,6},{5,7},{8}} => {{1},{2,4},{3,6,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,4},{2,3,7},{5},{6,8}} => {{1,3},{2,6,7},{4},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,2,4},{3,7},{5},{6,8}} => {{1,3},{2,6},{4},{5,7,8}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,3,4},{2,7},{5},{6,8}} => {{1,3},{2,7},{4},{5,6,8}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,2,7},{3},{4,5},{6,8}} => {{1,3},{2,7,8},{4,5},{6}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,2,6},{3},{4},{5,7,8}} => {{1,2,4},{3,7,8},{5},{6}} => [[1,2,4],[3,7,8],[5],[6]] => 0101100 => 0
{{1,7},{2,3,4},{5},{6,8}} => {{1,3},{2,8},{4},{5,6,7}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,7},{2,4},{3,6,8},{5}} => {{1,3,6},{2,8},{4},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,4},{2,7},{3,6,8},{5}} => {{1,3,6},{2,7},{4},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,4},{2,6},{3,5,7},{8}} => {{1},{2,4,6},{3,7},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,6},{2,4},{3,5,7},{8}} => {{1},{2,4,6},{3,8},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,6},{2,3,4},{5,7},{8}} => {{1},{2,4},{3,8},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,3},{2,5,7},{4,6},{8}} => {{1},{2,4,7},{3,5},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,3},{2,4,7},{5,6},{8}} => {{1},{2,5,7},{3,4},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5},{2,7,8},{3},{4,6}} => {{1,2,7},{3,5},{4,8},{6}} => [[1,2,7],[3,5],[4,8],[6]] => 0110101 => 0
{{1,7},{2,4},{3,5,6},{8}} => {{1},{2,8},{3,4,6},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,6},{2,5},{3,7,8},{4}} => {{1,2,6},{3,8},{4,7},{5}} => [[1,2,6],[3,7],[4,8],[5]] => 0111011 => 0
{{1,5},{2,6},{3,7,8},{4}} => {{1,2,6},{3,7},{4,8},{5}} => [[1,2,6],[3,7],[4,8],[5]] => 0111011 => 0
{{1,4},{2,8},{3,6,7},{5}} => {{1,7},{2,3,6},{4},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,4},{2,7},{3,5,6},{8}} => {{1},{2,7},{3,4,6},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,4},{2},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,8},{7}} => [[1,2,6],[3,4],[5,8],[7]] => 0101010 => 0
{{1,4,5},{2},{3,6},{7,8}} => {{1,2},{3,6},{4,5,8},{7}} => [[1,2,8],[3,5],[4,6],[7]] => 0110110 => 0
{{1,5},{2},{3,4,6},{7,8}} => {{1,2},{3,5,6},{4,8},{7}} => [[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0
{{1,6},{2},{3,4,7,8},{5}} => {{1,2,5,6},{3,8},{4},{7}} => [[1,2,5,6],[3,8],[4],[7]] => 0110010 => 0
{{1,5},{2},{3,4,7,8},{6}} => {{1,2,5,6},{3},{4,8},{7}} => [[1,2,5,6],[3,8],[4],[7]] => 0110010 => 0
{{1,4,5},{2},{3,7,8},{6}} => {{1,2,6},{3},{4,5,8},{7}} => [[1,2,6],[3,5,8],[4],[7]] => 0110010 => 0
{{1,4,5},{2},{3,8},{6,7}} => {{1,6},{2,3},{4,5,8},{7}} => [[1,3,8],[2,5],[4,6],[7]] => 1010110 => 1
{{1,6,7},{2},{3,4,8},{5}} => {{1,5,6},{2,3,8},{4},{7}} => [[1,3,6],[2,5,8],[4],[7]] => 1010010 => 1
{{1,7},{2},{3,4,8},{5,6}} => {{1,5,6},{2,8},{3,4},{7}} => [[1,4,6],[2,5],[3,8],[7]] => 1101010 => 2
{{1,4,6,7},{2},{3,8},{5}} => {{1,6},{2,3,5,8},{4},{7}} => [[1,3,5,8],[2,6],[4],[7]] => 1010110 => 1
{{1,4,6},{2},{3,7,8},{5}} => {{1,2,6},{3,5,8},{4},{7}} => [[1,2,6],[3,5,8],[4],[7]] => 0110010 => 0
{{1,3,6},{2},{4},{5,7,8}} => {{1,2,4},{3,6,8},{5},{7}} => [[1,2,4],[3,6,8],[5],[7]] => 0101010 => 0
{{1,2},{3,6},{4},{5,7,8}} => {{1,2,4},{3,6},{5},{7,8}} => [[1,2,4],[3,6],[5,8],[7]] => 0101010 => 0
{{1,4},{2},{3,5,7,8},{6}} => {{1,2,4,6},{3},{5,8},{7}} => [[1,2,4,6],[3,8],[5],[7]] => 0101010 => 0
{{1,6},{2,4},{3},{5,7,8}} => {{1,2,4},{3,8},{5,7},{6}} => [[1,2,4],[3,7],[5,8],[6]] => 0101101 => 0
{{1,6,7},{2,3},{4},{5,8}} => {{1,4},{2,3,8},{5},{6,7}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,7},{2,4},{3},{5,6,8}} => {{1,3,4},{2,8},{5,7},{6}} => [[1,3,4],[2,7],[5,8],[6]] => 1001101 => 1
{{1,6,7},{2,4},{3},{5,8}} => {{1,4},{2,3,8},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => 1011100 => 1
