Identifier
Mp00085:
Standard tableaux
—Schützenberger involution⟶
Standard tableaux
Mp00155: Standard tableaux —promotion⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00155: Standard tableaux —promotion⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-2
[[1]]=>[[1]]=>[[1]]=>
[[1,2]]=>[[1,2]]=>[[1,2]]=>0
[[1],[2]]=>[[1],[2]]=>[[1],[2]]=>1
[[1,2,3]]=>[[1,2,3]]=>[[1,2,3]]=>00
[[1,3],[2]]=>[[1,2],[3]]=>[[1,3],[2]]=>10
[[1,2],[3]]=>[[1,3],[2]]=>[[1,2],[3]]=>01
[[1],[2],[3]]=>[[1],[2],[3]]=>[[1],[2],[3]]=>11
[[1,2,3,4]]=>[[1,2,3,4]]=>[[1,2,3,4]]=>000
[[1,3,4],[2]]=>[[1,2,3],[4]]=>[[1,3,4],[2]]=>100
[[1,2,4],[3]]=>[[1,2,4],[3]]=>[[1,2,3],[4]]=>001
[[1,2,3],[4]]=>[[1,3,4],[2]]=>[[1,2,4],[3]]=>010
[[1,3],[2,4]]=>[[1,3],[2,4]]=>[[1,2],[3,4]]=>010
[[1,2],[3,4]]=>[[1,2],[3,4]]=>[[1,3],[2,4]]=>101
[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[[1,3],[2],[4]]=>101
[[1,3],[2],[4]]=>[[1,3],[2],[4]]=>[[1,4],[2],[3]]=>110
[[1,2],[3],[4]]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>011
[[1],[2],[3],[4]]=>[[1],[2],[3],[4]]=>[[1],[2],[3],[4]]=>111
[[1,2,3,4,5]]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]]=>0000
[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]=>1000
[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[[1,2,3,4],[5]]=>0001
[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>0010
[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]=>[[1,2,4,5],[3]]=>0100
[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]=>1010
[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>[[1,3,4],[2,5]]=>1001
[[1,3,4],[2,5]]=>[[1,3,4],[2,5]]=>[[1,2,5],[3,4]]=>0100
[[1,2,4],[3,5]]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>0101
[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>0010
[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[[1,3,4],[2],[5]]=>1001
[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]=>1010
[[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]=>[[1,2,3],[4],[5]]=>0011
[[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[[1,4,5],[2],[3]]=>1100
[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>0101
[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]=>[[1,2,5],[3],[4]]=>0110
[[1,4],[2,5],[3]]=>[[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]=>1101
[[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]=>1010
[[1,2],[3,5],[4]]=>[[1,2],[3,5],[4]]=>[[1,3],[2,4],[5]]=>1011
[[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]=>[[1,2],[3,5],[4]]=>0110
[[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>0101
[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[[1,3],[2],[4],[5]]=>1011
[[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>1101
[[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>[[1,5],[2],[3],[4]]=>1110
[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>0111
[[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]=>1111
[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>00000
[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]=>10000
[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]=>[[1,2,3,4,5],[6]]=>00001
[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]=>[[1,2,3,4,6],[5]]=>00010
[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]=>[[1,2,3,5,6],[4]]=>00100
[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]=>[[1,2,4,5,6],[3]]=>01000
[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]=>[[1,3,4,6],[2,5]]=>10010
[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[[1,3,4,5],[2,6]]=>10001
[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>[[1,3,5,6],[2,4]]=>10100
[[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]=>[[1,2,3,5],[4,6]]=>00101
[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]=>[[1,2,3,4],[5,6]]=>00010
[[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]=>[[1,2,5,6],[3,4]]=>01000
[[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>01001
[[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]=>[[1,2,4,6],[3,5]]=>01010
[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]=>[[1,2,3,6],[4,5]]=>00100
[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[[1,3,4,5],[2],[6]]=>10001
[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[[1,3,4,6],[2],[5]]=>10010
[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[[1,2,3,4],[5],[6]]=>00011
[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[[1,3,5,6],[2],[4]]=>10100
[[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]=>[[1,2,3,5],[4],[6]]=>00101
[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>00110
[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[[1,4,5,6],[2],[3]]=>11000
[[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>01001
[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]=>[[1,2,4,6],[3],[5]]=>01010
[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]=>[[1,2,5,6],[3],[4]]=>01100
[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]=>[[1,2,4],[3,5,6]]=>01010
[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]=>01001
[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]=>[[1,2,3],[4,5,6]]=>00100
[[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]=>[[1,3,5],[2,4,6]]=>10101
[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]=>[[1,3,4],[2,5,6]]=>10010
[[1,4,6],[2,5],[3]]=>[[1,2,4],[3,5],[6]]=>[[1,3,5],[2,6],[4]]=>10101
[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[[1,3,4],[2,6],[5]]=>10010
[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[[1,3,4],[2,5],[6]]=>10011
[[1,3,6],[2,4],[5]]=>[[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]=>10110
[[1,2,6],[3,4],[5]]=>[[1,2,4],[3,6],[5]]=>[[1,3,5],[2,4],[6]]=>10101
[[1,4,5],[2,6],[3]]=>[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]=>11001
[[1,3,5],[2,6],[4]]=>[[1,3,5],[2,4],[6]]=>[[1,4,6],[2,5],[3]]=>11010
[[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]=>[[1,2,4],[3,5],[6]]=>01011
[[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[[1,3,6],[2,5],[4]]=>10100
[[1,2,4],[3,6],[5]]=>[[1,2,6],[3,4],[5]]=>[[1,2,3],[4,5],[6]]=>00101
[[1,2,3],[4,6],[5]]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>00110
[[1,3,5],[2,4],[6]]=>[[1,3,5],[2,6],[4]]=>[[1,2,6],[3,4],[5]]=>01010
[[1,2,5],[3,4],[6]]=>[[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>01001
[[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]=>[[1,2,6],[3,5],[4]]=>01100
[[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]=>[[1,2,5],[3,6],[4]]=>01101
[[1,2,3],[4,5],[6]]=>[[1,3,6],[2,5],[4]]=>[[1,2,4],[3,6],[5]]=>01010
[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[[1,3,4],[2],[5],[6]]=>10011
[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[[1,3,5],[2],[4],[6]]=>10101
[[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]=>10110
[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]=>[[1,2,3],[4],[5],[6]]=>00111
[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>11001
[[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[[1,4,6],[2],[3],[5]]=>11010
[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]=>[[1,2,4],[3],[5],[6]]=>01011
[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[[1,5,6],[2],[3],[4]]=>11100
[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]=>[[1,2,5],[3],[4],[6]]=>01101
[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>01110
