Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0007;cc-rep-0
[[1]]=>[1]=>[1]=>[1]=>
[[1,2]]=>[1,2]=>[2,1]=>[2,1]=>1
[[1],[2]]=>[2,1]=>[1,2]=>[1,2]=>0
[[1,2,3]]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>11
[[1,3],[2]]=>[2,1,3]=>[3,1,2]=>[2,3,1]=>01
[[1,2],[3]]=>[3,1,2]=>[2,1,3]=>[2,1,3]=>10
[[1],[2],[3]]=>[3,2,1]=>[1,2,3]=>[1,2,3]=>00
[[1,2,3,4]]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>111
[[1,3,4],[2]]=>[2,1,3,4]=>[4,3,1,2]=>[3,4,2,1]=>011
[[1,2,4],[3]]=>[3,1,2,4]=>[4,2,1,3]=>[3,2,4,1]=>101
[[1,2,3],[4]]=>[4,1,2,3]=>[3,2,1,4]=>[3,2,1,4]=>110
[[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>[2,4,1,3]=>010
[[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]=>101
[[1,4],[2],[3]]=>[3,2,1,4]=>[4,1,2,3]=>[2,3,4,1]=>001
[[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,2,4]=>[2,3,1,4]=>010
[[1,2],[3],[4]]=>[4,3,1,2]=>[2,1,3,4]=>[2,1,3,4]=>100
[[1],[2],[3],[4]]=>[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]=>000
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[4,5,3,2,1]=>0111
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[4,3,5,2,1]=>1011
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[4,3,2,5,1]=>1101
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[5,3,1,4,2]=>[3,5,2,4,1]=>0101
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[3,2,5,4,1]=>1011
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[4,3,1,5,2]=>[3,5,2,1,4]=>0110
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[4,2,1,5,3]=>[3,2,5,1,4]=>1010
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[3,2,1,5,4]=>1101
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[3,4,5,2,1]=>0011
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[3,4,2,5,1]=>0101
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[3,2,4,5,1]=>1001
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[3,4,2,1,5]=>0110
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[3,2,4,1,5]=>1010
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,1,5,2,3]=>[2,4,5,1,3]=>0010
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,1,5,2,4]=>[2,4,1,5,3]=>0101
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[2,1,4,5,3]=>1001
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,1,4,2,5]=>[2,4,1,3,5]=>0100
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[2,1,4,3,5]=>1010
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[2,3,4,5,1]=>0001
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[2,3,4,1,5]=>0010
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[2,3,1,4,5]=>0100
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>01111
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>10111
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>11011
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>11101
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>[4,6,3,5,2,1]=>01011
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[4,3,6,5,2,1]=>10111
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>[4,6,3,2,5,1]=>01101
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>[4,3,6,2,5,1]=>10101
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[4,3,2,6,5,1]=>11011
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>[4,6,3,2,1,5]=>01110
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>[4,3,6,2,1,5]=>10110
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>[4,3,2,6,1,5]=>11010
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>11101
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>00111
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>01011
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>10011
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>01101
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>10101
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>11001
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>01110
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>10110
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>11010
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[3,6,2,5,1,4]=>01010
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[3,2,6,5,1,4]=>10110
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[3,6,2,1,5,4]=>01101
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[3,2,6,1,5,4]=>10101
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>11011
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>[3,5,6,2,4,1]=>00101
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>[3,5,2,6,4,1]=>01011
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[3,2,5,6,4,1]=>10011
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>[3,5,2,4,6,1]=>01001
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[3,2,5,4,6,1]=>10101
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>[3,5,6,2,1,4]=>00110
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>[3,5,2,6,1,4]=>01010
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>[3,2,5,6,1,4]=>10010
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>[3,5,2,1,6,4]=>01101
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>[3,2,5,1,6,4]=>10101
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[3,2,1,5,6,4]=>11001
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>[3,5,2,4,1,6]=>01010
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[3,2,5,4,1,6]=>10110
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>[3,5,2,1,4,6]=>01100
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>[3,2,5,1,4,6]=>10100
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>11010
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>00011
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>00101
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>01001
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>10001
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>00110
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>01010
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>10010
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>01100
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>10100
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[2,4,6,1,3,5]=>00100
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[2,4,1,6,3,5]=>01010
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>[2,1,4,6,3,5]=>10010
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>[2,4,1,3,6,5]=>01001
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>[2,4,5,6,1,3]=>00010
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>[2,4,5,1,6,3]=>00101
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>[2,4,1,5,6,3]=>01001
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>10001
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>[2,4,5,1,3,6]=>00100
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>[2,4,1,5,3,6]=>01010
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>10010
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>[2,4,1,3,5,6]=>01000
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>00001
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>00010
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>00100
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>01000
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>011111
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>101111
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>110111
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>111011
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>111101
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2]=>[5,7,4,6,3,2,1]=>010111
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[5,4,7,6,3,2,1]=>101111
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2]=>[5,7,4,3,6,2,1]=>011011
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3]=>[5,4,7,3,6,2,1]=>101011
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[5,4,3,7,6,2,1]=>110111
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[7,5,4,3,1,6,2]=>[5,7,4,3,2,6,1]=>011101
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3]=>[5,4,7,3,2,6,1]=>101101
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>[5,4,3,7,2,6,1]=>110101
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[5,4,3,2,7,6,1]=>111011
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>[5,7,4,3,2,1,6]=>011110
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>[5,4,7,3,2,1,6]=>101110
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>[5,4,3,7,2,1,6]=>110110
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>[5,4,3,2,7,1,6]=>111010
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>111101
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>001111
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>010111
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>100111
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>011011
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>101011
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>110011
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>011101
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>101101
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>110101
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>111001
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>011110
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>101110
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>110110
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>111010
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2]=>[4,7,3,6,2,5,1]=>010101
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[7,5,2,1,6,4,3]=>[4,3,7,6,2,5,1]=>101101
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2]=>[4,7,3,2,6,5,1]=>011011
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3]=>[4,3,7,2,6,5,1]=>101011
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[4,3,2,7,6,5,1]=>110111
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>[4,7,3,6,2,1,5]=>010110
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>[4,3,7,6,2,1,5]=>101110
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[6,4,3,1,7,5,2]=>[4,7,3,2,6,1,5]=>011010
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3]=>[4,3,7,2,6,1,5]=>101010
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>[4,3,2,7,6,1,5]=>110110
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2]=>[4,7,3,2,1,6,5]=>011101
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3]=>[4,3,7,2,1,6,5]=>101101
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>[4,3,2,7,1,6,5]=>110101
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>111011
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[7,6,4,1,5,2,3]=>[4,6,7,3,5,2,1]=>001011
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4]=>[4,6,3,7,5,2,1]=>010111
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[4,3,6,7,5,2,1]=>100111
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5]=>[4,6,3,5,7,2,1]=>010011
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[4,3,6,5,7,2,1]=>101011
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3]=>[4,6,7,3,2,5,1]=>001101
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4]=>[4,6,3,7,2,5,1]=>010101
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[7,5,2,1,6,3,4]=>[4,3,6,7,2,5,1]=>100101
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[7,4,3,1,6,2,5]=>[4,6,3,2,7,5,1]=>011011
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[7,4,2,1,6,3,5]=>[4,3,6,2,7,5,1]=>101011
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[4,3,2,6,7,5,1]=>110011
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6]=>[4,6,3,5,2,7,1]=>010101
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[4,3,6,5,2,7,1]=>101101
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[7,4,3,1,5,2,6]=>[4,6,3,2,5,7,1]=>011001
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[7,4,2,1,5,3,6]=>[4,3,6,2,5,7,1]=>101001
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[4,3,2,6,5,7,1]=>110101
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3]=>[4,6,7,3,2,1,5]=>001110
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4]=>[4,6,3,7,2,1,5]=>010110
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[6,5,2,1,7,3,4]=>[4,3,6,7,2,1,5]=>100110
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5]=>[4,6,3,2,7,1,5]=>011010
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5]=>[4,3,6,2,7,1,5]=>101010
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5]=>[4,3,2,6,7,1,5]=>110010
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6]=>[4,6,3,2,1,7,5]=>011101
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6]=>[4,3,6,2,1,7,5]=>101101
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6]=>[4,3,2,6,1,7,5]=>110101
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[4,3,2,1,6,7,5]=>111001
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>[4,6,3,5,2,1,7]=>010110
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[4,3,6,5,2,1,7]=>101110
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7]=>[4,6,3,2,5,1,7]=>011010
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7]=>[4,3,6,2,5,1,7]=>101010
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[4,3,2,6,5,1,7]=>110110
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7]=>[4,6,3,2,1,5,7]=>011100