{{1,2},{3,6,7},{4},{5,8}} => {{1,4},{2,3,6},{5},{7,8}} => [[1,3,6],[2,4],[5,8],[7]] => 1011010 => 1
{{1,3,6,7},{2},{4},{5,8}} => {{1,4},{2,3,6,8},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => 1011010 => 1
{{1,3,7},{2},{4},{5,6,8}} => {{1,3,4},{2,6,8},{5},{7}} => [[1,3,4],[2,6,8],[5],[7]] => 1001010 => 1
{{1,2},{3,7},{4},{5,6,8}} => {{1,3,4},{2,6},{5},{7,8}} => [[1,3,4],[2,6],[5,8],[7]] => 1001010 => 1
{{1,4,7},{2},{3,8},{5,6}} => {{1,6},{2,5,8},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5},{2},{3,6,7},{4,8}} => {{1,5},{2,3,6},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => 1010010 => 1
{{1,5},{2},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,8},{7}} => [[1,2,5],[3,6],[4,8],[7]] => 0110110 => 0
{{1,5},{2},{3,7},{4,6,8}} => {{1,3,5},{2,6},{4,8},{7}} => [[1,3,5],[2,6],[4,8],[7]] => 1010110 => 1
{{1,5},{2,6},{3},{4,7,8}} => {{1,2,5},{3,7},{4,8},{6}} => [[1,2,5],[3,7],[4,8],[6]] => 0110101 => 0
{{1,3,6},{2,5},{4},{7,8}} => {{1,2},{3,6,8},{4,7},{5}} => [[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0
{{1,5},{2,4,6},{3},{7,8}} => {{1,2},{3,5,7},{4,8},{6}} => [[1,2,7],[3,5],[4,8],[6]] => 0110101 => 0
{{1,4,5},{2,6},{3},{7,8}} => {{1,2},{3,7},{4,5,8},{6}} => [[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0
{{1,5,8},{2,7},{3,4},{6}} => {{1,4,8},{2,7},{3},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,4,5},{2,8},{3},{6,7}} => {{1,7},{2,3},{4,5,8},{6}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,6,7},{2,8},{3,5},{4}} => {{1,7},{2,3,8},{4,6},{5}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,6},{2,8},{3},{4,5,7}} => {{1,7},{2,4,5},{3,8},{6}} => [[1,4,5],[2,7],[3,8],[6]] => 1100101 => 2
{{1,6},{2,5,8},{3},{4,7}} => {{1,4,7},{2,5},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,6},{2,4,5,8},{3},{7}} => {{1,4,5,7},{2},{3,8},{6}} => [[1,4,5,7],[2,8],[3],[6]] => 1100101 => 2
{{1,5},{2,7},{3},{4,6,8}} => {{1,3,5},{2,7},{4,8},{6}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,7},{2,5},{3,6,8},{4}} => {{1,3,6},{2,8},{4,7},{5}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,8},{2,6},{3,5,7},{4}} => {{1,8},{2,4,6},{3,7},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,5,8},{2,3},{4,7},{6}} => {{1,4,8},{2,5},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,7},{2,3},{4,6,8},{5}} => {{1,3,5},{2,8},{4},{6,7}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,6,7},{2,3},{4,8},{5}} => {{1,5},{2,3,8},{4},{6,7}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,8},{2,5,6},{3,7},{4}} => {{1,8},{2,6},{3,4,7},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,3,8},{2,6},{4},{5,7}} => {{1,6,8},{2,4},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,6,7},{2,5},{3,8},{4}} => {{1,6},{2,3,8},{4,7},{5}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,5},{2,6,7},{3},{4,8}} => {{1,5},{2,3,7},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,3,8},{2,7},{4,5},{6}} => {{1,6,8},{2,7},{3},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => 1110110 => 3
{{1,5,6},{2,4,8},{3},{7}} => {{1,5,7},{2},{3,4,8},{6}} => [[1,4,7],[2,5,8],[3],[6]] => 1101101 => 2
{{1,5,6},{2,8},{3},{4,7}} => {{1,7},{2,5},{3,4,8},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,5,7},{2},{3,6,8},{4}} => {{1,3,6},{2,4,8},{5},{7}} => [[1,3,6],[2,4,8],[5],[7]] => 1011010 => 1
{{1,5},{2},{3,6,8},{4,7}} => {{1,3,6},{2,5},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => 1010010 => 1
{{1,6,8},{2,5},{3},{4,7}} => {{1,3,8},{2,5},{4,7},{6}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,5},{2,6,8},{3},{4,7}} => {{1,3,7},{2,5},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1
{{1,5,7},{2,6},{3},{4,8}} => {{1,5},{2,4,8},{3,7},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,6},{2,5,7},{3},{4,8}} => {{1,5},{2,4,7},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5,7},{2},{3,6},{4,8}} => {{1,5},{2,4,8},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5,7},{2},{3,8},{4,6}} => {{1,6},{2,4,8},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5,6},{2},{3,7},{4,8}} => {{1,5},{2,6},{3,4,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => 1101110 => 2