[[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]]=>[[1,2],[3,5],[4,6]]=>01101
[[1,3],[2,5],[4,6]]=>[[1,3],[2,5],[4,6]]=>[[1,2],[3,4],[5,6]]=>01010
[[1,2],[3,5],[4,6]]=>[[1,3],[2,4],[5,6]]=>[[1,4],[2,5],[3,6]]=>11011
[[1,3],[2,4],[5,6]]=>[[1,2],[3,5],[4,6]]=>[[1,3],[2,4],[5,6]]=>10110
[[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]]=>[[1,3],[2,5],[4,6]]=>10101
[[1,5],[2,6],[3],[4]]=>[[1,3],[2,4],[5],[6]]=>[[1,4],[2,5],[3],[6]]=>11011
[[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[[1,3],[2,5],[4],[6]]=>10101
[[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>10110
[[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[[1,3],[2,4],[5],[6]]=>10111
[[1,4],[2,5],[3],[6]]=>[[1,4],[2,5],[3],[6]]=>[[1,5],[2,6],[3],[4]]=>11101
[[1,3],[2,5],[4],[6]]=>[[1,3],[2,5],[4],[6]]=>[[1,4],[2,6],[3],[5]]=>11010
[[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>[[1,2],[3,4],[5],[6]]=>01011
[[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]=>[[1,2],[3,6],[4],[5]]=>01110
[[1,2],[3,4],[5],[6]]=>[[1,4],[2,6],[3],[5]]=>[[1,2],[3,5],[4],[6]]=>01101
[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[[1,3],[2],[4],[5],[6]]=>10111
[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>11011
[[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>11101
[[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>[[1,6],[2],[3],[4],[5]]=>11110
[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>01111
[[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]]=>11111
[[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]=>000000
[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]=>100000
[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]=>[[1,2,3,4,5,6],[7]]=>000001
[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,4,5,7],[6]]=>000010
[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>000100
[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,5,6,7],[4]]=>001000
[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]=>[[1,2,4,5,6,7],[3]]=>010000
[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]=>[[1,3,4,5,7],[2,6]]=>100010
[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[[1,3,4,5,6],[2,7]]=>100001
[[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]=>100100
[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]=>[[1,2,3,4,6],[5,7]]=>000101
[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,4,5],[6,7]]=>000010
[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]=>[[1,3,5,6,7],[2,4]]=>101000
[[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]=>[[1,2,3,5,6],[4,7]]=>001001
[[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]=>001010
[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]=>000100
[[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]=>[[1,2,5,6,7],[3,4]]=>010000
[[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]=>010001
[[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]=>[[1,2,4,5,7],[3,6]]=>010010
[[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]=>[[1,2,4,6,7],[3,5]]=>010100
[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,6,7],[4,5]]=>001000
[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[[1,3,4,5,6],[2],[7]]=>100001
[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,4,5,7],[2],[6]]=>100010
[[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,3,4,5],[6],[7]]=>000011
[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]=>100100
[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,3,4,6],[5],[7]]=>000101
[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,4,7],[5],[6]]=>000110
[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[[1,3,5,6,7],[2],[4]]=>101000
[[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]=>[[1,2,3,5,6],[4],[7]]=>001001
[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>001010
[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]=>[[1,2,3,6,7],[4],[5]]=>001100
[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[[1,4,5,6,7],[2],[3]]=>110000
[[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>010001
[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,4,5,7],[3],[6]]=>010010
[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,4,6,7],[3],[5]]=>010100
[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,5,6,7],[3],[4]]=>011000
[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]=>101010
[[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]=>[[1,3,5,6],[2,4,7]]=>101001
[[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]=>100100
[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]=>[[1,3,4,6],[2,5,7]]=>100101
[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>[[1,3,4,5],[2,6,7]]=>100010
[[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]=>[[1,2,5,7],[3,4,6]]=>010010
[[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]=>010001
[[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]=>[[1,2,4,7],[3,5,6]]=>010100
[[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>010101
[[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]=>[[1,2,4,5],[3,6,7]]=>010010
[[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]=>[[1,2,3,7],[4,5,6]]=>001000
[[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]=>[[1,2,3,6],[4,5,7]]=>001001
[[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]=>001010
[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>000100
[[1,4,6,7],[2,5],[3]]=>[[1,2,3,5],[4,6],[7]]=>[[1,3,4,6],[2,7],[5]]=>100101
[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[[1,3,4,5],[2,7],[6]]=>100010
[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[[1,3,4,5],[2,6],[7]]=>100011
[[1,3,6,7],[2,4],[5]]=>[[1,2,3,6],[4,7],[5]]=>[[1,3,4,7],[2,5],[6]]=>100110
[[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[[1,3,4,6],[2,5],[7]]=>100101
[[1,4,5,7],[2,6],[3]]=>[[1,2,4,5],[3,6],[7]]=>[[1,3,5,6],[2,7],[4]]=>101001
[[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]=>101010
[[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]=>[[1,2,3,5],[4,6],[7]]=>001011
[[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[[1,3,4,7],[2,6],[5]]=>100100
[[1,2,4,7],[3,6],[5]]=>[[1,2,3,7],[4,5],[6]]=>[[1,2,3,4],[5,6],[7]]=>000101
[[1,2,3,7],[4,6],[5]]=>[[1,2,3,7],[4,6],[5]]=>[[1,2,3,4],[5,7],[6]]=>000110
[[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]=>101010
[[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[[1,3,5,6],[2,4],[7]]=>101001
[[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]=>[[1,3,6,7],[2,4],[5]]=>101100
[[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]=>[[1,2,3,6],[4,7],[5]]=>001101
[[1,2,3,7],[4,5],[6]]=>[[1,2,4,7],[3,6],[5]]=>[[1,2,3,5],[4,7],[6]]=>001010
[[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]=>110001
[[1,3,5,6],[2,7],[4]]=>[[1,3,4,6],[2,5],[7]]=>[[1,4,5,7],[2,6],[3]]=>110010
[[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]=>[[1,2,4,5],[3,6],[7]]=>010011
[[1,3,4,6],[2,7],[5]]=>[[1,3,5,6],[2,4],[7]]=>[[1,4,6,7],[2,5],[3]]=>110100
[[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,5],[7]]=>010101
[[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]=>[[1,2,4,7],[3,5],[6]]=>010110
[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[[1,3,6,7],[2,5],[4]]=>101000
[[1,2,4,5],[3,7],[6]]=>[[1,2,5,7],[3,4],[6]]=>[[1,2,3,6],[4,5],[7]]=>001001
[[1,2,3,5],[4,7],[6]]=>[[1,2,6,7],[3,4],[5]]=>[[1,2,3,7],[4,5],[6]]=>001010