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7]=>[4,3,6,2,1,5,7]=>101100
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7]=>[4,3,2,6,1,5,7]=>110100
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>111010
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>000111
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>001011
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>010011
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>100011
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>001101
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>010101
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>100101
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>011001
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>101001
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>110001
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>001110
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>010110
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>100110
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>011010
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>101010
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>110010
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>011100
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>101100
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>110100
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[6,4,1,7,5,2,3]=>[3,6,7,2,5,1,4]=>001010
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4]=>[3,6,2,7,5,1,4]=>010110
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[6,2,1,7,5,3,4]=>[3,2,6,7,5,1,4]=>100110
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5]=>[3,6,2,5,7,1,4]=>010010
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[6,2,1,7,4,3,5]=>[3,2,6,5,7,1,4]=>101010
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[5,4,1,7,6,2,3]=>[3,6,7,2,1,5,4]=>001101
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[5,3,1,7,6,2,4]=>[3,6,2,7,1,5,4]=>010101
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4]=>[3,2,6,7,1,5,4]=>100101
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5]=>[3,6,2,1,7,5,4]=>011011
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[4,2,1,7,6,3,5]=>[3,2,6,1,7,5,4]=>101011
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[3,2,1,6,7,5,4]=>110011
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[5,3,1,7,4,2,6]=>[3,6,2,5,1,7,4]=>010101
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[5,2,1,7,4,3,6]=>[3,2,6,5,1,7,4]=>101101
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6]=>[3,6,2,1,5,7,4]=>011001
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6]=>[3,2,6,1,5,7,4]=>101001
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[3,2,1,6,5,7,4]=>110101
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7]=>[3,6,2,5,1,4,7]=>010100
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7]=>[3,2,6,5,1,4,7]=>101100
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7]=>[3,6,2,1,5,4,7]=>011010
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7]=>[3,2,6,1,5,4,7]=>101010
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>110110
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3]=>[3,5,7,2,4,6,1]=>001001
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4]=>[3,5,2,7,4,6,1]=>010101
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4]=>[3,2,5,7,4,6,1]=>100101
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5]=>[3,5,2,4,7,6,1]=>010011
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[3,2,5,4,7,6,1]=>101011
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3]=>[3,5,7,2,4,1,6]=>001010
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4]=>[3,5,2,7,4,1,6]=>010110
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4]=>[3,2,5,7,4,1,6]=>100110
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5]=>[3,5,2,4,7,1,6]=>010010
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5]=>[3,2,5,4,7,1,6]=>101010
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3]=>[3,5,7,2,1,4,6]=>001100
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4]=>[3,5,2,7,1,4,6]=>010100
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4]=>[3,2,5,7,1,4,6]=>100100
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5]=>[3,5,2,1,7,4,6]=>011010
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5]=>[3,2,5,1,7,4,6]=>101010
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5]=>[3,2,1,5,7,4,6]=>110010
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6]=>[3,5,2,4,1,7,6]=>010101
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[3,2,5,4,1,7,6]=>101101
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6]=>[3,5,2,1,4,7,6]=>011001
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6]=>[3,2,5,1,4,7,6]=>101001
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[7,5,1,6,2,3,4]=>[3,5,6,7,2,4,1]=>000101
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5]=>[3,5,6,2,7,4,1]=>001011
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[7,3,1,6,2,4,5]=>[3,5,2,6,7,4,1]=>010011
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[3,2,5,6,7,4,1]=>100011
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6]=>[3,5,6,2,4,7,1]=>001001
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6]=>[3,5,2,6,4,7,1]=>010101
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[3,2,5,6,4,7,1]=>100101
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[7,3,1,4,2,5,6]=>[3,5,2,4,6,7,1]=>010001
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[3,2,5,4,6,7,1]=>101001
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[6,5,1,7,2,3,4]=>[3,5,6,7,2,1,4]=>000110
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5]=>[3,5,6,2,7,1,4]=>001010
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[6,3,1,7,2,4,5]=>[3,5,2,6,7,1,4]=>010010
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,2,1,7,3,4,5]=>[3,2,5,6,7,1,4]=>100010
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[5,4,1,7,2,3,6]=>[3,5,6,2,1,7,4]=>001101
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6]=>[3,5,2,6,1,7,4]=>010101
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6]=>[3,2,5,6,1,7,4]=>100101
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[4,3,1,7,2,5,6]=>[3,5,2,1,6,7,4]=>011001
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6]=>[3,2,5,1,6,7,4]=>101001
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>110001
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7]=>[3,5,6,2,4,1,7]=>001010
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[6,3,1,5,2,4,7]=>[3,5,2,6,4,1,7]=>010110
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[3,2,5,6,4,1,7]=>100110
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[6,3,1,4,2,5,7]=>[3,5,2,4,6,1,7]=>010010
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[3,2,5,4,6,1,7]=>101010
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7]=>[3,5,6,2,1,4,7]=>001100
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7]=>[3,5,2,6,1,4,7]=>010100
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7]=>[3,2,5,6,1,4,7]=>100100
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7]=>[3,5,2,1,6,4,7]=>011010
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7]=>[3,2,5,1,6,4,7]=>101010
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>110010
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7]=>[3,5,2,4,1,6,7]=>010100
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[3,2,5,4,1,6,7]=>101100
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7]=>[3,5,2,1,4,6,7]=>011000
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7]=>[3,2,5,1,4,6,7]=>101000
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>000011
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>000101
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>001001
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>010001
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>100001
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>000110
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>001010
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>010010
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>100010
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>001100
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>010100
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>100100
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>011000
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>101000
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4]=>[2,4,6,7,1,3,5]=>000100
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5]=>[2,4,6,1,7,3,5]=>001010
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5]=>[2,4,1,6,7,3,5]=>010010
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5]=>[2,1,4,6,7,3,5]=>100010
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6]=>[2,4,6,1,3,7,5]=>001001
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6]=>[2,4,1,6,3,7,5]=>010101
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6]=>[2,1,4,6,3,7,5]=>100101
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6]=>[2,4,1,3,6,7,5]=>010001
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>101001
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7]=>[2,4,6,1,3,5,7]=>001000
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7]=>[2,4,1,6,3,5,7]=>010100
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7]=>[2,1,4,6,3,5,7]=>100100
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7]=>[2,4,1,3,6,5,7]=>010010
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5]=>[2,4,5,6,7,1,3]=>000010
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6]=>[2,4,5,6,1,7,3]=>000101
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6]=>[2,4,5,1,6,7,3]=>001001
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6]=>[2,4,1,5,6,7,3]=>010001
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>100001
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7]=>[2,4,5,6,1,3,7]=>000100
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7]=>[2,4,5,1,6,3,7]=>001010
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7]=>[2,4,1,5,6,3,7]=>010010
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>100010
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7]=>[2,4,5,1,3,6,7]=>001000
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7]=>[2,4,1,5,3,6,7]=>010100
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>100100
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>010000
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>000001
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>000010
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>000100
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>001000
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>0111111
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>1011111
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>1101111
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>1110111
[[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>1111011
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>1111101
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[8,7,6,5,3,1,4,2]=>[6,8,5,7,4,3,2,1]=>0101111
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[6,5,8,7,4,3,2,1]=>1011111
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[8,7,6,4,3,1,5,2]=>[6,8,5,4,7,3,2,1]=>0110111
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[8,7,6,4,2,1,5,3]=>[6,5,8,4,7,3,2,1]=>1010111
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>[6,5,4,8,7,3,2,1]=>1101111
[[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[8,7,5,4,3,1,6,2]=>[6,8,5,4,3,7,2,1]=>0111011
[[1,2,4,5,7,8],[3,6]]=>[3,6,1,2,4,5,7,8]=>[8,7,5,4,2,1,6,3]=>[6,5,8,4,3,7,2,1]=>1011011
[[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[8,7,5,3,2,1,6,4]=>[6,5,4,8,3,7,2,1]=>1101011
[[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>[6,5,4,3,8,7,2,1]=>1110111
[[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[8,6,5,4,3,1,7,2]=>[6,8,5,4,3,2,7,1]=>0111101
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[8,6,5,4,2,1,7,3]=>[6,5,8,4,3,2,7,1]=>1011101
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[8,6,5,3,2,1,7,4]=>[6,5,4,8,3,2,7,1]=>1101101
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[8,6,4,3,2,1,7,5]=>[6,5,4,3,8,2,7,1]=>1110101
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[6,5,4,3,2,8,7,1]=>1111011
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[7,6,5,4,3,1,8,2]=>[6,8,5,4,3,2,1,7]=>0111110
[[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[7,6,5,4,2,1,8,3]=>[6,5,8,4,3,2,1,7]=>1011110
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[7,6,5,3,2,1,8,4]=>[6,5,4,8,3,2,1,7]=>1101110
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[7,6,4,3,2,1,8,5]=>[6,5,4,3,8,2,1,7]=>1110110
[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6]=>[6,5,4,3,2,8,1,7]=>1111010
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>1111101
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>0011111
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>0101111
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>1001111
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>0110111
[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>1010111