{{1,5,8},{2,6},{3},{4,7}} => {{1,4,8},{2,5},{3,7},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,7},{2,5,8},{3,6},{4}} => {{1,4,7},{2,8},{3,6},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,7},{2,5,8},{3},{4,6}} => {{1,4,7},{2,8},{3,5},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,7},{2,5,6},{3},{4,8}} => {{1,5},{2,8},{3,4,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,6,7},{2,5},{3},{4,8}} => {{1,5},{2,3,8},{4,7},{6}} => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 1
{{1,6},{2,5},{3},{4,7,8}} => {{1,2,5},{3,8},{4,7},{6}} => [[1,2,5],[3,7],[4,8],[6]] => 0110101 => 0
{{1,5,6},{2,7},{3},{4,8}} => {{1,5},{2,7},{3,4,8},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,5,8},{2,7},{3},{4,6}} => {{1,4,8},{2,7},{3,5},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,6},{2,5,8},{3,7},{4}} => {{1,4,7},{2,6},{3,8},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,5,6},{2,8},{3,7},{4}} => {{1,7},{2,6},{3,4,8},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,5},{2,8},{3,6,7},{4}} => {{1,7},{2,3,6},{4,8},{5}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,5},{2,7,8},{3,6},{4}} => {{1,2,7},{3,6},{4,8},{5}} => [[1,2,7],[3,6],[4,8],[5]] => 0111001 => 0
{{1,8},{2,5},{3,6,7},{4}} => {{1,8},{2,3,6},{4,7},{5}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,8},{2,5,7},{3},{4,6}} => {{1,8},{2,4,7},{3,5},{6}} => [[1,4,7],[2,5],[3,8],[6]] => 1101101 => 2
{{1,5,7},{2,8},{3,6},{4}} => {{1,7},{2,4,8},{3,6},{5}} => [[1,4,8],[2,6],[3,7],[5]] => 1101010 => 2
{{1,5},{2,7},{3,6,8},{4}} => {{1,3,6},{2,7},{4,8},{5}} => [[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1
{{1,7},{2,5},{3},{4,6,8}} => {{1,3,5},{2,8},{4,7},{6}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,6,8},{2,5},{3,7},{4}} => {{1,3,8},{2,6},{4,7},{5}} => [[1,3,8],[2,6],[4,7],[5]] => 1011010 => 1
{{1,5},{2,6,8},{3,7},{4}} => {{1,3,7},{2,6},{4,8},{5}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
{{1,6},{2,5,7},{3,8},{4}} => {{1,6},{2,4,7},{3,8},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,5,7},{2,8},{3},{4,6}} => {{1,7},{2,4,8},{3,5},{6}} => [[1,4,8],[2,5],[3,7],[6]] => 1101100 => 2
{{1,5},{2,8},{3},{4,6,7}} => {{1,7},{2,3,5},{4,8},{6}} => [[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1
{{1,6},{2,7,8},{3,5},{4}} => {{1,2,7},{3,8},{4,6},{5}} => [[1,2,7],[3,6],[4,8],[5]] => 0111001 => 0
{{1,7},{2,8},{3,5,6},{4}} => {{1,7},{2,8},{3,4,6},{5}} => [[1,4,6],[2,7],[3,8],[5]] => 1101011 => 2
{{1,7},{2,5,6},{3,8},{4}} => {{1,6},{2,8},{3,4,7},{5}} => [[1,4,7],[2,6],[3,8],[5]] => 1101001 => 2
{{1,5},{2,6,7},{3,8},{4}} => {{1,6},{2,3,7},{4,8},{5}} => [[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,6,3,1 15,20,12,4,1 52,74,51,20,5,1 203,302,231,104,30,6,1
F2=1+q
F3=2+2 q+q2
F4=5+6 q+3 q2+q3
F5=15+20 q+12 q2+4 q3+q4
F6=52+74 q+51 q2+20 q3+5 q4+q5
F7=203+302 q+231 q2+104 q3+30 q4+6 q5+q6
Description
The number of leading ones in a binary word.
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complement
Description
The complement of a set partition obtained by replacing i with n+1−i.
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descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
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Standard tableau associated to a set partition
Description
Sends a set partition to the associated standard tableau.
The jth column of the standard tableau associated to a set partition is the set of jth smallest elements of its blocks arranged in increassing order.
The jth column of the standard tableau associated to a set partition is the set of jth smallest elements of its blocks arranged in increassing order.
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