[[1,2,3,4],[5,7],[6]]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,7],[4,6],[5]]=>001100
[[1,3,5,6],[2,4],[7]]=>[[1,3,4,6],[2,7],[5]]=>[[1,2,5,7],[3,4],[6]]=>010010
[[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>010001
[[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]=>[[1,2,6,7],[3,4],[5]]=>010100
[[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,7],[5]]=>010101
[[1,2,3,6],[4,5],[7]]=>[[1,3,4,7],[2,6],[5]]=>[[1,2,4,5],[3,7],[6]]=>010010
[[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]=>[[1,2,6,7],[3,5],[4]]=>011000
[[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]=>[[1,2,5,6],[3,7],[4]]=>011001
[[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]=>[[1,2,5,7],[3,6],[4]]=>011010
[[1,2,3,4],[5,6],[7]]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,4,7],[3,6],[5]]=>010100
[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[[1,3,4,5],[2],[6],[7]]=>100011
[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[[1,3,4,6],[2],[5],[7]]=>100101
[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,4,7],[2],[5],[6]]=>100110
[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,3,4],[5],[6],[7]]=>000111
[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[[1,3,5,6],[2],[4],[7]]=>101001
[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]=>101010
[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,3,5],[4],[6],[7]]=>001011
[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,6,7],[2],[4],[5]]=>101100
[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,3,6],[4],[5],[7]]=>001101
[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>001110
[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>110001
[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[[1,4,5,7],[2],[3],[6]]=>110010
[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,4,5],[3],[6],[7]]=>010011
[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[[1,4,6,7],[2],[3],[5]]=>110100
[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>010101
[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,4,7],[3],[5],[6]]=>010110
[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[[1,5,6,7],[2],[3],[4]]=>111000
[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,5,6],[3],[4],[7]]=>011001
[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,5,7],[3],[4],[6]]=>011010
[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,6,7],[3],[4],[5]]=>011100
[[1,4,6],[2,5,7],[3]]=>[[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]=>110101
[[1,3,6],[2,5,7],[4]]=>[[1,3,4],[2,5,6],[7]]=>[[1,4,5],[2,6,7],[3]]=>110010
[[1,2,6],[3,5,7],[4]]=>[[1,3,4],[2,5,7],[6]]=>[[1,2,5],[3,4,6],[7]]=>010011
[[1,3,6],[2,4,7],[5]]=>[[1,3,6],[2,4,7],[5]]=>[[1,2,4],[3,5,7],[6]]=>010110
[[1,2,6],[3,4,7],[5]]=>[[1,3,5],[2,4,7],[6]]=>[[1,2,4],[3,5,6],[7]]=>010101
[[1,4,5],[2,6,7],[3]]=>[[1,2,5],[3,4,6],[7]]=>[[1,3,6],[2,5,7],[4]]=>101001
[[1,3,5],[2,6,7],[4]]=>[[1,2,4],[3,5,6],[7]]=>[[1,3,5],[2,6,7],[4]]=>101010
[[1,2,5],[3,6,7],[4]]=>[[1,2,4],[3,5,7],[6]]=>[[1,3,5],[2,4,6],[7]]=>101011
[[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]=>100100
[[1,2,4],[3,6,7],[5]]=>[[1,2,3],[4,5,7],[6]]=>[[1,3,4],[2,5,6],[7]]=>100101
[[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[[1,3,4],[2,5,7],[6]]=>100110
[[1,3,5],[2,4,7],[6]]=>[[1,2,6],[3,4,7],[5]]=>[[1,2,3],[4,5,7],[6]]=>001010
[[1,2,5],[3,4,7],[6]]=>[[1,2,5],[3,4,7],[6]]=>[[1,2,3],[4,5,6],[7]]=>001001
[[1,3,4],[2,5,7],[6]]=>[[1,2,6],[3,5,7],[4]]=>[[1,2,3],[4,6,7],[5]]=>001100
[[1,2,4],[3,5,7],[6]]=>[[1,2,5],[3,6,7],[4]]=>[[1,3,6],[2,4,7],[5]]=>101101
[[1,2,3],[4,5,7],[6]]=>[[1,2,4],[3,6,7],[5]]=>[[1,3,5],[2,4,7],[6]]=>101010
[[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]=>[[1,2,5],[3,6,7],[4]]=>011010
[[1,2,5],[3,4,6],[7]]=>[[1,4,5],[2,6,7],[3]]=>[[1,2,6],[3,5,7],[4]]=>011001
[[1,3,4],[2,5,6],[7]]=>[[1,3,6],[2,5,7],[4]]=>[[1,2,4],[3,6,7],[5]]=>010100
[[1,2,4],[3,5,6],[7]]=>[[1,3,5],[2,6,7],[4]]=>[[1,2,6],[3,4,7],[5]]=>010101
[[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]=>[[1,2,5],[3,4,7],[6]]=>010010
[[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>[[1,3,6],[2,4],[5,7]]=>101101
[[1,3,7],[2,5],[4,6]]=>[[1,2,4],[3,6],[5,7]]=>[[1,3,5],[2,4],[6,7]]=>101010
[[1,2,7],[3,5],[4,6]]=>[[1,2,4],[3,5],[6,7]]=>[[1,3,5],[2,6],[4,7]]=>101011
[[1,3,7],[2,4],[5,6]]=>[[1,2,3],[4,6],[5,7]]=>[[1,3,4],[2,5],[6,7]]=>100110
[[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[[1,3,4],[2,6],[5,7]]=>100101
[[1,4,6],[2,5],[3,7]]=>[[1,3,5],[2,6],[4,7]]=>[[1,2,6],[3,4],[5,7]]=>010101
[[1,3,6],[2,5],[4,7]]=>[[1,3,4],[2,6],[5,7]]=>[[1,2,5],[3,4],[6,7]]=>010010
[[1,2,6],[3,5],[4,7]]=>[[1,3,4],[2,5],[6,7]]=>[[1,4,5],[2,6],[3,7]]=>110011
[[1,3,6],[2,4],[5,7]]=>[[1,3,6],[2,4],[5,7]]=>[[1,4,7],[2,5],[3,6]]=>110110
[[1,2,6],[3,4],[5,7]]=>[[1,3,5],[2,4],[6,7]]=>[[1,4,6],[2,5],[3,7]]=>110101
[[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]=>[[1,2,6],[3,5],[4,7]]=>011001
[[1,3,5],[2,6],[4,7]]=>[[1,4,6],[2,5],[3,7]]=>[[1,2,7],[3,5],[4,6]]=>011010
[[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>011011
[[1,3,4],[2,6],[5,7]]=>[[1,3,6],[2,5],[4,7]]=>[[1,2,7],[3,4],[5,6]]=>010100
[[1,2,4],[3,6],[5,7]]=>[[1,3,7],[2,5],[4,6]]=>[[1,2,4],[3,6],[5,7]]=>010101
[[1,2,3],[4,6],[5,7]]=>[[1,3,7],[2,4],[5,6]]=>[[1,2,4],[3,5],[6,7]]=>010110
[[1,3,5],[2,4],[6,7]]=>[[1,2,6],[3,4],[5,7]]=>[[1,3,7],[2,5],[4,6]]=>101010
[[1,2,5],[3,4],[6,7]]=>[[1,2,5],[3,4],[6,7]]=>[[1,3,6],[2,5],[4,7]]=>101001
[[1,3,4],[2,5],[6,7]]=>[[1,2,6],[3,5],[4,7]]=>[[1,3,7],[2,4],[5,6]]=>101100
[[1,2,4],[3,5],[6,7]]=>[[1,2,7],[3,5],[4,6]]=>[[1,2,3],[4,6],[5,7]]=>001101
[[1,2,3],[4,5],[6,7]]=>[[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>001010
[[1,5,7],[2,6],[3],[4]]=>[[1,2,4],[3,5],[6],[7]]=>[[1,3,5],[2,6],[4],[7]]=>101011
[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[[1,3,4],[2,6],[5],[7]]=>100101
[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[[1,3,4],[2,7],[5],[6]]=>100110
[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[[1,3,4],[2,5],[6],[7]]=>100111
[[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]=>[[1,3,6],[2,7],[4],[5]]=>101101
[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>101010
[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[[1,3,5],[2,4],[6],[7]]=>101011
[[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]=>101110
[[1,2,7],[3,4],[5],[6]]=>[[1,2,5],[3,7],[4],[6]]=>[[1,3,6],[2,4],[5],[7]]=>101101
[[1,5,6],[2,7],[3],[4]]=>[[1,3,4],[2,5],[6],[7]]=>[[1,4,5],[2,6],[3],[7]]=>110011
[[1,4,6],[2,7],[3],[5]]=>[[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,5],[3],[7]]=>110101
[[1,3,6],[2,7],[4],[5]]=>[[1,3,6],[2,4],[5],[7]]=>[[1,4,7],[2,5],[3],[6]]=>110110
[[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6],[7]]=>010111
[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[[1,3,6],[2,5],[4],[7]]=>101001
[[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[[1,3,7],[2,5],[4],[6]]=>101010
[[1,2,5],[3,7],[4],[6]]=>[[1,2,7],[3,4],[5],[6]]=>[[1,2,3],[4,5],[6],[7]]=>001011
[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,7],[2,6],[4],[5]]=>101100
[[1,2,4],[3,7],[5],[6]]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,3],[4,6],[5],[7]]=>001101
[[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>001110