[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>1100111
[[1,3,4,5,7,8],[2],[6]]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>0111011
[[1,2,4,5,7,8],[3],[6]]=>[6,3,1,2,4,5,7,8]=>[8,7,5,4,2,1,3,6]=>[6,5,7,4,3,8,2,1]=>1011011
[[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>1101011
[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>1110011
[[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>0111101
[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>1011101
[[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>1101101
[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>1110101
[[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>1111001
[[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>0111110
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>1011110
[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>1101110
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>1110110
[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>1111010
[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[8,7,5,3,1,6,4,2]=>[5,8,4,7,3,6,2,1]=>0101011
[[1,2,5,7,8],[3,4,6]]=>[3,4,6,1,2,5,7,8]=>[8,7,5,2,1,6,4,3]=>[5,4,8,7,3,6,2,1]=>1011011
[[1,3,4,7,8],[2,5,6]]=>[2,5,6,1,3,4,7,8]=>[8,7,4,3,1,6,5,2]=>[5,8,4,3,7,6,2,1]=>0110111
[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[5,4,3,8,7,6,2,1]=>1101111
[[1,3,5,6,8],[2,4,7]]=>[2,4,7,1,3,5,6,8]=>[8,6,5,3,1,7,4,2]=>[5,8,4,7,3,2,6,1]=>0101101
[[1,2,5,6,8],[3,4,7]]=>[3,4,7,1,2,5,6,8]=>[8,6,5,2,1,7,4,3]=>[5,4,8,7,3,2,6,1]=>1011101
[[1,3,4,6,8],[2,5,7]]=>[2,5,7,1,3,4,6,8]=>[8,6,4,3,1,7,5,2]=>[5,8,4,3,7,2,6,1]=>0110101
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[8,6,4,2,1,7,5,3]=>[5,4,8,3,7,2,6,1]=>1010101
[[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[8,5,4,3,1,7,6,2]=>[5,8,4,3,2,7,6,1]=>0111011
[[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>[8,5,4,2,1,7,6,3]=>[5,4,8,3,2,7,6,1]=>1011011
[[1,2,3,5,8],[4,6,7]]=>[4,6,7,1,2,3,5,8]=>[8,5,3,2,1,7,6,4]=>[5,4,3,8,2,7,6,1]=>1101011
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[5,4,3,2,8,7,6,1]=>1110111
[[1,3,5,6,7],[2,4,8]]=>[2,4,8,1,3,5,6,7]=>[7,6,5,3,1,8,4,2]=>[5,8,4,7,3,2,1,6]=>0101110
[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[7,6,5,2,1,8,4,3]=>[5,4,8,7,3,2,1,6]=>1011110
[[1,3,4,6,7],[2,5,8]]=>[2,5,8,1,3,4,6,7]=>[7,6,4,3,1,8,5,2]=>[5,8,4,3,7,2,1,6]=>0110110
[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[7,6,4,2,1,8,5,3]=>[5,4,8,3,7,2,1,6]=>1010110
[[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[7,5,4,3,1,8,6,2]=>[5,8,4,3,2,7,1,6]=>0111010
[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[7,5,4,2,1,8,6,3]=>[5,4,8,3,2,7,1,6]=>1011010
[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4]=>[5,4,3,8,2,7,1,6]=>1101010
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[7,4,3,2,1,8,6,5]=>[5,4,3,2,8,7,1,6]=>1110110
[[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[6,5,4,3,1,8,7,2]=>[5,8,4,3,2,1,7,6]=>0111101
[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[6,5,4,2,1,8,7,3]=>[5,4,8,3,2,1,7,6]=>1011101
[[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[6,5,3,2,1,8,7,4]=>[5,4,3,8,2,1,7,6]=>1101101
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[6,4,3,2,1,8,7,5]=>[5,4,3,2,8,1,7,6]=>1110101
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>1111011
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[8,7,6,4,1,5,2,3]=>[5,7,8,4,6,3,2,1]=>0010111
[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[8,7,6,3,1,5,2,4]=>[5,7,4,8,6,3,2,1]=>0101111
[[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[8,7,6,2,1,5,3,4]=>[5,4,7,8,6,3,2,1]=>1001111
[[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[8,7,6,3,1,4,2,5]=>[5,7,4,6,8,3,2,1]=>0100111
[[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>[5,4,7,6,8,3,2,1]=>1010111
[[1,4,5,7,8],[2,6],[3]]=>[3,2,6,1,4,5,7,8]=>[8,7,5,4,1,6,2,3]=>[5,7,8,4,3,6,2,1]=>0011011
[[1,3,5,7,8],[2,6],[4]]=>[4,2,6,1,3,5,7,8]=>[8,7,5,3,1,6,2,4]=>[5,7,4,8,3,6,2,1]=>0101011
[[1,2,5,7,8],[3,6],[4]]=>[4,3,6,1,2,5,7,8]=>[8,7,5,2,1,6,3,4]=>[5,4,7,8,3,6,2,1]=>1001011
[[1,3,4,7,8],[2,6],[5]]=>[5,2,6,1,3,4,7,8]=>[8,7,4,3,1,6,2,5]=>[5,7,4,3,8,6,2,1]=>0110111
[[1,2,3,7,8],[4,6],[5]]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>[5,4,3,7,8,6,2,1]=>1100111
[[1,3,5,7,8],[2,4],[6]]=>[6,2,4,1,3,5,7,8]=>[8,7,5,3,1,4,2,6]=>[5,7,4,6,3,8,2,1]=>0101011
[[1,2,5,7,8],[3,4],[6]]=>[6,3,4,1,2,5,7,8]=>[8,7,5,2,1,4,3,6]=>[5,4,7,6,3,8,2,1]=>1011011
[[1,3,4,7,8],[2,5],[6]]=>[6,2,5,1,3,4,7,8]=>[8,7,4,3,1,5,2,6]=>[5,7,4,3,6,8,2,1]=>0110011
[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[8,7,4,2,1,5,3,6]=>[5,4,7,3,6,8,2,1]=>1010011
[[1,4,5,6,8],[2,7],[3]]=>[3,2,7,1,4,5,6,8]=>[8,6,5,4,1,7,2,3]=>[5,7,8,4,3,2,6,1]=>0011101
[[1,2,5,6,8],[3,7],[4]]=>[4,3,7,1,2,5,6,8]=>[8,6,5,2,1,7,3,4]=>[5,4,7,8,3,2,6,1]=>1001101
[[1,3,4,6,8],[2,7],[5]]=>[5,2,7,1,3,4,6,8]=>[8,6,4,3,1,7,2,5]=>[5,7,4,3,8,2,6,1]=>0110101
[[1,2,4,6,8],[3,7],[5]]=>[5,3,7,1,2,4,6,8]=>[8,6,4,2,1,7,3,5]=>[5,4,7,3,8,2,6,1]=>1010101
[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[8,6,3,2,1,7,4,5]=>[5,4,3,7,8,2,6,1]=>1100101
[[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[8,5,4,3,1,7,2,6]=>[5,7,4,3,2,8,6,1]=>0111011
[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[8,5,4,2,1,7,3,6]=>[5,4,7,3,2,8,6,1]=>1011011
[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[8,5,3,2,1,7,4,6]=>[5,4,3,7,2,8,6,1]=>1101011
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>[5,4,3,2,7,8,6,1]=>1110011
[[1,3,4,6,8],[2,5],[7]]=>[7,2,5,1,3,4,6,8]=>[8,6,4,3,1,5,2,7]=>[5,7,4,3,6,2,8,1]=>0110101
[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[8,6,4,2,1,5,3,7]=>[5,4,7,3,6,2,8,1]=>1010101
[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>[5,4,3,7,6,2,8,1]=>1101101
[[1,2,4,5,8],[3,6],[7]]=>[7,3,6,1,2,4,5,8]=>[8,5,4,2,1,6,3,7]=>[5,4,7,3,2,6,8,1]=>1011001
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>[5,4,3,2,7,6,8,1]=>1110101
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[7,6,5,4,1,8,2,3]=>[5,7,8,4,3,2,1,6]=>0011110
[[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[7,6,5,3,1,8,2,4]=>[5,7,4,8,3,2,1,6]=>0101110
[[1,2,5,6,7],[3,8],[4]]=>[4,3,8,1,2,5,6,7]=>[7,6,5,2,1,8,3,4]=>[5,4,7,8,3,2,1,6]=>1001110
[[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[7,6,4,3,1,8,2,5]=>[5,7,4,3,8,2,1,6]=>0110110
[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[7,6,4,2,1,8,3,5]=>[5,4,7,3,8,2,1,6]=>1010110
[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[7,6,3,2,1,8,4,5]=>[5,4,3,7,8,2,1,6]=>1100110
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[7,5,4,3,1,8,2,6]=>[5,7,4,3,2,8,1,6]=>0111010
[[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[7,5,4,2,1,8,3,6]=>[5,4,7,3,2,8,1,6]=>1011010
[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[7,5,3,2,1,8,4,6]=>[5,4,3,7,2,8,1,6]=>1101010
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,6]=>[5,4,3,2,7,8,1,6]=>1110010
[[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[6,5,4,3,1,8,2,7]=>[5,7,4,3,2,1,8,6]=>0111101
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[6,4,3,2,1,8,5,7]=>[5,4,3,2,7,1,8,6]=>1110101
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>[5,4,3,2,1,7,8,6]=>1111001
[[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2,8]=>[5,7,4,6,3,2,1,8]=>0101110
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>[5,4,7,6,3,2,1,8]=>1011110
[[1,3,4,6,7],[2,5],[8]]=>[8,2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2,8]=>[5,7,4,3,6,2,1,8]=>0110110
[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3,8]=>[5,4,7,3,6,2,1,8]=>1010110
[[1,2,3,6,7],[4,5],[8]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>[5,4,3,7,6,2,1,8]=>1101110
[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4,8]=>[5,4,3,7,2,6,1,8]=>1101010
[[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>[5,4,3,2,7,6,1,8]=>1110110
[[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3,8]=>[5,4,7,3,2,1,6,8]=>1011100
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8]=>[5,4,3,2,7,1,6,8]=>1110100
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>1111010
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>0001111
[[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>0010111
[[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>0100111
[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>1000111
[[1,4,5,7,8],[2],[3],[6]]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>0011011
[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>1001011
[[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>1100011
[[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>0011101
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>1010101
[[1,2,3,6,8],[4],[5],[7]]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>1100101
[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>1011001
[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>1101001
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>1110001
[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>0011110
[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4,8]=>[5,6,4,7,3,2,1,8]=>0101110
[[1,2,5,6,7],[3],[4],[8]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>1001110
[[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>0110110
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>1010110
[[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>1100110
[[1,2,4,5,7],[3],[6],[8]]=>[8,6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6,8]=>[5,4,6,3,2,7,1,8]=>1011010
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>1101010
[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>1110010
[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>0111100
[[1,2,4,5,6],[3],[7],[8]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>1011100
[[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>1101100
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>1110100
[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>0101010
[[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[7,5,2,1,8,6,4,3]=>[4,3,8,7,2,6,1,5]=>1011010
[[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>[4,8,3,2,7,6,1,5]=>0110110
[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>[4,3,8,2,7,6,1,5]=>1010110
[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[7,3,2,1,8,6,5,4]=>[4,3,2,8,7,6,1,5]=>1101110
[[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>[4,8,3,7,2,1,6,5]=>0101101
[[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>[4,3,8,7,2,1,6,5]=>1011101
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>[4,3,8,2,7,1,6,5]=>1010101
[[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[6,3,2,1,8,7,5,4]=>[4,3,2,8,7,1,6,5]=>1101101
[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[5,4,3,1,8,7,6,2]=>[4,8,3,2,1,7,6,5]=>0111011
[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>[4,3,2,8,1,7,6,5]=>1101011
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>1110111
[[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[8,6,4,1,7,5,2,3]=>[4,7,8,3,6,2,5,1]=>0010101
[[1,3,6,8],[2,5,7],[4]]=>[4,2,5,7,1,3,6,8]=>[8,6,3,1,7,5,2,4]=>[4,7,3,8,6,2,5,1]=>0101101
[[1,2,6,8],[3,5,7],[4]]=>[4,3,5,7,1,2,6,8]=>[8,6,2,1,7,5,3,4]=>[4,3,7,8,6,2,5,1]=>1001101
[[1,3,6,8],[2,4,7],[5]]=>[5,2,4,7,1,3,6,8]=>[8,6,3,1,7,4,2,5]=>[4,7,3,6,8,2,5,1]=>0100101
[[1,2,6,8],[3,4,7],[5]]=>[5,3,4,7,1,2,6,8]=>[8,6,2,1,7,4,3,5]=>[4,3,7,6,8,2,5,1]=>1010101
[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[8,5,3,1,7,6,2,4]=>[4,7,3,8,2,6,5,1]=>0101011
[[1,2,5,8],[3,6,7],[4]]=>[4,3,6,7,1,2,5,8]=>[8,5,2,1,7,6,3,4]=>[4,3,7,8,2,6,5,1]=>1001011
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[8,4,3,1,7,6,2,5]=>[4,7,3,2,8,6,5,1]=>0110111
[[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[8,4,2,1,7,6,3,5]=>[4,3,7,2,8,6,5,1]=>1010111
[[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>[4,3,2,7,8,6,5,1]=>1100111
[[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[8,4,3,1,7,5,2,6]=>[4,7,3,2,6,8,5,1]=>0110011
[[1,2,4,8],[3,5,7],[6]]=>[6,3,5,7,1,2,4,8]=>[8,4,2,1,7,5,3,6]=>[4,3,7,2,6,8,5,1]=>1010011
[[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[8,5,3,1,6,4,2,7]=>[4,7,3,6,2,5,8,1]=>0101001
[[1,2,4,8],[3,5,6],[7]]=>[7,3,5,6,1,2,4,8]=>[8,4,2,1,6,5,3,7]=>[4,3,7,2,6,5,8,1]=>1010101
[[1,2,3,8],[4,5,6],[7]]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>[4,3,2,7,6,5,8,1]=>1101101
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[7,6,3,1,8,5,2,4]=>[4,7,3,8,6,2,1,5]=>0101110
[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[7,6,3,1,8,4,2,5]=>[4,7,3,6,8,2,1,5]=>0100110
[[1,2,6,7],[3,4,8],[5]]=>[5,3,4,8,1,2,6,7]=>[7,6,2,1,8,4,3,5]=>[4,3,7,6,8,2,1,5]=>1010110
[[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[7,5,3,1,8,6,2,4]=>[4,7,3,8,2,6,1,5]=>0101010
[[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[7,5,2,1,8,6,3,4]=>[4,3,7,8,2,6,1,5]=>1001010
[[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[7,4,3,1,8,6,2,5]=>[4,7,3,2,8,6,1,5]=>0110110
[[1,2,4,7],[3,6,8],[5]]=>[5,3,6,8,1,2,4,7]=>[7,4,2,1,8,6,3,5]=>[4,3,7,2,8,6,1,5]=>1010110
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[7,5,3,1,8,4,2,6]=>[4,7,3,6,2,8,1,5]=>0101010
[[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[7,4,3,1,8,5,2,6]=>[4,7,3,2,6,8,1,5]=>0110010