[[1,4,6],[2,5],[3],[7]]=>[[1,3,5],[2,6],[4],[7]]=>[[1,4,6],[2,7],[3],[5]]=>110101
[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[[1,4,5],[2,7],[3],[6]]=>110010
[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,5],[3,4],[6],[7]]=>010011
[[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]=>[[1,2,7],[3,4],[5],[6]]=>010110
[[1,2,6],[3,4],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>010101
[[1,4,5],[2,6],[3],[7]]=>[[1,4,5],[2,6],[3],[7]]=>[[1,5,6],[2,7],[3],[4]]=>111001
[[1,3,5],[2,6],[4],[7]]=>[[1,4,6],[2,5],[3],[7]]=>[[1,5,7],[2,6],[3],[4]]=>111010
[[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]=>011011
[[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[[1,4,7],[2,6],[3],[5]]=>110100
[[1,2,4],[3,6],[5],[7]]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>010101
[[1,2,3],[4,6],[5],[7]]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,4],[3,7],[5],[6]]=>010110
[[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]=>[[1,2,7],[3,5],[4],[6]]=>011010
[[1,2,5],[3,4],[6],[7]]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,6],[3,5],[4],[7]]=>011001
[[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]=>[[1,2,7],[3,6],[4],[5]]=>011100
[[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]=>[[1,2,6],[3,7],[4],[5]]=>011101
[[1,2,3],[4,5],[6],[7]]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,5],[3,7],[4],[6]]=>011010
[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>100111
[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>101011
[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>101101
[[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]=>101110
[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7]]=>001111
[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>110011
[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>110101
[[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[[1,4,7],[2],[3],[5],[6]]=>110110
[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>010111
[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>111001
[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,5,7],[2],[3],[4],[6]]=>111010
[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>011011
[[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>111100
[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>011101
[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,7],[3],[4],[5],[6]]=>011110
[[1,5],[2,6],[3,7],[4]]=>[[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]=>111011
[[1,4],[2,6],[3,7],[5]]=>[[1,3],[2,5],[4,6],[7]]=>[[1,4],[2,6],[3,7],[5]]=>110101
[[1,3],[2,6],[4,7],[5]]=>[[1,3],[2,4],[5,6],[7]]=>[[1,4],[2,5],[3,7],[6]]=>110110
[[1,2],[3,6],[4,7],[5]]=>[[1,3],[2,4],[5,7],[6]]=>[[1,4],[2,5],[3,6],[7]]=>110111
[[1,4],[2,5],[3,7],[6]]=>[[1,2],[3,5],[4,6],[7]]=>[[1,3],[2,6],[4,7],[5]]=>101101
[[1,3],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]=>101010
[[1,2],[3,5],[4,7],[6]]=>[[1,2],[3,4],[5,7],[6]]=>[[1,3],[2,5],[4,6],[7]]=>101011
[[1,3],[2,4],[5,7],[6]]=>[[1,2],[3,6],[4,7],[5]]=>[[1,3],[2,4],[5,7],[6]]=>101110
[[1,2],[3,4],[5,7],[6]]=>[[1,2],[3,5],[4,7],[6]]=>[[1,3],[2,4],[5,6],[7]]=>101101
[[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]=>[[1,2],[3,6],[4,7],[5]]=>011101
[[1,3],[2,5],[4,6],[7]]=>[[1,4],[2,6],[3,7],[5]]=>[[1,2],[3,5],[4,7],[6]]=>011010
[[1,2],[3,5],[4,6],[7]]=>[[1,4],[2,5],[3,7],[6]]=>[[1,2],[3,5],[4,6],[7]]=>011011
[[1,3],[2,4],[5,6],[7]]=>[[1,3],[2,6],[4,7],[5]]=>[[1,2],[3,4],[5,7],[6]]=>010110
[[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>010101
[[1,6],[2,7],[3],[4],[5]]=>[[1,3],[2,4],[5],[6],[7]]=>[[1,4],[2,5],[3],[6],[7]]=>110111
[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>101011
[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>101101
[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>101110
[[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[[1,3],[2,4],[5],[6],[7]]=>101111
[[1,5],[2,6],[3],[4],[7]]=>[[1,4],[2,5],[3],[6],[7]]=>[[1,5],[2,6],[3],[4],[7]]=>111011
[[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>110101
[[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>110110
[[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>010111
[[1,4],[2,5],[3],[6],[7]]=>[[1,5],[2,6],[3],[4],[7]]=>[[1,6],[2,7],[3],[4],[5]]=>111101
[[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>[[1,5],[2,7],[3],[4],[6]]=>111010
[[1,2],[3,5],[4],[6],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>011011
[[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]=>[[1,2],[3,7],[4],[5],[6]]=>011110
[[1,2],[3,4],[5],[6],[7]]=>[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>011101
[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>101111
[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>110111
[[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>111011
[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>111101
[[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>111110
[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>011111
[[1],[2],[3],[4],[5],[6],[7]]=>[[1],[2],[3],[4],[5],[6],[7]]=>[[1],[2],[3],[4],[5],[6],[7]]=>111111
[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>0000000
[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]=>1000000
[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]=>[[1,2,3,4,5,6,7],[8]]=>0000001
[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,4,5,6,8],[7]]=>0000010
[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,5,7,8],[6]]=>0000100
[[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,6,7,8],[5]]=>0001000
[[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,5,6,7,8],[4]]=>0010000
[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,4,5,6,7,8],[3]]=>0100000
[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]]=>[[1,3,4,5,6,8],[2,7]]=>1000010
[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[[1,3,4,5,6,7],[2,8]]=>1000001
[[1,3,4,6,7,8],[2,5]]=>[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,5,7,8],[2,6]]=>1000100
[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]=>[[1,2,3,4,5,7],[6,8]]=>0000101
[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,4,5,6],[7,8]]=>0000010
[[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,6,7,8],[2,5]]=>1001000
[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]=>[[1,2,3,4,6,7],[5,8]]=>0001001
[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,5,7,8],[4,6]]=>[[1,2,3,4,6,8],[5,7]]=>0001010
[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,7,8],[5,6]]=>[[1,2,3,4,5,8],[6,7]]=>0000100
[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]=>[[1,3,5,6,7,8],[2,4]]=>1010000
[[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]=>[[1,2,3,5,6,7],[4,8]]=>0010001
[[1,2,3,5,6,8],[4,7]]=>[[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]=>0010010
[[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]=>[[1,2,3,5,7,8],[4,6]]=>0010100
[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,7,8],[5,6]]=>0001000
[[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]=>[[1,2,5,6,7,8],[3,4]]=>0100000
[[1,2,4,5,6,7],[3,8]]=>[[1,3,4,5,6,8],[2,7]]=>[[1,2,4,5,6,7],[3,8]]=>0100001
[[1,2,3,5,6,7],[4,8]]=>[[1,3,4,5,7,8],[2,6]]=>[[1,2,4,5,6,8],[3,7]]=>0100010
[[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]=>[[1,2,4,5,7,8],[3,6]]=>0100100