[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,6]=>[4,3,7,2,6,8,1,5]=>1010010
[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[6,5,4,1,8,7,2,3]=>[4,7,8,3,2,1,6,5]=>0011101
[[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>[6,5,2,1,8,7,3,4]=>[4,3,7,8,2,1,6,5]=>1001101
[[1,3,4,6],[2,7,8],[5]]=>[5,2,7,8,1,3,4,6]=>[6,4,3,1,8,7,2,5]=>[4,7,3,2,8,1,6,5]=>0110101
[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[6,3,2,1,8,7,4,5]=>[4,3,2,7,8,1,6,5]=>1100101
[[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[5,4,3,1,8,7,2,6]=>[4,7,3,2,1,8,6,5]=>0111011
[[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[5,4,2,1,8,7,3,6]=>[4,3,7,2,1,8,6,5]=>1011011
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>[4,3,2,1,7,8,6,5]=>1110011
[[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[6,5,3,1,8,4,2,7]=>[4,7,3,6,2,1,8,5]=>0101101
[[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[6,5,2,1,8,4,3,7]=>[4,3,7,6,2,1,8,5]=>1011101
[[1,2,3,5],[4,6,8],[7]]=>[7,4,6,8,1,2,3,5]=>[5,3,2,1,8,6,4,7]=>[4,3,2,7,1,6,8,5]=>1101001
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>[4,3,2,1,7,6,8,5]=>1110101
[[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>0101010
[[1,3,4,7],[2,5,6],[8]]=>[8,2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2,8]=>[4,7,3,2,6,5,1,8]=>0110110
[[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3,8]=>[4,3,7,2,6,5,1,8]=>1010110
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>1010100
[[1,2,3,6],[4,5,7],[8]]=>[8,4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4,8]=>[4,3,2,7,6,1,5,8]=>1101100
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2,8]=>[4,7,3,2,1,6,5,8]=>0111010
[[1,2,4,5],[3,6,7],[8]]=>[8,3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3,8]=>[4,3,7,2,1,6,5,8]=>1011010
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>1110110
[[1,4,7,8],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8]=>[8,7,4,1,5,2,6,3]=>[4,6,8,3,5,7,2,1]=>0010011
[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[8,7,3,1,5,2,6,4]=>[4,6,3,8,5,7,2,1]=>0101011
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[8,7,2,1,5,3,6,4]=>[4,3,6,8,5,7,2,1]=>1001011
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>[4,3,6,5,8,7,2,1]=>1010111
[[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[8,6,4,1,5,2,7,3]=>[4,6,8,3,5,2,7,1]=>0010101
[[1,3,6,8],[2,5],[4,7]]=>[4,7,2,5,1,3,6,8]=>[8,6,3,1,5,2,7,4]=>[4,6,3,8,5,2,7,1]=>0101101
[[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[8,6,2,1,5,3,7,4]=>[4,3,6,8,5,2,7,1]=>1001101
[[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[8,6,3,1,4,2,7,5]=>[4,6,3,5,8,2,7,1]=>0100101
[[1,2,6,8],[3,4],[5,7]]=>[5,7,3,4,1,2,6,8]=>[8,6,2,1,4,3,7,5]=>[4,3,6,5,8,2,7,1]=>1010101
[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[8,5,4,1,6,2,7,3]=>[4,6,8,3,2,5,7,1]=>0011001
[[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[8,4,3,1,6,2,7,5]=>[4,6,3,2,8,5,7,1]=>0110101
[[1,2,3,8],[4,6],[5,7]]=>[5,7,4,6,1,2,3,8]=>[8,3,2,1,6,4,7,5]=>[4,3,2,6,8,5,7,1]=>1100101
[[1,3,5,8],[2,4],[6,7]]=>[6,7,2,4,1,3,5,8]=>[8,5,3,1,4,2,7,6]=>[4,6,3,5,2,8,7,1]=>0101011
[[1,2,5,8],[3,4],[6,7]]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>[4,3,6,5,2,8,7,1]=>1011011
[[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>[8,4,3,1,5,2,7,6]=>[4,6,3,2,5,8,7,1]=>0110011
[[1,2,3,8],[4,5],[6,7]]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>[4,3,2,6,5,8,7,1]=>1101011
[[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[7,6,3,1,5,2,8,4]=>[4,6,3,8,5,2,1,7]=>0101110
[[1,2,6,7],[3,5],[4,8]]=>[4,8,3,5,1,2,6,7]=>[7,6,2,1,5,3,8,4]=>[4,3,6,8,5,2,1,7]=>1001110
[[1,3,6,7],[2,4],[5,8]]=>[5,8,2,4,1,3,6,7]=>[7,6,3,1,4,2,8,5]=>[4,6,3,5,8,2,1,7]=>0100110
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[7,6,2,1,4,3,8,5]=>[4,3,6,5,8,2,1,7]=>1010110
[[1,4,5,7],[2,6],[3,8]]=>[3,8,2,6,1,4,5,7]=>[7,5,4,1,6,2,8,3]=>[4,6,8,3,2,5,1,7]=>0011010
[[1,3,5,7],[2,6],[4,8]]=>[4,8,2,6,1,3,5,7]=>[7,5,3,1,6,2,8,4]=>[4,6,3,8,2,5,1,7]=>0101010
[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[7,4,2,1,6,3,8,5]=>[4,3,6,2,8,5,1,7]=>1010110
[[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[7,3,2,1,6,4,8,5]=>[4,3,2,6,8,5,1,7]=>1100110
[[1,3,5,7],[2,4],[6,8]]=>[6,8,2,4,1,3,5,7]=>[7,5,3,1,4,2,8,6]=>[4,6,3,5,2,8,1,7]=>0101010
[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[6,5,4,1,7,2,8,3]=>[4,6,8,3,2,1,5,7]=>0011100
[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[6,5,3,1,7,2,8,4]=>[4,6,3,8,2,1,5,7]=>0101100
[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[6,5,2,1,7,3,8,4]=>[4,3,6,8,2,1,5,7]=>1001100
[[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[6,4,3,1,7,2,8,5]=>[4,6,3,2,8,1,5,7]=>0110100
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[6,4,2,1,7,3,8,5]=>[4,3,6,2,8,1,5,7]=>1010100
[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5]=>[4,3,2,6,8,1,5,7]=>1100100
[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[5,4,3,1,7,2,8,6]=>[4,6,3,2,1,8,5,7]=>0111010
[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[5,4,2,1,7,3,8,6]=>[4,3,6,2,1,8,5,7]=>1011010
[[1,2,3,5],[4,7],[6,8]]=>[6,8,4,7,1,2,3,5]=>[5,3,2,1,7,4,8,6]=>[4,3,2,6,1,8,5,7]=>1101010
[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[4,3,2,1,7,5,8,6]=>[4,3,2,1,6,8,5,7]=>1110010
[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[6,5,3,1,4,2,8,7]=>[4,6,3,5,2,1,8,7]=>0101101
[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>[4,3,6,5,2,1,8,7]=>1011101
[[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[6,4,3,1,5,2,8,7]=>[4,6,3,2,5,1,8,7]=>0110101
[[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[6,4,2,1,5,3,8,7]=>[4,3,6,2,5,1,8,7]=>1010101
[[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>[4,3,2,6,5,1,8,7]=>1101101
[[1,3,4,5],[2,6],[7,8]]=>[7,8,2,6,1,3,4,5]=>[5,4,3,1,6,2,8,7]=>[4,6,3,2,1,5,8,7]=>0111001
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[5,3,2,1,6,4,8,7]=>[4,3,2,6,1,5,8,7]=>1101001
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[8,7,5,1,6,2,3,4]=>[4,6,7,8,3,5,2,1]=>0001011
[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[8,7,4,1,6,2,3,5]=>[4,6,7,3,8,5,2,1]=>0010111
[[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[8,7,3,1,6,2,4,5]=>[4,6,3,7,8,5,2,1]=>0100111
[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>[4,3,6,7,8,5,2,1]=>1000111
[[1,4,7,8],[2,5],[3],[6]]=>[6,3,2,5,1,4,7,8]=>[8,7,4,1,5,2,3,6]=>[4,6,7,3,5,8,2,1]=>0010011
[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[8,7,3,1,4,2,5,6]=>[4,6,3,5,7,8,2,1]=>0100011
[[1,2,7,8],[3,4],[5],[6]]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>[4,3,6,5,7,8,2,1]=>1010011
[[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[8,6,4,1,7,2,3,5]=>[4,6,7,3,8,2,5,1]=>0010101
[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[8,5,4,1,7,2,3,6]=>[4,6,7,3,2,8,5,1]=>0011011
[[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[8,5,3,1,7,2,4,6]=>[4,6,3,7,2,8,5,1]=>0101011
[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[8,5,2,1,7,3,4,6]=>[4,3,6,7,2,8,5,1]=>1001011
[[1,3,4,8],[2,7],[5],[6]]=>[6,5,2,7,1,3,4,8]=>[8,4,3,1,7,2,5,6]=>[4,6,3,2,7,8,5,1]=>0110011
[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[8,4,2,1,7,3,5,6]=>[4,3,6,2,7,8,5,1]=>1010011
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[8,6,3,1,5,2,4,7]=>[4,6,3,7,5,2,8,1]=>0101101
[[1,2,6,8],[3,5],[4],[7]]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>[4,3,6,7,5,2,8,1]=>1001101
[[1,3,6,8],[2,4],[5],[7]]=>[7,5,2,4,1,3,6,8]=>[8,6,3,1,4,2,5,7]=>[4,6,3,5,7,2,8,1]=>0100101
[[1,2,6,8],[3,4],[5],[7]]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>[4,3,6,5,7,2,8,1]=>1010101
[[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[8,5,4,1,6,2,3,7]=>[4,6,7,3,2,5,8,1]=>0011001
[[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[8,5,3,1,6,2,4,7]=>[4,6,3,7,2,5,8,1]=>0101001
[[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[8,4,2,1,6,3,5,7]=>[4,3,6,2,7,5,8,1]=>1010101
[[1,2,3,8],[4,6],[5],[7]]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>[4,3,2,6,7,5,8,1]=>1100101
[[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[8,4,2,1,5,3,6,7]=>[4,3,6,2,5,7,8,1]=>1010001
[[1,2,3,8],[4,5],[6],[7]]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>[4,3,2,6,5,7,8,1]=>1101001
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[7,6,5,1,8,2,3,4]=>[4,6,7,8,3,2,1,5]=>0001110
[[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[7,6,4,1,8,2,3,5]=>[4,6,7,3,8,2,1,5]=>0010110
[[1,3,6,7],[2,8],[4],[5]]=>[5,4,2,8,1,3,6,7]=>[7,6,3,1,8,2,4,5]=>[4,6,3,7,8,2,1,5]=>0100110
[[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[7,5,4,1,8,2,3,6]=>[4,6,7,3,2,8,1,5]=>0011010
[[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[7,5,3,1,8,2,4,6]=>[4,6,3,7,2,8,1,5]=>0101010
[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[7,5,2,1,8,3,4,6]=>[4,3,6,7,2,8,1,5]=>1001010
[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[7,4,2,1,8,3,5,6]=>[4,3,6,2,7,8,1,5]=>1010010
[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[7,3,2,1,8,4,5,6]=>[4,3,2,6,7,8,1,5]=>1100010
[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[6,5,3,1,8,2,4,7]=>[4,6,3,7,2,1,8,5]=>0101101
[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,5,2,1,8,3,4,7]=>[4,3,6,7,2,1,8,5]=>1001101
[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,4,2,1,8,3,5,7]=>[4,3,6,2,7,1,8,5]=>1010101
[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[6,3,2,1,8,4,5,7]=>[4,3,2,6,7,1,8,5]=>1100101
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>[4,3,2,1,6,7,8,5]=>1110001
[[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4,8]=>[4,6,3,7,5,2,1,8]=>0101110
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5,8]=>[4,3,6,5,7,2,1,8]=>1010110
[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4,8]=>[4,6,3,7,2,5,1,8]=>0101010
[[1,3,4,7],[2,6],[5],[8]]=>[8,5,2,6,1,3,4,7]=>[7,4,3,1,6,2,5,8]=>[4,6,3,2,7,5,1,8]=>0110110
[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[7,4,2,1,6,3,5,8]=>[4,3,6,2,7,5,1,8]=>1010110
[[1,2,3,7],[4,6],[5],[8]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>[4,3,2,6,7,5,1,8]=>1100110
[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6,8]=>[4,6,3,5,2,7,1,8]=>0101010
[[1,2,4,7],[3,5],[6],[8]]=>[8,6,3,5,1,2,4,7]=>[7,4,2,1,5,3,6,8]=>[4,3,6,2,5,7,1,8]=>1010010
[[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>[4,3,2,6,5,7,1,8]=>1101010
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4,8]=>[4,6,3,7,2,1,5,8]=>0101100
[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[6,5,2,1,7,3,4,8]=>[4,3,6,7,2,1,5,8]=>1001100
[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5,8]=>[4,3,2,6,7,1,5,8]=>1100100
[[1,3,4,5],[2,7],[6],[8]]=>[8,6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6,8]=>[4,6,3,2,1,7,5,8]=>0111010
[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6,8]=>[4,3,6,2,1,7,5,8]=>1011010
[[1,2,3,5],[4,7],[6],[8]]=>[8,6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6,8]=>[4,3,2,6,1,7,5,8]=>1101010
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>[4,3,2,1,6,7,5,8]=>1110010
[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7,8]=>[4,3,6,5,2,1,7,8]=>1011100
[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>0110100
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7,8]=>[4,3,6,2,5,1,7,8]=>1010100
[[1,2,3,6],[4,5],[7],[8]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>[4,3,2,6,5,1,7,8]=>1101100
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>1101000
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>0000111
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>0001011
[[1,4,7,8],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>0010011
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>1000011
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>0001101
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>0010101
[[1,3,6,8],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6,8]=>[8,6,3,1,2,4,5,7]=>[4,5,3,6,7,2,8,1]=>0100101
[[1,2,6,8],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6,8]=>[8,6,2,1,3,4,5,7]=>[4,3,5,6,7,2,8,1]=>1000101
[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>0011001
[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>1001001
[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[8,4,3,1,2,5,6,7]=>[4,5,3,2,6,7,8,1]=>0110001
[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>1010001
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>1100001
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>0001110
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>0101010
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6,8]=>[4,3,5,6,2,7,1,8]=>1001010
[[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>1100010
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>0011100
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>0110100
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>1010100
[[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>1100100
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>0111000
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>1011000
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>1101000
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[7,4,1,8,5,2,6,3]=>[3,6,8,2,5,7,1,4]=>0010010
[[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[7,3,1,8,5,2,6,4]=>[3,6,2,8,5,7,1,4]=>0101010