[[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,4,6,7,8],[3,5]]=>0101000
[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,6,7,8],[4,5]]=>0010000
[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,3,4,5,6,7],[2],[8]]=>1000001
[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]=>[[1,3,4,5,6,8],[2],[7]]=>1000010
[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,4,5,8],[6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>0000011
[[1,3,4,6,7,8],[2],[5]]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,5,7,8],[2],[6]]=>1000100
[[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,3,4,5,7],[6],[8]]=>0000101
[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,4,5,8],[6],[7]]=>0000110
[[1,3,4,5,7,8],[2],[6]]=>[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,6,7,8],[2],[5]]=>1001000
[[1,2,4,5,7,8],[3],[6]]=>[[1,2,3,5,6,8],[4],[7]]=>[[1,2,3,4,6,7],[5],[8]]=>0001001
[[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,4,6,8],[5],[7]]=>0001010
[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>0001100
[[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]=>[[1,3,5,6,7,8],[2],[4]]=>1010000
[[1,2,4,5,6,8],[3],[7]]=>[[1,2,4,5,6,8],[3],[7]]=>[[1,2,3,5,6,7],[4],[8]]=>0010001
[[1,2,3,5,6,8],[4],[7]]=>[[1,2,4,5,7,8],[3],[6]]=>[[1,2,3,5,6,8],[4],[7]]=>0010010
[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,5,7,8],[4],[6]]=>0010100
[[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,6,7,8],[4],[5]]=>0011000
[[1,3,4,5,6,7],[2],[8]]=>[[1,3,4,5,6,7],[2],[8]]=>[[1,4,5,6,7,8],[2],[3]]=>1100000
[[1,2,4,5,6,7],[3],[8]]=>[[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]=>0100001
[[1,2,3,5,6,7],[4],[8]]=>[[1,3,4,5,7,8],[2],[6]]=>[[1,2,4,5,6,8],[3],[7]]=>0100010
[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]=>[[1,2,4,5,7,8],[3],[6]]=>0100100
[[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,4,6,7,8],[3],[5]]=>0101000
[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,5,6,7,8],[3],[4]]=>0110000
[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]]=>[[1,3,4,6,8],[2,5,7]]=>1001010
[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,5,6],[4,7,8]]=>[[1,3,4,6,7],[2,5,8]]=>1001001
[[1,3,4,7,8],[2,5,6]]=>[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,5,8],[2,6,7]]=>1000100
[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,4,6],[5,7,8]]=>[[1,3,4,5,7],[2,6,8]]=>1000101
[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]=>[[1,3,4,5,6],[2,7,8]]=>1000010
[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]=>1010010
[[1,2,5,6,8],[3,4,7]]=>[[1,2,4,5,6],[3,7,8]]=>[[1,3,5,6,7],[2,4,8]]=>1010001
[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,6,7],[3,5,8]]=>[[1,3,5,7,8],[2,4,6]]=>1010100
[[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]=>[[1,2,3,5,7],[4,6,8]]=>0010101
[[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,5,6],[4,7,8]]=>0010010
[[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,7,8],[2,5,6]]=>1001000
[[1,2,4,5,8],[3,6,7]]=>[[1,2,3,6,8],[4,5,7]]=>[[1,2,3,4,7],[5,6,8]]=>0001001
[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,5,8],[4,6,7]]=>[[1,2,3,4,6],[5,7,8]]=>0001010
[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,5],[6,7,8]]=>0000100
[[1,3,5,6,7],[2,4,8]]=>[[1,3,4,5,7],[2,6,8]]=>[[1,2,5,6,8],[3,4,7]]=>0100010
[[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]=>0100001
[[1,3,4,6,7],[2,5,8]]=>[[1,3,4,6,7],[2,5,8]]=>[[1,2,5,7,8],[3,4,6]]=>0100100
[[1,2,4,6,7],[3,5,8]]=>[[1,3,4,6,8],[2,5,7]]=>[[1,2,4,5,7],[3,6,8]]=>0100101
[[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]=>[[1,2,4,5,6],[3,7,8]]=>0100010
[[1,3,4,5,7],[2,6,8]]=>[[1,3,5,6,7],[2,4,8]]=>[[1,2,4,7,8],[3,5,6]]=>0101000
[[1,2,4,5,7],[3,6,8]]=>[[1,3,5,6,8],[2,4,7]]=>[[1,2,4,6,7],[3,5,8]]=>0101001
[[1,2,3,5,7],[4,6,8]]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,4,6,8],[3,5,7]]=>0101010
[[1,2,3,4,7],[5,6,8]]=>[[1,3,4,7,8],[2,5,6]]=>[[1,2,4,5,8],[3,6,7]]=>0100100
[[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]=>[[1,2,3,7,8],[4,5,6]]=>0010000
[[1,2,4,5,6],[3,7,8]]=>[[1,2,5,6,8],[3,4,7]]=>[[1,2,3,6,7],[4,5,8]]=>0010001
[[1,2,3,5,6],[4,7,8]]=>[[1,2,5,7,8],[3,4,6]]=>[[1,2,3,6,8],[4,5,7]]=>0010010
[[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]=>[[1,2,3,5,8],[4,6,7]]=>0010100
[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,8],[5,6,7]]=>0001000
[[1,4,6,7,8],[2,5],[3]]=>[[1,2,3,4,6],[5,7],[8]]=>[[1,3,4,5,7],[2,8],[6]]=>1000101
[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[[1,3,4,5,6],[2,8],[7]]=>1000010
[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[[1,3,4,5,6],[2,7],[8]]=>1000011
[[1,3,6,7,8],[2,4],[5]]=>[[1,2,3,4,7],[5,8],[6]]=>[[1,3,4,5,8],[2,6],[7]]=>1000110
[[1,2,6,7,8],[3,4],[5]]=>[[1,2,3,4,6],[5,8],[7]]=>[[1,3,4,5,7],[2,6],[8]]=>1000101
[[1,4,5,7,8],[2,6],[3]]=>[[1,2,3,5,6],[4,7],[8]]=>[[1,3,4,6,7],[2,8],[5]]=>1001001
[[1,3,5,7,8],[2,6],[4]]=>[[1,2,3,5,7],[4,6],[8]]=>[[1,3,4,6,8],[2,7],[5]]=>1001010
[[1,2,5,7,8],[3,6],[4]]=>[[1,2,3,5,8],[4,6],[7]]=>[[1,2,3,4,6],[5,7],[8]]=>0001011
[[1,3,4,7,8],[2,6],[5]]=>[[1,2,3,4,7],[5,6],[8]]=>[[1,3,4,5,8],[2,7],[6]]=>1000100
[[1,2,4,7,8],[3,6],[5]]=>[[1,2,3,4,8],[5,6],[7]]=>[[1,2,3,4,5],[6,7],[8]]=>0000101
[[1,2,3,7,8],[4,6],[5]]=>[[1,2,3,4,8],[5,7],[6]]=>[[1,2,3,4,5],[6,8],[7]]=>0000110
[[1,3,5,7,8],[2,4],[6]]=>[[1,2,3,5,7],[4,8],[6]]=>[[1,3,4,6,8],[2,5],[7]]=>1001010
[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,5,6],[4,8],[7]]=>[[1,3,4,6,7],[2,5],[8]]=>1001001
[[1,3,4,7,8],[2,5],[6]]=>[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]=>1001100
[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]=>[[1,2,3,4,7],[5,8],[6]]=>0001101
[[1,2,3,7,8],[4,5],[6]]=>[[1,2,3,5,8],[4,7],[6]]=>[[1,2,3,4,6],[5,8],[7]]=>0001010
[[1,4,5,6,8],[2,7],[3]]=>[[1,2,4,5,6],[3,7],[8]]=>[[1,3,5,6,7],[2,8],[4]]=>1010001
[[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]=>1010010
[[1,2,5,6,8],[3,7],[4]]=>[[1,2,4,5,8],[3,6],[7]]=>[[1,2,3,5,6],[4,7],[8]]=>0010011
[[1,3,4,6,8],[2,7],[5]]=>[[1,2,4,6,7],[3,5],[8]]=>[[1,3,5,7,8],[2,6],[4]]=>1010100
[[1,2,4,6,8],[3,7],[5]]=>[[1,2,4,6,8],[3,5],[7]]=>[[1,2,3,5,7],[4,6],[8]]=>0010101
[[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,5,8],[4,6],[7]]=>0010110
[[1,3,4,5,8],[2,7],[6]]=>[[1,2,3,6,7],[4,5],[8]]=>[[1,3,4,7,8],[2,6],[5]]=>1001000
[[1,2,4,5,8],[3,7],[6]]=>[[1,2,3,6,8],[4,5],[7]]=>[[1,2,3,4,7],[5,6],[8]]=>0001001
[[1,2,3,5,8],[4,7],[6]]=>[[1,2,3,7,8],[4,5],[6]]=>[[1,2,3,4,8],[5,6],[7]]=>0001010
[[1,2,3,4,8],[5,7],[6]]=>[[1,2,3,7,8],[4,6],[5]]=>[[1,2,3,4,8],[5,7],[6]]=>0001100
[[1,3,5,6,8],[2,4],[7]]=>[[1,2,4,5,7],[3,8],[6]]=>[[1,3,5,6,8],[2,4],[7]]=>1010010
[[1,2,5,6,8],[3,4],[7]]=>[[1,2,4,5,6],[3,8],[7]]=>[[1,3,5,6,7],[2,4],[8]]=>1010001
[[1,3,4,6,8],[2,5],[7]]=>[[1,2,4,6,7],[3,8],[5]]=>[[1,3,5,7,8],[2,4],[6]]=>1010100
[[1,2,4,6,8],[3,5],[7]]=>[[1,2,4,6,8],[3,7],[5]]=>[[1,2,3,5,7],[4,8],[6]]=>0010101
[[1,2,3,6,8],[4,5],[7]]=>[[1,2,4,5,8],[3,7],[6]]=>[[1,2,3,5,6],[4,8],[7]]=>0010010
[[1,3,4,5,8],[2,6],[7]]=>[[1,2,5,6,7],[3,8],[4]]=>[[1,3,6,7,8],[2,4],[5]]=>1011000
[[1,2,4,5,8],[3,6],[7]]=>[[1,2,5,6,8],[3,7],[4]]=>[[1,2,3,6,7],[4,8],[5]]=>0011001
[[1,2,3,5,8],[4,6],[7]]=>[[1,2,5,7,8],[3,6],[4]]=>[[1,2,3,6,8],[4,7],[5]]=>0011010
[[1,2,3,4,8],[5,6],[7]]=>[[1,2,4,7,8],[3,6],[5]]=>[[1,2,3,5,8],[4,7],[6]]=>0010100
[[1,4,5,6,7],[2,8],[3]]=>[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]=>1100001
[[1,3,5,6,7],[2,8],[4]]=>[[1,3,4,5,7],[2,6],[8]]=>[[1,4,5,6,8],[2,7],[3]]=>1100010
[[1,2,5,6,7],[3,8],[4]]=>[[1,3,4,5,8],[2,6],[7]]=>[[1,2,4,5,6],[3,7],[8]]=>0100011
[[1,3,4,6,7],[2,8],[5]]=>[[1,3,4,6,7],[2,5],[8]]=>[[1,4,5,7,8],[2,6],[3]]=>1100100
[[1,2,4,6,7],[3,8],[5]]=>[[1,3,4,6,8],[2,5],[7]]=>[[1,2,4,5,7],[3,6],[8]]=>0100101
[[1,2,3,6,7],[4,8],[5]]=>[[1,3,4,7,8],[2,5],[6]]=>[[1,2,4,5,8],[3,6],[7]]=>0100110
[[1,3,4,5,7],[2,8],[6]]=>[[1,3,5,6,7],[2,4],[8]]=>[[1,4,6,7,8],[2,5],[3]]=>1101000
[[1,2,4,5,7],[3,8],[6]]=>[[1,3,5,6,8],[2,4],[7]]=>[[1,2,4,6,7],[3,5],[8]]=>0101001
[[1,2,3,5,7],[4,8],[6]]=>[[1,3,5,7,8],[2,4],[6]]=>[[1,2,4,6,8],[3,5],[7]]=>0101010
[[1,2,3,4,7],[5,8],[6]]=>[[1,3,6,7,8],[2,4],[5]]=>[[1,2,4,7,8],[3,5],[6]]=>0101100
[[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>[[1,3,6,7,8],[2,5],[4]]=>1010000
[[1,2,4,5,6],[3,8],[7]]=>[[1,2,5,6,8],[3,4],[7]]=>[[1,2,3,6,7],[4,5],[8]]=>0010001
[[1,2,3,5,6],[4,8],[7]]=>[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,6,8],[4,5],[7]]=>0010010
[[1,2,3,4,6],[5,8],[7]]=>[[1,2,6,7,8],[3,4],[5]]=>[[1,2,3,7,8],[4,5],[6]]=>0010100
[[1,2,3,4,5],[6,8],[7]]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,7,8],[4,6],[5]]=>0011000
[[1,3,5,6,7],[2,4],[8]]=>[[1,3,4,5,7],[2,8],[6]]=>[[1,2,5,6,8],[3,4],[7]]=>0100010
[[1,2,5,6,7],[3,4],[8]]=>[[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>0100001
[[1,3,4,6,7],[2,5],[8]]=>[[1,3,4,6,7],[2,8],[5]]=>[[1,2,5,7,8],[3,4],[6]]=>0100100
[[1,2,4,6,7],[3,5],[8]]=>[[1,3,4,6,8],[2,7],[5]]=>[[1,2,4,5,7],[3,8],[6]]=>0100101
[[1,2,3,6,7],[4,5],[8]]=>[[1,3,4,5,8],[2,7],[6]]=>[[1,2,4,5,6],[3,8],[7]]=>0100010
[[1,3,4,5,7],[2,6],[8]]=>[[1,3,5,6,7],[2,8],[4]]=>[[1,2,6,7,8],[3,4],[5]]=>0101000
[[1,2,4,5,7],[3,6],[8]]=>[[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,6,7],[3,8],[5]]=>0101001
[[1,2,3,5,7],[4,6],[8]]=>[[1,3,5,7,8],[2,6],[4]]=>[[1,2,4,6,8],[3,7],[5]]=>0101010
[[1,2,3,4,7],[5,6],[8]]=>[[1,3,4,7,8],[2,6],[5]]=>[[1,2,4,5,8],[3,7],[6]]=>0100100
[[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]=>[[1,2,6,7,8],[3,5],[4]]=>0110000
[[1,2,4,5,6],[3,7],[8]]=>[[1,4,5,6,8],[2,7],[3]]=>[[1,2,5,6,7],[3,8],[4]]=>0110001
[[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]=>[[1,2,5,6,8],[3,7],[4]]=>0110010
[[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]=>[[1,2,5,7,8],[3,6],[4]]=>0110100
[[1,2,3,4,5],[6,7],[8]]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,4,7,8],[3,6],[5]]=>0101000
[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011
[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101
[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110
[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111
[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001
[[1,3,5,7,8],[2],[4],[6]]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010
[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011
[[1,3,4,7,8],[2],[5],[6]]=>[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100
[[1,2,4,7,8],[3],[5],[6]]=>[[1,2,3,6,8],[4],[5],[7]]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101
[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110
[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001
[[1,3,5,6,8],[2],[4],[7]]=>[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010
[[1,2,5,6,8],[3],[4],[7]]=>[[1,2,4,5,8],[3],[6],[7]]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011
[[1,3,4,6,8],[2],[5],[7]]=>[[1,2,4,6,7],[3],[5],[8]]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100
[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101
[[1,2,3,6,8],[4],[5],[7]]=>[[1,2,4,7,8],[3],[5],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110
[[1,3,4,5,8],[2],[6],[7]]=>[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000
[[1,2,4,5,8],[3],[6],[7]]=>[[1,2,5,6,8],[3],[4],[7]]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001
[[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010
[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100
[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001
[[1,3,5,6,7],[2],[4],[8]]=>[[1,3,4,5,7],[2],[6],[8]]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010
[[1,2,5,6,7],[3],[4],[8]]=>[[1,3,4,5,8],[2],[6],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011
[[1,3,4,6,7],[2],[5],[8]]=>[[1,3,4,6,7],[2],[5],[8]]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100
[[1,2,4,6,7],[3],[5],[8]]=>[[1,3,4,6,8],[2],[5],[7]]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101
[[1,2,3,6,7],[4],[5],[8]]=>[[1,3,4,7,8],[2],[5],[6]]=>[[1,2,4,5,8],[3],[6],[7]]=>0100110
[[1,3,4,5,7],[2],[6],[8]]=>[[1,3,5,6,7],[2],[4],[8]]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000
[[1,2,4,5,7],[3],[6],[8]]=>[[1,3,5,6,8],[2],[4],[7]]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001
[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010
[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100
[[1,3,4,5,6],[2],[7],[8]]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000
[[1,2,4,5,6],[3],[7],[8]]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001
[[1,2,3,5,6],[4],[7],[8]]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010
[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100
[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000
[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]=>[[1,2,4,6],[3,5,7,8]]=>0101010
[[1,2,5,7],[3,4,6,8]]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,4,7],[3,5,6,8]]=>0101001
[[1,3,4,7],[2,5,6,8]]=>[[1,3,4,7],[2,5,6,8]]=>[[1,2,4,5],[3,6,7,8]]=>0100100
[[1,2,4,7],[3,5,6,8]]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,5,7],[3,4,6,8]]=>0100101
[[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,5,6],[3,4,7,8]]=>0100010
[[1,3,5,6],[2,4,7,8]]=>[[1,2,5,7],[3,4,6,8]]=>[[1,2,3,6],[4,5,7,8]]=>0010010
[[1,2,5,6],[3,4,7,8]]=>[[1,2,5,6],[3,4,7,8]]=>[[1,2,3,7],[4,5,6,8]]=>0010001
[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,7],[3,5,6,8]]=>[[1,2,3,5],[4,6,7,8]]=>0010100
[[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]=>[[1,3,5,7],[2,4,6,8]]=>1010101
[[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]=>[[1,3,5,6],[2,4,7,8]]=>1010010
[[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]=>[[1,2,3,4],[5,6,7,8]]=>0001000
[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,6],[4,5,7,8]]=>[[1,3,4,7],[2,5,6,8]]=>1001001
[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]=>[[1,3,4,6],[2,5,7,8]]=>1001010
[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]=>[[1,3,4,5],[2,6,7,8]]=>1000100
[[1,4,6,8],[2,5,7],[3]]=>[[1,2,4,6],[3,5,7],[8]]=>[[1,3,5,7],[2,6,8],[4]]=>1010101
[[1,3,6,8],[2,5,7],[4]]=>[[1,2,4,5],[3,6,7],[8]]=>[[1,3,5,6],[2,7,8],[4]]=>1010010
[[1,2,6,8],[3,5,7],[4]]=>[[1,2,4,5],[3,6,8],[7]]=>[[1,3,5,6],[2,4,7],[8]]=>1010011
[[1,3,6,8],[2,4,7],[5]]=>[[1,2,4,7],[3,5,8],[6]]=>[[1,3,5,8],[2,4,6],[7]]=>1010110
[[1,2,6,8],[3,4,7],[5]]=>[[1,2,4,6],[3,5,8],[7]]=>[[1,3,5,7],[2,4,6],[8]]=>1010101
[[1,4,5,8],[2,6,7],[3]]=>[[1,2,3,6],[4,5,7],[8]]=>[[1,3,4,7],[2,6,8],[5]]=>1001001
[[1,3,5,8],[2,6,7],[4]]=>[[1,2,3,5],[4,6,7],[8]]=>[[1,3,4,6],[2,7,8],[5]]=>1001010
[[1,2,5,8],[3,6,7],[4]]=>[[1,2,3,5],[4,6,8],[7]]=>[[1,3,4,6],[2,5,7],[8]]=>1001011
[[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[[1,3,4,5],[2,7,8],[6]]=>1000100