[[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[7,2,1,8,5,3,6,4]=>[3,2,6,8,5,7,1,4]=>1001010
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[7,3,1,8,4,2,6,5]=>[3,6,2,5,8,7,1,4]=>0100110
[[1,2,7],[3,4,8],[5,6]]=>[5,6,3,4,8,1,2,7]=>[7,2,1,8,4,3,6,5]=>[3,2,6,5,8,7,1,4]=>1010110
[[1,4,6],[2,5,8],[3,7]]=>[3,7,2,5,8,1,4,6]=>[6,4,1,8,5,2,7,3]=>[3,6,8,2,5,1,7,4]=>0010101
[[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[6,3,1,8,5,2,7,4]=>[3,6,2,8,5,1,7,4]=>0101101
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[6,2,1,8,5,3,7,4]=>[3,2,6,8,5,1,7,4]=>1001101
[[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[6,3,1,8,4,2,7,5]=>[3,6,2,5,8,1,7,4]=>0100101
[[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[6,2,1,8,4,3,7,5]=>[3,2,6,5,8,1,7,4]=>1010101
[[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[5,4,1,8,6,2,7,3]=>[3,6,8,2,1,5,7,4]=>0011001
[[1,3,5],[2,6,8],[4,7]]=>[4,7,2,6,8,1,3,5]=>[5,3,1,8,6,2,7,4]=>[3,6,2,8,1,5,7,4]=>0101001
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[5,2,1,8,6,3,7,4]=>[3,2,6,8,1,5,7,4]=>1001001
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[3,2,1,8,6,4,7,5]=>[3,2,1,6,8,5,7,4]=>1100101
[[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[5,2,1,8,4,3,7,6]=>[3,2,6,5,1,8,7,4]=>1011011
[[1,3,4],[2,5,8],[6,7]]=>[6,7,2,5,8,1,3,4]=>[4,3,1,8,5,2,7,6]=>[3,6,2,1,5,8,7,4]=>0110011
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[4,2,1,8,5,3,7,6]=>[3,2,6,1,5,8,7,4]=>1010011
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>[3,2,1,6,5,8,7,4]=>1101011
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[6,4,1,7,5,2,8,3]=>[3,6,8,2,5,1,4,7]=>0010100
[[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[6,3,1,7,5,2,8,4]=>[3,6,2,8,5,1,4,7]=>0101100
[[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[6,2,1,7,5,3,8,4]=>[3,2,6,8,5,1,4,7]=>1001100
[[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5]=>[3,6,2,5,8,1,4,7]=>0100100
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[5,4,1,7,6,2,8,3]=>[3,6,8,2,1,5,4,7]=>0011010
[[1,3,5],[2,6,7],[4,8]]=>[4,8,2,6,7,1,3,5]=>[5,3,1,7,6,2,8,4]=>[3,6,2,8,1,5,4,7]=>0101010
[[1,2,5],[3,6,7],[4,8]]=>[4,8,3,6,7,1,2,5]=>[5,2,1,7,6,3,8,4]=>[3,2,6,8,1,5,4,7]=>1001010
[[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[4,3,1,7,6,2,8,5]=>[3,6,2,1,8,5,4,7]=>0110110
[[1,2,3],[4,6,7],[5,8]]=>[5,8,4,6,7,1,2,3]=>[3,2,1,7,6,4,8,5]=>[3,2,1,6,8,5,4,7]=>1100110
[[1,2,5],[3,4,7],[6,8]]=>[6,8,3,4,7,1,2,5]=>[5,2,1,7,4,3,8,6]=>[3,2,6,5,1,8,4,7]=>1011010
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[4,3,1,7,5,2,8,6]=>[3,6,2,1,5,8,4,7]=>0110010
[[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[4,2,1,7,5,3,8,6]=>[3,2,6,1,5,8,4,7]=>1010010
[[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[3,2,1,7,5,4,8,6]=>[3,2,1,6,5,8,4,7]=>1101010
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[5,3,1,6,4,2,8,7]=>[3,6,2,5,1,4,8,7]=>0101001
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[5,2,1,6,4,3,8,7]=>[3,2,6,5,1,4,8,7]=>1011001
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[4,3,1,6,5,2,8,7]=>[3,6,2,1,5,4,8,7]=>0110101
[[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[4,2,1,6,5,3,8,7]=>[3,2,6,1,5,4,8,7]=>1010101
[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>[3,2,1,6,5,4,8,7]=>1101101
[[1,4,7],[2,6,8],[3],[5]]=>[5,3,2,6,8,1,4,7]=>[7,4,1,8,6,2,3,5]=>[3,6,7,2,8,5,1,4]=>0010110
[[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[7,3,1,8,6,2,4,5]=>[3,6,2,7,8,5,1,4]=>0100110
[[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[7,4,1,8,5,2,3,6]=>[3,6,7,2,5,8,1,4]=>0010010
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[7,2,1,8,5,3,4,6]=>[3,2,6,7,5,8,1,4]=>1001010
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[7,3,1,8,4,2,5,6]=>[3,6,2,5,7,8,1,4]=>0100010
[[1,2,7],[3,4,8],[5],[6]]=>[6,5,3,4,8,1,2,7]=>[7,2,1,8,4,3,5,6]=>[3,2,6,5,7,8,1,4]=>1010010
[[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[6,4,1,8,7,2,3,5]=>[3,6,7,2,8,1,5,4]=>0010101
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[6,3,1,8,7,2,4,5]=>[3,6,2,7,8,1,5,4]=>0100101
[[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[6,2,1,8,7,3,4,5]=>[3,2,6,7,8,1,5,4]=>1000101
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[5,4,1,8,7,2,3,6]=>[3,6,7,2,1,8,5,4]=>0011011
[[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[5,3,1,8,7,2,4,6]=>[3,6,2,7,1,8,5,4]=>0101011
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[5,2,1,8,7,3,4,6]=>[3,2,6,7,1,8,5,4]=>1001011
[[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[4,3,1,8,7,2,5,6]=>[3,6,2,1,7,8,5,4]=>0110011
[[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[4,2,1,8,7,3,5,6]=>[3,2,6,1,7,8,5,4]=>1010011
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>[3,2,1,6,7,8,5,4]=>1100011
[[1,4,6],[2,5,8],[3],[7]]=>[7,3,2,5,8,1,4,6]=>[6,4,1,8,5,2,3,7]=>[3,6,7,2,5,1,8,4]=>0010101
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[6,3,1,8,5,2,4,7]=>[3,6,2,7,5,1,8,4]=>0101101
[[1,2,6],[3,4,8],[5],[7]]=>[7,5,3,4,8,1,2,6]=>[6,2,1,8,4,3,5,7]=>[3,2,6,5,7,1,8,4]=>1010101
[[1,4,5],[2,6,8],[3],[7]]=>[7,3,2,6,8,1,4,5]=>[5,4,1,8,6,2,3,7]=>[3,6,7,2,1,5,8,4]=>0011001
[[1,3,5],[2,6,8],[4],[7]]=>[7,4,2,6,8,1,3,5]=>[5,3,1,8,6,2,4,7]=>[3,6,2,7,1,5,8,4]=>0101001
[[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[4,3,1,8,6,2,5,7]=>[3,6,2,1,7,5,8,4]=>0110101
[[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[4,2,1,8,6,3,5,7]=>[3,2,6,1,7,5,8,4]=>1010101
[[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>[3,2,1,6,7,5,8,4]=>1100101
[[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[5,3,1,8,4,2,6,7]=>[3,6,2,5,1,7,8,4]=>0101001
[[1,2,5],[3,4,8],[6],[7]]=>[7,6,3,4,8,1,2,5]=>[5,2,1,8,4,3,6,7]=>[3,2,6,5,1,7,8,4]=>1011001
[[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[4,2,1,8,5,3,6,7]=>[3,2,6,1,5,7,8,4]=>1010001
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>[3,2,1,6,5,7,8,4]=>1101001
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4,8]=>[3,6,2,7,5,1,4,8]=>0101100
[[1,2,6],[3,5,7],[4],[8]]=>[8,4,3,5,7,1,2,6]=>[6,2,1,7,5,3,4,8]=>[3,2,6,7,5,1,4,8]=>1001100
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5,8]=>[3,6,2,5,7,1,4,8]=>0100100
[[1,2,6],[3,4,7],[5],[8]]=>[8,5,3,4,7,1,2,6]=>[6,2,1,7,4,3,5,8]=>[3,2,6,5,7,1,4,8]=>1010100
[[1,2,5],[3,6,7],[4],[8]]=>[8,4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4,8]=>[3,2,6,7,1,5,4,8]=>1001010
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5,8]=>[3,6,2,1,7,5,4,8]=>0110110
[[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>[3,2,1,6,7,5,4,8]=>1100110
[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6,8]=>[3,2,6,1,5,7,4,8]=>1010010
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>0101000
[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7,8]=>[3,6,2,1,5,4,7,8]=>0110100
[[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7,8]=>[3,2,6,1,5,4,7,8]=>1010100
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>[3,2,1,6,5,4,7,8]=>1101100
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[8,5,1,6,2,7,3,4]=>[3,5,7,8,2,4,6,1]=>0001001
[[1,4,8],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4,8]=>[8,4,1,6,2,7,3,5]=>[3,5,7,2,8,4,6,1]=>0010101
[[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[8,3,1,6,2,7,4,5]=>[3,5,2,7,8,4,6,1]=>0100101
[[1,2,8],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2,8]=>[8,2,1,6,3,7,4,5]=>[3,2,5,7,8,4,6,1]=>1000101
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[8,4,1,5,2,7,3,6]=>[3,5,7,2,4,8,6,1]=>0010011
[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[8,3,1,5,2,7,4,6]=>[3,5,2,7,4,8,6,1]=>0101011
[[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[8,2,1,5,3,7,4,6]=>[3,2,5,7,4,8,6,1]=>1001011
[[1,3,8],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3,8]=>[8,3,1,4,2,7,5,6]=>[3,5,2,4,7,8,6,1]=>0100011
[[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[8,2,1,4,3,7,5,6]=>[3,2,5,4,7,8,6,1]=>1010011
[[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[8,4,1,5,2,6,3,7]=>[3,5,7,2,4,6,8,1]=>0010001
[[1,3,8],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3,8]=>[8,3,1,5,2,6,4,7]=>[3,5,2,7,4,6,8,1]=>0101001
[[1,2,8],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2,8]=>[8,2,1,5,3,6,4,7]=>[3,2,5,7,4,6,8,1]=>1001001
[[1,3,8],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3,8]=>[8,3,1,4,2,6,5,7]=>[3,5,2,4,7,6,8,1]=>0100101
[[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>[3,2,5,4,7,6,8,1]=>1010101
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[7,5,1,6,2,8,3,4]=>[3,5,7,8,2,4,1,6]=>0001010
[[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[7,4,1,6,2,8,3,5]=>[3,5,7,2,8,4,1,6]=>0010110
[[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[7,3,1,6,2,8,4,5]=>[3,5,2,7,8,4,1,6]=>0100110
[[1,2,7],[3,6],[4,8],[5]]=>[5,4,8,3,6,1,2,7]=>[7,2,1,6,3,8,4,5]=>[3,2,5,7,8,4,1,6]=>1000110
[[1,4,7],[2,5],[3,8],[6]]=>[6,3,8,2,5,1,4,7]=>[7,4,1,5,2,8,3,6]=>[3,5,7,2,4,8,1,6]=>0010010
[[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[7,3,1,5,2,8,4,6]=>[3,5,2,7,4,8,1,6]=>0101010
[[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[7,2,1,5,3,8,4,6]=>[3,2,5,7,4,8,1,6]=>1001010
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[7,2,1,4,3,8,5,6]=>[3,2,5,4,7,8,1,6]=>1010010
[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[6,5,1,7,2,8,3,4]=>[3,5,7,8,2,1,4,6]=>0001100
[[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[6,4,1,7,2,8,3,5]=>[3,5,7,2,8,1,4,6]=>0010100
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[5,3,1,7,2,8,4,6]=>[3,5,2,7,1,8,4,6]=>0101010
[[1,2,5],[3,7],[4,8],[6]]=>[6,4,8,3,7,1,2,5]=>[5,2,1,7,3,8,4,6]=>[3,2,5,7,1,8,4,6]=>1001010
[[1,3,4],[2,7],[5,8],[6]]=>[6,5,8,2,7,1,3,4]=>[4,3,1,7,2,8,5,6]=>[3,5,2,1,7,8,4,6]=>0110010
[[1,2,4],[3,7],[5,8],[6]]=>[6,5,8,3,7,1,2,4]=>[4,2,1,7,3,8,5,6]=>[3,2,5,1,7,8,4,6]=>1010010
[[1,2,3],[4,7],[5,8],[6]]=>[6,5,8,4,7,1,2,3]=>[3,2,1,7,4,8,5,6]=>[3,2,1,5,7,8,4,6]=>1100010
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[6,4,1,5,2,8,3,7]=>[3,5,7,2,4,1,8,6]=>0010101
[[1,3,6],[2,5],[4,8],[7]]=>[7,4,8,2,5,1,3,6]=>[6,3,1,5,2,8,4,7]=>[3,5,2,7,4,1,8,6]=>0101101
[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[6,2,1,5,3,8,4,7]=>[3,2,5,7,4,1,8,6]=>1001101
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[6,3,1,4,2,8,5,7]=>[3,5,2,4,7,1,8,6]=>0100101
[[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[6,2,1,4,3,8,5,7]=>[3,2,5,4,7,1,8,6]=>1010101
[[1,4,5],[2,6],[3,8],[7]]=>[7,3,8,2,6,1,4,5]=>[5,4,1,6,2,8,3,7]=>[3,5,7,2,1,4,8,6]=>0011001
[[1,3,5],[2,6],[4,8],[7]]=>[7,4,8,2,6,1,3,5]=>[5,3,1,6,2,8,4,7]=>[3,5,2,7,1,4,8,6]=>0101001
[[1,2,5],[3,6],[4,8],[7]]=>[7,4,8,3,6,1,2,5]=>[5,2,1,6,3,8,4,7]=>[3,2,5,7,1,4,8,6]=>1001001
[[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[4,2,1,6,3,8,5,7]=>[3,2,5,1,7,4,8,6]=>1010101
[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[3,2,1,6,4,8,5,7]=>[3,2,1,5,7,4,8,6]=>1100101
[[1,3,5],[2,4],[6,8],[7]]=>[7,6,8,2,4,1,3,5]=>[5,3,1,4,2,8,6,7]=>[3,5,2,4,1,7,8,6]=>0101001
[[1,2,5],[3,4],[6,8],[7]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>[3,2,5,4,1,7,8,6]=>1011001
[[1,2,4],[3,5],[6,8],[7]]=>[7,6,8,3,5,1,2,4]=>[4,2,1,5,3,8,6,7]=>[3,2,5,1,4,7,8,6]=>1010001
[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3,8]=>[3,5,7,2,4,6,1,8]=>0010010
[[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4,8]=>[3,5,2,7,4,6,1,8]=>0101010
[[1,2,7],[3,5],[4,6],[8]]=>[8,4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4,8]=>[3,2,5,7,4,6,1,8]=>1001010
[[1,3,7],[2,4],[5,6],[8]]=>[8,5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5,8]=>[3,5,2,4,7,6,1,8]=>0100110
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>[3,2,5,4,7,6,1,8]=>1010110
[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3,8]=>[3,5,7,2,4,1,6,8]=>0010100
[[1,3,6],[2,5],[4,7],[8]]=>[8,4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4,8]=>[3,5,2,7,4,1,6,8]=>0101100
[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4,8]=>[3,2,5,7,4,1,6,8]=>1001100
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5,8]=>[3,5,2,4,7,1,6,8]=>0100100
[[1,2,6],[3,4],[5,7],[8]]=>[8,5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5,8]=>[3,2,5,4,7,1,6,8]=>1010100
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3,8]=>[3,5,7,2,1,4,6,8]=>0011000
[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4,8]=>[3,5,2,7,1,4,6,8]=>0101000
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8]=>[3,2,5,7,1,4,6,8]=>1001000
[[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5,8]=>[3,5,2,1,7,4,6,8]=>0110100
[[1,2,4],[3,6],[5,7],[8]]=>[8,5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5,8]=>[3,2,5,1,7,4,6,8]=>1010100
[[1,2,3],[4,6],[5,7],[8]]=>[8,5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5,8]=>[3,2,1,5,7,4,6,8]=>1100100
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6,8]=>[3,5,2,4,1,7,6,8]=>0101010
[[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>[3,2,5,4,1,7,6,8]=>1011010
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6,8]=>[3,5,2,1,4,7,6,8]=>0110010
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6,8]=>[3,2,5,1,4,7,6,8]=>1010010
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010
[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[8,6,1,7,2,3,4,5]=>[3,5,6,7,8,2,4,1]=>0000101
[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[8,5,1,7,2,3,4,6]=>[3,5,6,7,2,8,4,1]=>0001011
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[8,4,1,7,2,3,5,6]=>[3,5,6,2,7,8,4,1]=>0010011
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[8,3,1,7,2,4,5,6]=>[3,5,2,6,7,8,4,1]=>0100011
[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>[3,2,5,6,7,8,4,1]=>1000011
[[1,5,8],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5,8]=>[8,5,1,6,2,3,4,7]=>[3,5,6,7,2,4,8,1]=>0001001
[[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[8,4,1,6,2,3,5,7]=>[3,5,6,2,7,4,8,1]=>0010101
[[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[8,3,1,6,2,4,5,7]=>[3,5,2,6,7,4,8,1]=>0100101
[[1,2,8],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>[3,2,5,6,7,4,8,1]=>1000101
[[1,4,8],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4,8]=>[8,4,1,5,2,3,6,7]=>[3,5,6,2,4,7,8,1]=>0010001
[[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[8,3,1,5,2,4,6,7]=>[3,5,2,6,4,7,8,1]=>0101001
[[1,2,8],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2,8]=>[8,2,1,5,3,4,6,7]=>[3,2,5,6,4,7,8,1]=>1001001
[[1,3,8],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3,8]=>[8,3,1,4,2,5,6,7]=>[3,5,2,4,6,7,8,1]=>0100001
[[1,2,8],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2,8]=>[8,2,1,4,3,5,6,7]=>[3,2,5,4,6,7,8,1]=>1010001
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[7,6,1,8,2,3,4,5]=>[3,5,6,7,8,2,1,4]=>0000110
[[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[7,4,1,8,2,3,5,6]=>[3,5,6,2,7,8,1,4]=>0010010
[[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[7,3,1,8,2,4,5,6]=>[3,5,2,6,7,8,1,4]=>0100010
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[7,2,1,8,3,4,5,6]=>[3,2,5,6,7,8,1,4]=>1000010
[[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[6,4,1,8,2,3,5,7]=>[3,5,6,2,7,1,8,4]=>0010101
[[1,3,6],[2,8],[4],[5],[7]]=>[7,5,4,2,8,1,3,6]=>[6,3,1,8,2,4,5,7]=>[3,5,2,6,7,1,8,4]=>0100101
[[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[5,4,1,8,2,3,6,7]=>[3,5,6,2,1,7,8,4]=>0011001
[[1,3,5],[2,8],[4],[6],[7]]=>[7,6,4,2,8,1,3,5]=>[5,3,1,8,2,4,6,7]=>[3,5,2,6,1,7,8,4]=>0101001
[[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[5,2,1,8,3,4,6,7]=>[3,2,5,6,1,7,8,4]=>1001001
[[1,3,4],[2,8],[5],[6],[7]]=>[7,6,5,2,8,1,3,4]=>[4,3,1,8,2,5,6,7]=>[3,5,2,1,6,7,8,4]=>0110001
[[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[4,2,1,8,3,5,6,7]=>[3,2,5,1,6,7,8,4]=>1010001
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>[3,2,1,5,6,7,8,4]=>1100001
[[1,5,7],[2,6],[3],[4],[8]]=>[8,4,3,2,6,1,5,7]=>[7,5,1,6,2,3,4,8]=>[3,5,6,7,2,4,1,8]=>0001010
[[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5,8]=>[3,5,6,2,7,4,1,8]=>0010110
[[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5,8]=>[3,2,5,6,7,4,1,8]=>1000110
[[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6,8]=>[3,5,6,2,4,7,1,8]=>0010010
[[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6,8]=>[3,5,2,6,4,7,1,8]=>0101010
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5,8]=>[3,5,6,2,7,1,4,8]=>0010100
[[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[5,4,1,7,2,3,6,8]=>[3,5,6,2,1,7,4,8]=>0011010
[[1,3,5],[2,7],[4],[6],[8]]=>[8,6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6,8]=>[3,5,2,6,1,7,4,8]=>0101010
[[1,2,4],[3,7],[5],[6],[8]]=>[8,6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6,8]=>[3,2,5,1,6,7,4,8]=>1010010
[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>[3,2,1,5,6,7,4,8]=>1100010
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7,8]=>[3,5,6,2,4,1,7,8]=>0010100
[[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7,8]=>[3,5,6,2,1,4,7,8]=>0011000
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7,8]=>[3,5,2,6,1,4,7,8]=>0101000
[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7,8]=>[3,2,5,6,1,4,7,8]=>1001000
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8]=>[3,5,2,1,6,4,7,8]=>0110100
[[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7,8]=>[3,2,5,1,6,4,7,8]=>1010100
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>[3,2,1,5,6,4,7,8]=>1100100
[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7,8]=>[3,5,2,4,1,6,7,8]=>0101000
[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>[3,2,5,4,1,6,7,8]=>1011000
[[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7,8]=>[3,5,2,1,4,6,7,8]=>0110000
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8]=>[3,2,5,1,4,6,7,8]=>1010000
[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000
[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>0000011
[[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>0000101
[[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>0001001
[[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>0010001
[[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>0100001
[[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>1000001
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>0000110
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>0001010
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>0010010
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>0100010
[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>1000010
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>0001100
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>0010100
[[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>[3,4,2,5,6,1,7,8]=>0100100
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>1000100
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>0011000
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>0101000
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>1001000
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>0110000
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>1010000
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>[2,4,6,8,1,3,5,7]=>0001000
[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>[2,4,6,1,8,3,5,7]=>0010100
[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5]=>[2,4,1,6,8,3,5,7]=>0100100
[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5]=>[2,1,4,6,8,3,5,7]=>1000100
[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6]=>[2,4,6,1,3,8,5,7]=>0010010
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>[2,4,1,6,3,8,5,7]=>0101010
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6]=>[2,1,4,6,3,8,5,7]=>1001010
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>[2,4,1,3,6,8,5,7]=>0100010
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,6,8,5,7]=>1010010
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7]=>[2,4,6,1,3,5,8,7]=>0010001
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7]=>[2,4,1,6,3,5,8,7]=>0101001
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>[2,1,4,6,3,5,8,7]=>1001001
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>0100101
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101
[[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[6,1,7,2,8,3,4,5]=>[2,4,6,7,8,1,3,5]=>0000100
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[5,1,7,2,8,3,4,6]=>[2,4,6,7,1,8,3,5]=>0001010
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[4,1,7,2,8,3,5,6]=>[2,4,6,1,7,8,3,5]=>0010010
[[1,3],[2,7],[4,8],[5],[6]]=>[6,5,4,8,2,7,1,3]=>[3,1,7,2,8,4,5,6]=>[2,4,1,6,7,8,3,5]=>0100010
[[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[2,1,7,3,8,4,5,6]=>[2,1,4,6,7,8,3,5]=>1000010
[[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[5,1,6,2,8,3,4,7]=>[2,4,6,7,1,3,8,5]=>0001001
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[4,1,6,2,8,3,5,7]=>[2,4,6,1,7,3,8,5]=>0010101
[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[3,1,6,2,8,4,5,7]=>[2,4,1,6,7,3,8,5]=>0100101
[[1,2],[3,6],[4,8],[5],[7]]=>[7,5,4,8,3,6,1,2]=>[2,1,6,3,8,4,5,7]=>[2,1,4,6,7,3,8,5]=>1000101
[[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[4,1,5,2,8,3,6,7]=>[2,4,6,1,3,7,8,5]=>0010001
[[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[3,1,5,2,8,4,6,7]=>[2,4,1,6,3,7,8,5]=>0101001
[[1,2],[3,5],[4,8],[6],[7]]=>[7,6,4,8,3,5,1,2]=>[2,1,5,3,8,4,6,7]=>[2,1,4,6,3,7,8,5]=>1001001
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[3,1,4,2,8,5,6,7]=>[2,4,1,3,6,7,8,5]=>0100001
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,6,7,8,5]=>1010001
[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4,8]=>[2,4,6,7,1,3,5,8]=>0001000
[[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6,8]=>[2,4,6,1,3,7,5,8]=>0010010
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6,8]=>[2,4,1,6,3,7,5,8]=>0101010
[[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6,8]=>[2,1,4,6,3,7,5,8]=>1001010
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8]=>[2,4,6,1,3,5,7,8]=>0010000
[[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7,8]=>[2,4,1,6,3,5,7,8]=>0101000
[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7,8]=>[2,1,4,6,3,5,7,8]=>1001000
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>0100100
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[7,1,8,2,3,4,5,6]=>[2,4,5,6,7,8,1,3]=>0000010
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[6,1,8,2,3,4,5,7]=>[2,4,5,6,7,1,8,3]=>0000101
[[1,5],[2,8],[3],[4],[6],[7]]=>[7,6,4,3,2,8,1,5]=>[5,1,8,2,3,4,6,7]=>[2,4,5,6,1,7,8,3]=>0001001
[[1,4],[2,8],[3],[5],[6],[7]]=>[7,6,5,3,2,8,1,4]=>[4,1,8,2,3,5,6,7]=>[2,4,5,1,6,7,8,3]=>0010001
[[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[3,1,8,2,4,5,6,7]=>[2,4,1,5,6,7,8,3]=>0100001
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>1000001
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5,8]=>[2,4,5,6,7,1,3,8]=>0000100
[[1,5],[2,7],[3],[4],[6],[8]]=>[8,6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6,8]=>[2,4,5,6,1,7,3,8]=>0001010
[[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6,8]=>[2,4,1,5,6,7,3,8]=>0100010
[[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>[2,1,4,5,6,7,3,8]=>1000010
[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7,8]=>[2,4,5,6,1,3,7,8]=>0001000
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7,8]=>[2,4,5,1,6,3,7,8]=>0010100
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7,8]=>[2,4,1,5,6,3,7,8]=>0100100
[[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>0010000
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7,8]=>[2,4,1,5,3,6,7,8]=>0101000
[[1,2],[3,5],[4],[6],[7],[8]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>1001000
[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0100000
[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>0000001
[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>0000010
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>0000100
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[9,7,5,3,1,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>010101010
[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>01010101010
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>11111011111
[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>11111101
[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>11111011
[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9]=>[6,5,4,3,2,1,8,7,9]=>11111010
[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>11110111
[[1,2,3,4,5],[6,7,8],[9]]=>[9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9]=>[5,4,3,2,1,8,7,6,9]=>11110110
[[1,2,3,4,5],[6,7],[8,9]]=>[8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8]=>[5,4,3,2,1,7,6,9,8]=>11110101
[[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9]=>[5,4,3,2,1,7,6,8,9]=>11110100
[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[1,2,3,4],[5,6,7,8],[9]]=>[9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9]=>[4,3,2,1,8,7,6,5,9]=>11101110
[[1,2,3,4],[5,6,7],[8,9]]=>[8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8]=>[4,3,2,1,7,6,5,9,8]=>11101101
[[1,2,3,4],[5,6,7],[8],[9]]=>[9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9]=>[4,3,2,1,7,6,5,8,9]=>11101100
[[1,2,3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>11101010
[[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>11101000
[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>[3,2,1,6,5,4,9,8,7]=>11011011
[[1,2,3],[4,5,6],[7,8],[9]]=>[9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9]=>[3,2,1,6,5,4,8,7,9]=>11011010
[[1,2,3],[4,5,6],[7],[8],[9]]=>[9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9]=>[3,2,1,6,5,4,7,8,9]=>11011000
[[1,2,3],[4,5],[6,7],[8,9]]=>[8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>11010101
[[1,2,3],[4,5],[6,7],[8],[9]]=>[9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9]=>[3,2,1,5,4,7,6,8,9]=>11010100
[[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>11010000
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>10101010
[[1,2],[3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>10101000
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8,10]=>[7,6,5,4,3,2,1,9,8,10]=>111111010
[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[[1,2,3,4,5,6],[7,8,9],[10]]=>[10,7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7,10]=>[6,5,4,3,2,1,9,8,7,10]=>111110110
[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>111110101
[[1,2,3,4,5,6],[7,8],[9],[10]]=>[10,9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9,10]=>[6,5,4,3,2,1,8,7,9,10]=>111110100
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6,10]=>[5,4,3,2,1,9,8,7,6,10]=>111101110