[[1,2,4,8],[3,6,7],[5]]=>[[1,2,3,4],[5,6,8],[7]]=>[[1,3,4,5],[2,6,7],[8]]=>1000101
[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[[1,3,4,5],[2,6,8],[7]]=>1000110
[[1,3,5,8],[2,4,7],[6]]=>[[1,2,3,7],[4,5,8],[6]]=>[[1,3,4,8],[2,5,6],[7]]=>1001010
[[1,2,5,8],[3,4,7],[6]]=>[[1,2,3,6],[4,5,8],[7]]=>[[1,3,4,7],[2,5,6],[8]]=>1001001
[[1,3,4,8],[2,5,7],[6]]=>[[1,2,3,7],[4,6,8],[5]]=>[[1,3,4,8],[2,5,7],[6]]=>1001100
[[1,2,4,8],[3,5,7],[6]]=>[[1,2,3,6],[4,7,8],[5]]=>[[1,3,4,7],[2,5,8],[6]]=>1001101
[[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,5],[4,7,8],[6]]=>[[1,3,4,6],[2,5,8],[7]]=>1001010
[[1,3,5,8],[2,4,6],[7]]=>[[1,2,5,7],[3,6,8],[4]]=>[[1,3,6,8],[2,4,7],[5]]=>1011010
[[1,2,5,8],[3,4,6],[7]]=>[[1,2,5,6],[3,7,8],[4]]=>[[1,3,6,7],[2,4,8],[5]]=>1011001
[[1,3,4,8],[2,5,6],[7]]=>[[1,2,4,7],[3,6,8],[5]]=>[[1,3,5,8],[2,4,7],[6]]=>1010100
[[1,2,4,8],[3,5,6],[7]]=>[[1,2,4,6],[3,7,8],[5]]=>[[1,3,5,7],[2,4,8],[6]]=>1010101
[[1,2,3,8],[4,5,6],[7]]=>[[1,2,4,5],[3,7,8],[6]]=>[[1,3,5,6],[2,4,8],[7]]=>1010010
[[1,4,6,7],[2,5,8],[3]]=>[[1,3,4,6],[2,5,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]=>1100101
[[1,3,6,7],[2,5,8],[4]]=>[[1,3,4,5],[2,6,7],[8]]=>[[1,4,5,6],[2,7,8],[3]]=>1100010
[[1,2,6,7],[3,5,8],[4]]=>[[1,3,4,5],[2,6,8],[7]]=>[[1,2,5,6],[3,4,7],[8]]=>0100011
[[1,3,6,7],[2,4,8],[5]]=>[[1,3,4,7],[2,5,8],[6]]=>[[1,2,5,8],[3,4,6],[7]]=>0100110
[[1,2,6,7],[3,4,8],[5]]=>[[1,3,4,6],[2,5,8],[7]]=>[[1,2,5,7],[3,4,6],[8]]=>0100101
[[1,4,5,7],[2,6,8],[3]]=>[[1,3,5,6],[2,4,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]=>1101001
[[1,3,5,7],[2,6,8],[4]]=>[[1,3,5,7],[2,4,6],[8]]=>[[1,4,6,8],[2,5,7],[3]]=>1101010
[[1,2,5,7],[3,6,8],[4]]=>[[1,3,5,8],[2,4,6],[7]]=>[[1,2,4,6],[3,5,7],[8]]=>0101011
[[1,3,4,7],[2,6,8],[5]]=>[[1,3,4,7],[2,5,6],[8]]=>[[1,4,5,8],[2,6,7],[3]]=>1100100
[[1,2,4,7],[3,6,8],[5]]=>[[1,3,4,8],[2,5,6],[7]]=>[[1,2,4,5],[3,6,7],[8]]=>0100101
[[1,2,3,7],[4,6,8],[5]]=>[[1,3,4,8],[2,5,7],[6]]=>[[1,2,4,5],[3,6,8],[7]]=>0100110
[[1,3,5,7],[2,4,8],[6]]=>[[1,3,5,7],[2,4,8],[6]]=>[[1,2,4,8],[3,5,6],[7]]=>0101010
[[1,2,5,7],[3,4,8],[6]]=>[[1,3,5,6],[2,4,8],[7]]=>[[1,2,4,7],[3,5,6],[8]]=>0101001
[[1,3,4,7],[2,5,8],[6]]=>[[1,3,6,7],[2,4,8],[5]]=>[[1,2,4,8],[3,5,7],[6]]=>0101100
[[1,2,4,7],[3,5,8],[6]]=>[[1,3,6,8],[2,4,7],[5]]=>[[1,2,4,7],[3,5,8],[6]]=>0101101
[[1,2,3,7],[4,5,8],[6]]=>[[1,3,5,8],[2,4,7],[6]]=>[[1,2,4,6],[3,5,8],[7]]=>0101010
[[1,4,5,6],[2,7,8],[3]]=>[[1,2,5,6],[3,4,7],[8]]=>[[1,3,6,7],[2,5,8],[4]]=>1010001
[[1,3,5,6],[2,7,8],[4]]=>[[1,2,5,7],[3,4,6],[8]]=>[[1,3,6,8],[2,5,7],[4]]=>1010010
[[1,2,5,6],[3,7,8],[4]]=>[[1,2,5,8],[3,4,6],[7]]=>[[1,2,3,6],[4,5,7],[8]]=>0010011
[[1,3,4,6],[2,7,8],[5]]=>[[1,2,4,7],[3,5,6],[8]]=>[[1,3,5,8],[2,6,7],[4]]=>1010100
[[1,2,4,6],[3,7,8],[5]]=>[[1,2,4,8],[3,5,6],[7]]=>[[1,2,3,5],[4,6,7],[8]]=>0010101
[[1,2,3,6],[4,7,8],[5]]=>[[1,2,4,8],[3,5,7],[6]]=>[[1,2,3,5],[4,6,8],[7]]=>0010110
[[1,3,4,5],[2,7,8],[6]]=>[[1,2,3,7],[4,5,6],[8]]=>[[1,3,4,8],[2,6,7],[5]]=>1001000
[[1,2,4,5],[3,7,8],[6]]=>[[1,2,3,8],[4,5,6],[7]]=>[[1,2,3,4],[5,6,7],[8]]=>0001001
[[1,2,3,5],[4,7,8],[6]]=>[[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,4],[5,6,8],[7]]=>0001010
[[1,2,3,4],[5,7,8],[6]]=>[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>0001100
[[1,3,5,6],[2,4,8],[7]]=>[[1,2,5,7],[3,4,8],[6]]=>[[1,2,3,8],[4,5,6],[7]]=>0010010
[[1,2,5,6],[3,4,8],[7]]=>[[1,2,5,6],[3,4,8],[7]]=>[[1,2,3,7],[4,5,6],[8]]=>0010001
[[1,3,4,6],[2,5,8],[7]]=>[[1,2,6,7],[3,4,8],[5]]=>[[1,2,3,8],[4,5,7],[6]]=>0010100
[[1,2,4,6],[3,5,8],[7]]=>[[1,2,6,8],[3,4,7],[5]]=>[[1,2,3,7],[4,5,8],[6]]=>0010101
[[1,2,3,6],[4,5,8],[7]]=>[[1,2,5,8],[3,4,7],[6]]=>[[1,2,3,6],[4,5,8],[7]]=>0010010
[[1,3,4,5],[2,6,8],[7]]=>[[1,2,6,7],[3,5,8],[4]]=>[[1,2,3,8],[4,6,7],[5]]=>0011000
[[1,2,4,5],[3,6,8],[7]]=>[[1,2,6,8],[3,5,7],[4]]=>[[1,2,3,7],[4,6,8],[5]]=>0011001
[[1,2,3,5],[4,6,8],[7]]=>[[1,2,5,8],[3,6,7],[4]]=>[[1,2,3,6],[4,7,8],[5]]=>0011010
[[1,2,3,4],[5,6,8],[7]]=>[[1,2,4,8],[3,6,7],[5]]=>[[1,2,3,5],[4,7,8],[6]]=>0010100
[[1,3,5,7],[2,4,6],[8]]=>[[1,3,5,7],[2,6,8],[4]]=>[[1,2,6,8],[3,4,7],[5]]=>0101010
[[1,2,5,7],[3,4,6],[8]]=>[[1,3,5,6],[2,7,8],[4]]=>[[1,2,6,7],[3,4,8],[5]]=>0101001
[[1,3,4,7],[2,5,6],[8]]=>[[1,3,4,7],[2,6,8],[5]]=>[[1,2,5,8],[3,4,7],[6]]=>0100100
[[1,2,4,7],[3,5,6],[8]]=>[[1,3,4,6],[2,7,8],[5]]=>[[1,2,5,7],[3,4,8],[6]]=>0100101
[[1,2,3,7],[4,5,6],[8]]=>[[1,3,4,5],[2,7,8],[6]]=>[[1,2,5,6],[3,4,8],[7]]=>0100010
[[1,3,5,6],[2,4,7],[8]]=>[[1,4,5,7],[2,6,8],[3]]=>[[1,2,6,8],[3,5,7],[4]]=>0110010
[[1,2,5,6],[3,4,7],[8]]=>[[1,4,5,6],[2,7,8],[3]]=>[[1,2,6,7],[3,5,8],[4]]=>0110001
[[1,3,4,6],[2,5,7],[8]]=>[[1,4,6,7],[2,5,8],[3]]=>[[1,2,5,8],[3,6,7],[4]]=>0110100
[[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]=>[[1,2,5,7],[3,6,8],[4]]=>0110101
[[1,2,3,6],[4,5,7],[8]]=>[[1,4,5,8],[2,6,7],[3]]=>[[1,2,5,6],[3,7,8],[4]]=>0110010
[[1,3,4,5],[2,6,7],[8]]=>[[1,3,6,7],[2,5,8],[4]]=>[[1,2,4,8],[3,6,7],[5]]=>0101000
[[1,2,4,5],[3,6,7],[8]]=>[[1,3,6,8],[2,5,7],[4]]=>[[1,2,4,7],[3,6,8],[5]]=>0101001
[[1,2,3,5],[4,6,7],[8]]=>[[1,3,5,8],[2,6,7],[4]]=>[[1,2,4,6],[3,7,8],[5]]=>0101010
[[1,2,3,4],[5,6,7],[8]]=>[[1,3,4,8],[2,6,7],[5]]=>[[1,2,4,5],[3,7,8],[6]]=>0100100
[[1,4,7,8],[2,5],[3,6]]=>[[1,2,3,6],[4,7],[5,8]]=>[[1,3,4,7],[2,5],[6,8]]=>1001101
[[1,3,7,8],[2,5],[4,6]]=>[[1,2,3,5],[4,7],[6,8]]=>[[1,3,4,6],[2,5],[7,8]]=>1001010
[[1,2,7,8],[3,5],[4,6]]=>[[1,2,3,5],[4,6],[7,8]]=>[[1,3,4,6],[2,7],[5,8]]=>1001011
[[1,3,7,8],[2,4],[5,6]]=>[[1,2,3,4],[5,7],[6,8]]=>[[1,3,4,5],[2,6],[7,8]]=>1000110
[[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[[1,3,4,5],[2,7],[6,8]]=>1000101
[[1,4,6,8],[2,5],[3,7]]=>[[1,2,4,6],[3,7],[5,8]]=>[[1,3,5,7],[2,4],[6,8]]=>1010101
[[1,3,6,8],[2,5],[4,7]]=>[[1,2,4,5],[3,7],[6,8]]=>[[1,3,5,6],[2,4],[7,8]]=>1010010
[[1,2,6,8],[3,5],[4,7]]=>[[1,2,4,5],[3,6],[7,8]]=>[[1,3,5,6],[2,7],[4,8]]=>1010011
[[1,3,6,8],[2,4],[5,7]]=>[[1,2,4,7],[3,5],[6,8]]=>[[1,3,5,8],[2,6],[4,7]]=>1010110
[[1,2,6,8],[3,4],[5,7]]=>[[1,2,4,6],[3,5],[7,8]]=>[[1,3,5,7],[2,6],[4,8]]=>1010101
[[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]=>[[1,3,6,7],[2,4],[5,8]]=>1011001
[[1,3,5,8],[2,6],[4,7]]=>[[1,2,5,7],[3,6],[4,8]]=>[[1,3,6,8],[2,4],[5,7]]=>1011010
[[1,2,5,8],[3,6],[4,7]]=>[[1,2,5,8],[3,6],[4,7]]=>[[1,2,3,6],[4,7],[5,8]]=>0011011
[[1,3,4,8],[2,6],[5,7]]=>[[1,2,4,7],[3,6],[5,8]]=>[[1,3,5,8],[2,4],[6,7]]=>1010100
[[1,2,4,8],[3,6],[5,7]]=>[[1,2,4,8],[3,6],[5,7]]=>[[1,2,3,5],[4,7],[6,8]]=>0010101
[[1,2,3,8],[4,6],[5,7]]=>[[1,2,4,8],[3,5],[6,7]]=>[[1,2,3,5],[4,6],[7,8]]=>0010110
[[1,3,5,8],[2,4],[6,7]]=>[[1,2,3,7],[4,5],[6,8]]=>[[1,3,4,8],[2,6],[5,7]]=>1001010
[[1,2,5,8],[3,4],[6,7]]=>[[1,2,3,6],[4,5],[7,8]]=>[[1,3,4,7],[2,6],[5,8]]=>1001001
[[1,3,4,8],[2,5],[6,7]]=>[[1,2,3,7],[4,6],[5,8]]=>[[1,3,4,8],[2,5],[6,7]]=>1001100
[[1,2,4,8],[3,5],[6,7]]=>[[1,2,3,8],[4,6],[5,7]]=>[[1,2,3,4],[5,7],[6,8]]=>0001101
[[1,2,3,8],[4,5],[6,7]]=>[[1,2,3,8],[4,5],[6,7]]=>[[1,2,3,4],[5,6],[7,8]]=>0001010
[[1,4,6,7],[2,5],[3,8]]=>[[1,3,4,6],[2,7],[5,8]]=>[[1,2,5,7],[3,4],[6,8]]=>0100101
[[1,3,6,7],[2,5],[4,8]]=>[[1,3,4,5],[2,7],[6,8]]=>[[1,2,5,6],[3,4],[7,8]]=>0100010
[[1,2,6,7],[3,5],[4,8]]=>[[1,3,4,5],[2,6],[7,8]]=>[[1,4,5,6],[2,7],[3,8]]=>1100011
[[1,3,6,7],[2,4],[5,8]]=>[[1,3,4,7],[2,5],[6,8]]=>[[1,4,5,8],[2,6],[3,7]]=>1100110