[[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,10,9]=>[5,4,3,2,1,8,7,6,10,9]=>111101101
[[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9,10]=>[5,4,3,2,1,8,7,6,9,10]=>111101100
[[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8,10]=>[5,4,3,2,1,7,6,9,8,10]=>111101010
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9,10]=>[5,4,3,2,1,7,6,8,9,10]=>111101000
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>111011101
[[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9,10]=>[4,3,2,1,8,7,6,5,9,10]=>111011100
[[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,10,9,8]=>[4,3,2,1,7,6,5,10,9,8]=>111011011
[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8,10]=>[4,3,2,1,7,6,5,9,8,10]=>111011010
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[10,9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9,10]=>[4,3,2,1,7,6,5,8,9,10]=>111011000
[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>111010101
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9,10]=>[4,3,2,1,6,5,8,7,9,10]=>111010100
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9,10]=>[4,3,2,1,6,5,7,8,9,10]=>111010000
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7,10]=>[3,2,1,6,5,4,9,8,7,10]=>110110110
[[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,10,9]=>[3,2,1,6,5,4,8,7,10,9]=>110110101
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[10,9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9,10]=>[3,2,1,6,5,4,8,7,9,10]=>110110100
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9,10]=>[3,2,1,6,5,4,7,8,9,10]=>110110000
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>110101010
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9,10]=>[3,2,1,5,4,7,6,8,9,10]=>110101000
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9,10]=>[3,2,1,5,4,6,7,8,9,10]=>110100000
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>101010100
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>101010000
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>101000000
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000
[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>01111111
[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>[7,6,9,8,5,4,3,2,1]=>10111111
[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>00111111
[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[9,8,7,3,2,1,6,5,4]=>[6,5,4,9,8,7,3,2,1]=>11011111
[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[9,8,7,6,3,1,5,2,4]=>[6,8,5,9,7,4,3,2,1]=>01011111
[[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>00011111
[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[9,4,3,2,1,8,7,6,5]=>[5,4,3,2,9,8,7,6,1]=>11101111
[[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[9,8,4,3,1,7,6,2,5]=>[5,8,4,3,9,7,6,2,1]=>01101111
[[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[9,8,7,2,1,4,3,6,5]=>[5,4,7,6,9,8,3,2,1]=>10101111
[[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[9,8,7,4,1,6,2,3,5]=>[5,7,8,4,9,6,3,2,1]=>00101111
[[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>00001111
[[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[5,4,3,1,9,8,7,2,6]=>[4,8,3,2,1,9,7,6,5]=>01110111
[[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[9,5,2,1,8,4,3,7,6]=>[4,3,7,6,2,9,8,5,1]=>10110111
[[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[9,5,4,1,8,7,2,3,6]=>[4,7,8,3,2,9,6,5,1]=>00110111
[[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[9,8,3,1,5,2,7,4,6]=>[4,6,3,8,5,9,7,2,1]=>01010111
[[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[9,8,5,1,7,2,3,4,6]=>[4,6,7,8,3,9,5,2,1]=>00010111
[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>00000111
[[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[6,3,1,9,5,2,8,4,7]=>[3,6,2,8,5,1,9,7,4]=>01011011
[[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[6,5,1,9,8,2,3,4,7]=>[3,6,7,8,2,1,9,5,4]=>00011011
[[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[9,2,1,4,3,6,5,8,7]=>[3,2,5,4,7,6,9,8,1]=>10101011
[[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[9,4,1,6,2,8,3,5,7]=>[3,5,7,2,8,4,9,6,1]=>00101011
[[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[9,6,1,8,2,3,4,5,7]=>[3,5,6,7,8,2,9,4,1]=>00001011
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>00000011
[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,8]=>[2,4,1,6,3,8,5,9,7]=>01010101
[[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[5,1,7,2,9,3,4,6,8]=>[2,4,6,7,1,8,3,9,5]=>00010101
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[7,1,9,2,3,4,5,6,8]=>[2,4,5,6,7,8,1,9,3]=>00000101
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>00000001
[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>011111111
[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,1,4,3]=>[8,7,10,9,6,5,4,3,2,1]=>101111111
[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>001111111
[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[10,9,8,7,3,2,1,6,5,4]=>[7,6,5,10,9,8,4,3,2,1]=>110111111
[[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[10,9,8,7,6,3,1,5,2,4]=>[7,9,6,10,8,5,4,3,2,1]=>010111111
[[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>000111111
[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[10,9,4,3,2,1,8,7,6,5]=>[6,5,4,3,10,9,8,7,2,1]=>111011111
[[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[10,9,8,4,3,1,7,6,2,5]=>[6,9,5,4,10,8,7,3,2,1]=>011011111
[[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[10,9,8,7,2,1,4,3,6,5]=>[6,5,8,7,10,9,4,3,2,1]=>101011111
[[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[10,9,8,7,4,1,6,2,3,5]=>[6,8,9,5,10,7,4,3,2,1]=>001011111
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>000011111
[[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[10,5,4,3,1,9,8,7,2,6]=>[5,9,4,3,2,10,8,7,6,1]=>011101111
[[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[10,9,5,2,1,8,4,3,7,6]=>[5,4,8,7,3,10,9,6,2,1]=>101101111
[[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[10,9,5,4,1,8,7,2,3,6]=>[5,8,9,4,3,10,7,6,2,1]=>001101111
[[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[10,9,8,3,1,5,2,7,4,6]=>[5,7,4,9,6,10,8,3,2,1]=>010101111
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[10,9,8,5,1,7,2,3,4,6]=>[5,7,8,9,4,10,6,3,2,1]=>000101111
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>000001111
[[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[6,5,2,1,10,9,4,3,8,7]=>[4,3,8,7,2,1,10,9,6,5]=>101110111
[[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[6,5,4,1,10,9,8,2,3,7]=>[4,8,9,3,2,1,10,7,6,5]=>001110111
[[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[10,3,2,1,6,5,4,9,8,7]=>[4,3,2,7,6,5,10,9,8,1]=>110110111
[[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[10,6,3,1,9,5,2,8,4,7]=>[4,7,3,9,6,2,10,8,5,1]=>010110111
[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10]=>[10,6,5,1,9,8,2,3,4,7]=>[4,7,8,9,3,2,10,6,5,1]=>000110111
[[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[10,9,2,1,4,3,6,5,8,7]=>[4,3,6,5,8,7,10,9,2,1]=>101010111
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[10,9,4,1,6,2,8,3,5,7]=>[4,6,8,3,9,5,10,7,2,1]=>001010111
[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9,10]=>[10,9,6,1,8,2,3,4,5,7]=>[4,6,7,8,9,3,10,5,2,1]=>000010111
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>000000111
[[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[4,3,1,7,6,2,10,9,5,8]=>[3,6,2,1,9,5,4,10,8,7]=>011011011
[[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[7,2,1,10,4,3,6,5,9,8]=>[3,2,6,5,8,7,1,10,9,4]=>101011011
[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7]=>[7,4,1,10,6,2,9,3,5,8]=>[3,6,8,2,9,5,1,10,7,4]=>001011011
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[8,5,4,3,2,9,10,1,6,7]=>[7,6,1,10,9,2,3,4,5,8]=>[3,6,7,8,9,2,1,10,5,4]=>000011011
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[10,3,1,5,2,7,4,9,6,8]=>[3,5,2,7,4,9,6,10,8,1]=>010101011
[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5,10]=>[10,5,1,7,2,9,3,4,6,8]=>[3,5,7,8,2,9,4,10,6,1]=>000101011
[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7,10]=>[10,7,1,9,2,3,4,5,6,8]=>[3,5,6,7,8,9,2,10,4,1]=>000001011
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>000000011
[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[4,1,6,2,8,3,10,5,7,9]=>[2,4,6,1,8,3,9,5,10,7]=>001010101
[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[9,7,5,4,3,10,2,8,1,6]=>[6,1,8,2,10,3,4,5,7,9]=>[2,4,6,7,8,1,9,3,10,5]=>000010101
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[8,1,10,2,3,4,5,6,7,9]=>[2,4,5,6,7,8,9,1,10,3]=>000000101
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[8,1,9,2,3,4,5,6,7]=>[2,4,5,6,7,8,9,1,3]=>00000010
[[1,7],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7]=>[7,1,8,2,9,3,4,5,6]=>[2,4,6,7,8,9,1,3,5]=>00000100
[[1,7,9],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9]=>[9,7,1,8,2,3,4,5,6]=>[3,5,6,7,8,9,2,4,1]=>00000101
[[1,4,7],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7]=>[7,4,1,8,5,2,9,6,3]=>[3,6,9,2,5,8,1,4,7]=>00100100
[[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,4,2]=>[7,9,6,8,5,4,3,2,1]=>01011111
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[9,1,10,2,3,4,5,6,7,8]=>[2,4,5,6,7,8,9,10,1,3]=>000000010
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,10,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,10,5]=>[2,4,6,8,10,1,3,5,7,9]=>000010000
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>01000000
[[1,4],[2,5],[3,6],[7],[8],[9]]=>[9,8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8,9]=>[2,4,6,1,3,5,7,8,9]=>00100000
[[1,2,4],[3,5],[6],[7],[8],[9]]=>[9,8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8,9]=>[3,2,5,1,4,6,7,8,9]=>10100000
[[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,9]=>[2,4,6,8,1,3,5,7,9]=>00010000
[[1,2,5],[3,6],[4,7],[8],[9]]=>[9,8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8,9]=>[3,2,5,7,1,4,6,8,9]=>10010000
[[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8,9]=>[3,6,2,5,1,4,7,8,9]=>01010000
[[1,2,3,5],[4,6],[7],[8],[9]]=>[9,8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8,9]=>[4,3,2,6,1,5,7,8,9]=>11010000
[[1,2,6],[3,7],[4,8],[5,9]]=>[5,9,4,8,3,7,1,2,6]=>[6,2,1,7,3,8,4,9,5]=>[3,2,5,7,9,1,4,6,8]=>10001000
[[1,3,6],[2,4,7],[5,8],[9]]=>[9,5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5,9]=>[3,6,2,5,8,1,4,7,9]=>01001000
[[1,2,3,6],[4,7],[5,8],[9]]=>[9,5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5,9]=>[4,3,2,6,8,1,5,7,9]=>11001000
[[1,2,4,6],[3,5,7],[8],[9]]=>[9,8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8,9]=>[4,3,7,2,6,1,5,8,9]=>10101000
[[1,2,3,4,6],[5,7],[8],[9]]=>[9,8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8,9]=>[5,4,3,2,7,1,6,8,9]=>11101000
[[1,2,4,7],[3,5,8],[6,9]]=>[6,9,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,9,6]=>[4,3,7,2,6,9,1,5,8]=>10100100
[[1,2,3,4,7],[5,8],[6,9]]=>[6,9,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,9,6]=>[5,4,3,2,7,9,1,6,8]=>11100100
[[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2,9]=>[4,8,3,7,2,6,1,5,9]=>01010100
[[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4,9]=>[5,4,3,8,2,7,1,6,9]=>11010100
[[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6,9]=>[6,5,4,3,2,8,1,7,9]=>11110100
[[1,2,4,6,8],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8]=>[8,6,4,2,1,9,7,5,3]=>[5,4,9,3,8,2,7,1,6]=>10101010
[[1,2,3,4,6,8],[5,7,9]]=>[5,7,9,1,2,3,4,6,8]=>[8,6,4,3,2,1,9,7,5]=>[6,5,4,3,9,2,8,1,7]=>11101010
[[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,9,7]=>[7,6,5,4,3,2,9,1,8]=>11111010
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>010000000
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[10,9,8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8,9,10]=>[2,4,6,1,3,5,7,8,9,10]=>001000000
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8,9,10]=>[3,2,5,1,4,6,7,8,9,10]=>101000000
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[10,9,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,9,10]=>[2,4,6,8,1,3,5,7,9,10]=>000100000
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[10,9,8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8,9,10]=>[3,2,5,7,1,4,6,8,9,10]=>100100000
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>[10,9,8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8,9,10]=>[3,6,2,5,1,4,7,8,9,10]=>010100000
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[10,9,8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8,9,10]=>[4,3,2,6,1,5,7,8,9,10]=>110100000
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[6,2,1,7,3,8,4,9,5,10]=>[3,2,5,7,9,1,4,6,8,10]=>100010000
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>[10,9,5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5,9,10]=>[3,6,2,5,8,1,4,7,9,10]=>010010000
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>[10,9,5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5,9,10]=>[4,3,2,6,8,1,5,7,9,10]=>110010000
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>[10,9,8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8,9,10]=>[4,3,7,2,6,1,5,8,9,10]=>101010000
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>[10,9,8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8,9,10]=>[5,4,3,2,7,1,6,8,9,10]=>111010000
[[1,3,7],[2,4,8],[5,9],[6,10]]=>[6,10,5,9,2,4,8,1,3,7]=>[7,3,1,8,4,2,9,5,10,6]=>[3,6,2,5,8,10,1,4,7,9]=>010001000
[[1,2,3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,1,2,3,7]=>[7,3,2,1,8,4,9,5,10,6]=>[4,3,2,6,8,10,1,5,7,9]=>110001000
[[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[7,4,1,8,5,2,9,6,3,10]=>[3,6,9,2,5,8,1,4,7,10]=>001001000
[[1,2,4,7],[3,5,8],[6,9],[10]]=>[10,6,9,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,9,6,10]=>[4,3,7,2,6,9,1,5,8,10]=>101001000
[[1,2,3,4,7],[5,8],[6,9],[10]]=>[10,6,9,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,9,6,10]=>[5,4,3,2,7,9,1,6,8,10]=>111001000
[[1,3,5,7],[2,4,6,8],[9],[10]]=>[10,9,2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2,9,10]=>[4,8,3,7,2,6,1,5,9,10]=>010101000
[[1,2,3,5,7],[4,6,8],[9],[10]]=>[10,9,4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4,9,10]=>[5,4,3,8,2,7,1,6,9,10]=>110101000
[[1,2,3,4,5,7],[6,8],[9],[10]]=>[10,9,6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6,9,10]=>[6,5,4,3,2,8,1,7,9,10]=>111101000
[[1,2,5,8],[3,6,9],[4,7,10]]=>[4,7,10,3,6,9,1,2,5,8]=>[8,5,2,1,9,6,3,10,7,4]=>[4,3,7,10,2,6,9,1,5,8]=>100100100
[[1,3,5,8],[2,4,6,9],[7,10]]=>[7,10,2,4,6,9,1,3,5,8]=>[8,5,3,1,9,6,4,2,10,7]=>[4,8,3,7,2,6,10,1,5,9]=>010100100
[[1,2,3,5,8],[4,6,9],[7,10]]=>[7,10,4,6,9,1,2,3,5,8]=>[8,5,3,2,1,9,6,4,10,7]=>[5,4,3,8,2,7,10,1,6,9]=>110100100
[[1,2,3,4,5,8],[6,9],[7,10]]=>[7,10,6,9,1,2,3,4,5,8]=>[8,5,4,3,2,1,9,6,10,7]=>[6,5,4,3,2,8,10,1,7,9]=>111100100
[[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[8,6,4,2,1,9,7,5,3,10]=>[5,4,9,3,8,2,7,1,6,10]=>101010100
[[1,2,3,4,6,8],[5,7,9],[10]]=>[10,5,7,9,1,2,3,4,6,8]=>[8,6,4,3,2,1,9,7,5,10]=>[6,5,4,3,9,2,8,1,7,10]=>111010100
[[1,2,3,4,5,6,8],[7,9],[10]]=>[10,7,9,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,9,7,10]=>[7,6,5,4,3,2,9,1,8,10]=>111110100
[[1,2,3,5,7,9],[4,6,8,10]]=>[4,6,8,10,1,2,3,5,7,9]=>[9,7,5,3,2,1,10,8,6,4]=>[6,5,4,10,3,9,2,8,1,7]=>110101010
[[1,2,3,4,5,7,9],[6,8,10]]=>[6,8,10,1,2,3,4,5,7,9]=>[9,7,5,4,3,2,1,10,8,6]=>[7,6,5,4,3,10,2,9,1,8]=>111101010
[[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,10,8]=>[8,7,6,5,4,3,2,10,1,9]=>111111010
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7,10,9]=>[2,4,1,3,6,5,8,7,10,9]=>010010101
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7,10,9]=>[2,4,1,6,3,5,8,7,10,9]=>010100101
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6,10,9]=>[2,4,1,6,3,8,5,7,10,9]=>010101001
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,10,8]=>[2,4,1,6,3,8,5,10,7,9]=>010101010
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>00000100000
[[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>11111101
[[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,9,8,1]=>11111011
[[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,9,1]=>11111001
[[1,2,3,4,5,9],[6],[7],[8]]=>[8,7,6,1,2,3,4,5,9]=>[9,5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,9,1]=>11110001
[[1,2,3,4,9],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4,9]=>[9,4,3,2,1,5,6,7,8]=>[5,4,3,2,6,7,8,9,1]=>11100001
[[1,2,3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3,9]=>[9,3,2,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,9,1]=>11000001
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>10000001
[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,9,1,3]=>[3,1,9,2,4,5,6,7,8]=>[2,4,1,5,6,7,8,9,3]=>01000001
[[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>111111101
[[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,10,9,1]=>111111011
[[1,2,3,4,5,6,7,10],[8],[9]]=>[9,8,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,10,1]=>111111001
[[1,2,3,4,5,6,10],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6,10]=>[10,6,5,4,3,2,1,7,8,9]=>[7,6,5,4,3,2,8,9,10,1]=>111110001
[[1,2,3,4,5,10],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5,10]=>[10,5,4,3,2,1,6,7,8,9]=>[6,5,4,3,2,7,8,9,10,1]=>111100001
[[1,2,3,4,10],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4,10]=>[10,4,3,2,1,5,6,7,8,9]=>[5,4,3,2,6,7,8,9,10,1]=>111000001
[[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3,10]=>[10,3,2,1,4,5,6,7,8,9]=>[4,3,2,5,6,7,8,9,10,1]=>110000001
[[1,2,10],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2,10]=>[10,2,1,4,3,6,5,8,7,9]=>[3,2,5,4,7,6,9,8,10,1]=>101010101
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2,10]=>[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>100000001
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,10,1,3]=>[3,1,10,2,4,5,6,7,8,9]=>[2,4,1,5,6,7,8,9,10,3]=>010000001
[[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>10111111
[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>00000101
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>00000010
[[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>101111111
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8,10]=>[10,8,1,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,9,2,10,1]=>000000101
[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[10,8,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,8,10]=>[2,4,1,6,3,8,5,9,7,10]=>010101010
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,9,2]=>[7,9,6,5,4,3,2,1,8]=>01111110
[[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>01111110
[[1,3,4,5,6,7],[2,9],[8]]=>[8,2,9,1,3,4,5,6,7]=>[7,6,5,4,3,1,9,2,8]=>[6,8,5,4,3,2,1,9,7]=>01111101
[[1,3,4,5,6,7],[2],[8],[9]]=>[9,8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8,9]=>[6,7,5,4,3,2,1,8,9]=>01111100
[[1,3,4,5,6],[2,8],[7],[9]]=>[9,7,2,8,1,3,4,5,6]=>[6,5,4,3,1,8,2,7,9]=>[5,7,4,3,2,1,8,6,9]=>01111010
[[1,3,4,5,6],[2],[7],[8],[9]]=>[9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>01111000
[[1,3,4,5],[2,7],[6],[8],[9]]=>[9,8,6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6,8,9]=>[4,6,3,2,1,7,5,8,9]=>01110100
[[1,3,4,5],[2],[6],[7],[8],[9]]=>[9,8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>01110000
[[1,3,4],[2,6],[5],[7],[8],[9]]=>[9,8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8,9]=>[3,5,2,1,6,4,7,8,9]=>01101000
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>01100000
[[1,3],[2,5],[4,7],[6],[8],[9]]=>[9,8,6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6,8,9]=>[2,4,1,6,3,7,5,8,9]=>01010100
[[1,3],[2,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7,8,9]=>[2,4,1,5,3,6,7,8,9]=>01010000
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000
[[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,10,2]=>[8,10,7,6,5,4,3,2,1,9]=>011111110
[[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>011111110
[[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,10,9,2]=>[7,10,6,5,4,3,2,1,9,8]=>011111101
[[1,3,4,5,6,7,8],[2,10],[9]]=>[9,2,10,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,10,2,9]=>[7,9,6,5,4,3,2,1,10,8]=>011111101
[[1,3,4,5,6,7],[2,9],[8],[10]]=>[10,8,2,9,1,3,4,5,6,7]=>[7,6,5,4,3,1,9,2,8,10]=>[6,8,5,4,3,2,1,9,7,10]=>011111010
[[1,3,4,5,6,7],[2],[8],[9],[10]]=>[10,9,8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8,9,10]=>[6,7,5,4,3,2,1,8,9,10]=>011111000
[[1,3,4,5,6],[2,8],[7],[9],[10]]=>[10,9,7,2,8,1,3,4,5,6]=>[6,5,4,3,1,8,2,7,9,10]=>[5,7,4,3,2,1,8,6,9,10]=>011110100
[[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[10,9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,4,3,2,1,7,8,9,10]=>011110000
[[1,3,4,5],[2,7,8],[6,10],[9]]=>[9,6,10,2,7,8,1,3,4,5]=>[5,4,3,1,8,7,2,10,6,9]=>[4,7,3,2,1,9,6,5,10,8]=>011101101
[[1,3,4,5],[2,7],[6],[8],[9],[10]]=>[10,9,8,6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6,8,9,10]=>[4,6,3,2,1,7,5,8,9,10]=>011101000
[[1,3,4],[2,6],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8,9,10]=>[3,5,2,1,6,4,7,8,9,10]=>011010000
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9,10]=>[3,4,2,1,5,6,7,8,9,10]=>011000000
[[1,3],[2,5],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7,8,9,10]=>[2,4,1,5,3,6,7,8,9,10]=>010100000
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>110111111
[[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>111011111
[[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>111111011
[[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>111110111
[[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>111101111
[[1,2,5,6,7,8],[3,4],[9]]=>[9,3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3,9]=>[6,5,8,7,4,3,2,1,9]=>10111110
[[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>00111110
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6,9]=>[3,4,5,6,7,8,2,1,9]=>00000110
[[1,4,5,6,7,8,9],[2],[3],[10]]=>[10,3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3,10]=>[7,8,9,6,5,4,3,2,1,10]=>001111110
[[1,2,3,4,9],[5,6,7,8],[10]]=>[10,5,6,7,8,1,2,3,4,9]=>[9,4,3,2,1,8,7,6,5,10]=>[5,4,3,2,9,8,7,6,1,10]=>111011110
[[1,2,5,9],[3,4,8],[6,7],[10]]=>[10,6,7,3,4,8,1,2,5,9]=>[9,5,2,1,8,4,3,7,6,10]=>[4,3,7,6,2,9,8,5,1,10]=>101101110
[[1,2,9],[3,4],[5,6],[7,8],[10]]=>[10,7,8,5,6,3,4,1,2,9]=>[9,2,1,4,3,6,5,8,7,10]=>[3,2,5,4,7,6,9,8,1,10]=>101010110
[[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,3,4]=>[7,6,8,9,5,4,3,2,1]=>10011111
[[1,2,6,7,8,9],[3],[4],[5]]=>[5,4,3,1,2,6,7,8,9]=>[9,8,7,6,2,1,3,4,5]=>[6,5,7,8,9,4,3,2,1]=>10001111
[[1,2,7,8,9],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9]=>[9,8,7,2,1,3,4,5,6]=>[5,4,6,7,8,9,3,2,1]=>10000111
[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7,9]=>[2,1,4,5,6,7,8,3,9]=>10000010
[[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,1,3,4]=>[8,7,9,10,6,5,4,3,2,1]=>100111111
[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9,10]=>[10,9,8,7,2,1,3,4,5,6]=>[6,5,7,8,9,10,4,3,2,1]=>100001111
[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8,9,10]=>[10,9,8,2,1,3,4,5,6,7]=>[5,4,6,7,8,9,10,3,2,1]=>100000111
[[1,2,4,7],[3,6,10],[5,9],[8]]=>[8,5,9,3,6,10,1,2,4,7]=>[7,4,2,1,10,6,3,9,5,8]=>[4,3,7,2,9,6,1,10,8,5]=>101011011
[[1,2,5,6,7,8],[3],[4],[9]]=>[9,4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4,9]=>[6,5,7,8,4,3,2,1,9]=>10011110
[[1,2,4,5,6,7,8,9],[3],[10]]=>[10,3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3,10]=>[8,7,9,6,5,4,3,2,1,10]=>101111110
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>001000000
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>000100000
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>000000100
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>000001000
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>000010000
[[1,2],[3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8,9]=>[2,1,4,5,3,6,7,8,9]=>10010000
[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>10100000
[[1,2,3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>11010000
[[1,2,3,4,6],[5],[7],[8],[9]]=>[9,8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8,9]=>[5,4,3,2,6,1,7,8,9]=>11101000
[[1,2,3,4,5,7],[6],[8],[9]]=>[9,8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8,9]=>[6,5,4,3,2,7,1,8,9]=>11110100
[[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>11111010
[[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[9,7,5,4,3,2,1,8,6]=>[7,6,5,4,3,9,2,8,1]=>11110101
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>101000000
[[1,2,3,4,5,6,7,9],[8],[10]]=>[10,8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>111111010
[[1,2,8],[3,9],[4],[5],[6],[7]]=>[7,6,5,4,3,9,1,2,8]=>[8,2,1,9,3,4,5,6,7]=>[3,2,5,6,7,8,9,1,4]=>10000010
[[1,7],[2,8],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,8,1,7]=>[7,1,8,2,3,4,5,6,9]=>[2,4,5,6,7,8,1,3,9]=>00000100
[[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,9,3]=>[7,6,9,5,4,3,2,1,8]=>10111110
[[1,2,4,5,6,7,8,9],[3,10]]=>[3,10,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,10,3]=>[8,7,10,6,5,4,3,2,1,9]=>101111110
[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,9,1,2]=>[2,1,9,3,4,5,6,7,8]=>[2,1,4,5,6,7,8,9,3]=>10000001
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,10,1,2]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,4,5,6,7,8,9,10,3]=>100000001
[[1,2,3],[4,9],[5],[6],[7],[8]]=>[8,7,6,5,4,9,1,2,3]=>[3,2,1,9,4,5,6,7,8]=>[3,2,1,5,6,7,8,9,4]=>11000001
[[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,7,8]=>[6,5,4,3,2,1,8,9,7]=>11111001
[[1,2,3,4,5,6,7],[8,10],[9]]=>[9,8,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,8,9]=>[7,6,5,4,3,2,1,9,10,8]=>111111001
[[1,3,5,9],[2,4,6,10],[7,11],[8,12]]=>[8,12,7,11,2,4,6,10,1,3,5,9]=>[9,5,3,1,10,6,4,2,11,7,12,8]=>[4,8,3,7,2,6,10,12,1,5,9,11]=>01010001000
[[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[9,7,6,5,4,3,1,8,2]=>[7,9,6,5,4,3,2,8,1]=>01111101
[[1,2,3,4,5,7],[6,9],[8]]=>[8,6,9,1,2,3,4,5,7]=>[7,5,4,3,2,1,9,6,8]=>[6,5,4,3,2,8,1,9,7]=>11110101
[[1,2,3,4,5,6,8],[7,10],[9]]=>[9,7,10,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,10,7,9]=>[7,6,5,4,3,2,9,1,10,8]=>111110101
[[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,9,6]=>[7,6,5,4,3,9,2,1,8]=>11110110
[[1,3,4,5,6,7,8,10],[2],[9]]=>[9,2,1,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,1,2,9]=>[8,9,7,6,5,4,3,2,10,1]=>011111101
[[1,3,6,7],[2,5,10],[4,9],[8]]=>[8,4,9,2,5,10,1,3,6,7]=>[7,6,3,1,10,5,2,9,4,8]=>[4,7,3,9,6,2,1,10,8,5]=>010111011
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
inverse
Description
Sends a permutation to its inverse.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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