[[1,2,6,7],[3,4],[5,8]]=>[[1,3,4,6],[2,5],[7,8]]=>[[1,4,5,7],[2,6],[3,8]]=>1100101
[[1,4,5,7],[2,6],[3,8]]=>[[1,3,5,6],[2,7],[4,8]]=>[[1,2,6,7],[3,4],[5,8]]=>0101001
[[1,3,5,7],[2,6],[4,8]]=>[[1,3,5,7],[2,6],[4,8]]=>[[1,2,6,8],[3,4],[5,7]]=>0101010
[[1,2,5,7],[3,6],[4,8]]=>[[1,3,5,8],[2,6],[4,7]]=>[[1,2,4,6],[3,7],[5,8]]=>0101011
[[1,3,4,7],[2,6],[5,8]]=>[[1,3,4,7],[2,6],[5,8]]=>[[1,2,5,8],[3,4],[6,7]]=>0100100
[[1,2,4,7],[3,6],[5,8]]=>[[1,3,4,8],[2,6],[5,7]]=>[[1,2,4,5],[3,7],[6,8]]=>0100101
[[1,2,3,7],[4,6],[5,8]]=>[[1,3,4,8],[2,5],[6,7]]=>[[1,2,4,5],[3,6],[7,8]]=>0100110
[[1,3,5,7],[2,4],[6,8]]=>[[1,3,5,7],[2,4],[6,8]]=>[[1,4,6,8],[2,5],[3,7]]=>1101010
[[1,2,5,7],[3,4],[6,8]]=>[[1,3,5,6],[2,4],[7,8]]=>[[1,4,6,7],[2,5],[3,8]]=>1101001
[[1,3,4,7],[2,5],[6,8]]=>[[1,3,6,7],[2,4],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]=>1101100
[[1,2,4,7],[3,5],[6,8]]=>[[1,3,6,8],[2,4],[5,7]]=>[[1,2,4,7],[3,5],[6,8]]=>0101101
[[1,2,3,7],[4,5],[6,8]]=>[[1,3,5,8],[2,4],[6,7]]=>[[1,2,4,6],[3,5],[7,8]]=>0101010
[[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]=>[[1,2,6,7],[3,5],[4,8]]=>0110001
[[1,3,5,6],[2,7],[4,8]]=>[[1,4,5,7],[2,6],[3,8]]=>[[1,2,6,8],[3,5],[4,7]]=>0110010
[[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]=>0110011
[[1,3,4,6],[2,7],[5,8]]=>[[1,4,6,7],[2,5],[3,8]]=>[[1,2,7,8],[3,5],[4,6]]=>0110100
[[1,2,4,6],[3,7],[5,8]]=>[[1,4,6,8],[2,5],[3,7]]=>[[1,2,5,7],[3,6],[4,8]]=>0110101
[[1,2,3,6],[4,7],[5,8]]=>[[1,4,7,8],[2,5],[3,6]]=>[[1,2,5,8],[3,6],[4,7]]=>0110110
[[1,3,4,5],[2,7],[6,8]]=>[[1,3,6,7],[2,5],[4,8]]=>[[1,2,7,8],[3,4],[5,6]]=>0101000
[[1,2,4,5],[3,7],[6,8]]=>[[1,3,6,8],[2,5],[4,7]]=>[[1,2,4,7],[3,6],[5,8]]=>0101001
[[1,2,3,5],[4,7],[6,8]]=>[[1,3,7,8],[2,5],[4,6]]=>[[1,2,4,8],[3,6],[5,7]]=>0101010
[[1,2,3,4],[5,7],[6,8]]=>[[1,3,7,8],[2,4],[5,6]]=>[[1,2,4,8],[3,5],[6,7]]=>0101100
[[1,3,5,6],[2,4],[7,8]]=>[[1,2,5,7],[3,4],[6,8]]=>[[1,3,6,8],[2,5],[4,7]]=>1010010
[[1,2,5,6],[3,4],[7,8]]=>[[1,2,5,6],[3,4],[7,8]]=>[[1,3,6,7],[2,5],[4,8]]=>1010001
[[1,3,4,6],[2,5],[7,8]]=>[[1,2,6,7],[3,4],[5,8]]=>[[1,3,7,8],[2,5],[4,6]]=>1010100
[[1,2,4,6],[3,5],[7,8]]=>[[1,2,6,8],[3,4],[5,7]]=>[[1,2,3,7],[4,5],[6,8]]=>0010101
[[1,2,3,6],[4,5],[7,8]]=>[[1,2,5,8],[3,4],[6,7]]=>[[1,2,3,6],[4,5],[7,8]]=>0010010
[[1,3,4,5],[2,6],[7,8]]=>[[1,2,6,7],[3,5],[4,8]]=>[[1,3,7,8],[2,4],[5,6]]=>1011000
[[1,2,4,5],[3,6],[7,8]]=>[[1,2,6,8],[3,5],[4,7]]=>[[1,2,3,7],[4,6],[5,8]]=>0011001
[[1,2,3,5],[4,6],[7,8]]=>[[1,2,7,8],[3,5],[4,6]]=>[[1,2,3,8],[4,6],[5,7]]=>0011010
[[1,2,3,4],[5,6],[7,8]]=>[[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,8],[4,5],[6,7]]=>0010100
[[1,5,7,8],[2,6],[3],[4]]=>[[1,2,3,5],[4,6],[7],[8]]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011
[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101
[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110
[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111
[[1,4,7,8],[2,5],[3],[6]]=>[[1,2,3,6],[4,7],[5],[8]]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101
[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010
[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011
[[1,3,7,8],[2,4],[5],[6]]=>[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110
[[1,2,7,8],[3,4],[5],[6]]=>[[1,2,3,6],[4,8],[5],[7]]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101
[[1,5,6,8],[2,7],[3],[4]]=>[[1,2,4,5],[3,6],[7],[8]]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011
[[1,4,6,8],[2,7],[3],[5]]=>[[1,2,4,6],[3,5],[7],[8]]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101
[[1,3,6,8],[2,7],[4],[5]]=>[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110
[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111
[[1,4,5,8],[2,7],[3],[6]]=>[[1,2,3,6],[4,5],[7],[8]]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001
[[1,3,5,8],[2,7],[4],[6]]=>[[1,2,3,7],[4,5],[6],[8]]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010
[[1,2,5,8],[3,7],[4],[6]]=>[[1,2,3,8],[4,5],[6],[7]]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011
[[1,3,4,8],[2,7],[5],[6]]=>[[1,2,3,7],[4,6],[5],[8]]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100
[[1,2,4,8],[3,7],[5],[6]]=>[[1,2,3,8],[4,6],[5],[7]]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101
[[1,2,3,8],[4,7],[5],[6]]=>[[1,2,3,8],[4,7],[5],[6]]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110
[[1,4,6,8],[2,5],[3],[7]]=>[[1,2,4,6],[3,7],[5],[8]]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101
[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010
[[1,2,6,8],[3,5],[4],[7]]=>[[1,2,4,5],[3,8],[6],[7]]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011
[[1,3,6,8],[2,4],[5],[7]]=>[[1,2,4,7],[3,8],[5],[6]]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110
[[1,2,6,8],[3,4],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101
[[1,4,5,8],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4],[8]]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001
[[1,3,5,8],[2,6],[4],[7]]=>[[1,2,5,7],[3,6],[4],[8]]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010
[[1,2,5,8],[3,6],[4],[7]]=>[[1,2,5,8],[3,6],[4],[7]]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011
[[1,3,4,8],[2,6],[5],[7]]=>[[1,2,4,7],[3,6],[5],[8]]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100
[[1,2,4,8],[3,6],[5],[7]]=>[[1,2,4,8],[3,6],[5],[7]]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101
[[1,2,3,8],[4,6],[5],[7]]=>[[1,2,4,8],[3,7],[5],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110
[[1,3,5,8],[2,4],[6],[7]]=>[[1,2,5,7],[3,8],[4],[6]]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010
[[1,2,5,8],[3,4],[6],[7]]=>[[1,2,5,6],[3,8],[4],[7]]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001
[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100
[[1,2,4,8],[3,5],[6],[7]]=>[[1,2,6,8],[3,7],[4],[5]]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101
[[1,2,3,8],[4,5],[6],[7]]=>[[1,2,5,8],[3,7],[4],[6]]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010
[[1,5,6,7],[2,8],[3],[4]]=>[[1,3,4,5],[2,6],[7],[8]]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011
[[1,4,6,7],[2,8],[3],[5]]=>[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101
[[1,3,6,7],[2,8],[4],[5]]=>[[1,3,4,7],[2,5],[6],[8]]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110
[[1,2,6,7],[3,8],[4],[5]]=>[[1,3,4,8],[2,5],[6],[7]]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111
[[1,4,5,7],[2,8],[3],[6]]=>[[1,3,5,6],[2,4],[7],[8]]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001
[[1,3,5,7],[2,8],[4],[6]]=>[[1,3,5,7],[2,4],[6],[8]]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010
[[1,2,5,7],[3,8],[4],[6]]=>[[1,3,5,8],[2,4],[6],[7]]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011
[[1,3,4,7],[2,8],[5],[6]]=>[[1,3,6,7],[2,4],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100
[[1,2,4,7],[3,8],[5],[6]]=>[[1,3,6,8],[2,4],[5],[7]]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101
[[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110
[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001
[[1,3,5,6],[2,8],[4],[7]]=>[[1,2,5,7],[3,4],[6],[8]]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010
[[1,2,5,6],[3,8],[4],[7]]=>[[1,2,5,8],[3,4],[6],[7]]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011
[[1,3,4,6],[2,8],[5],[7]]=>[[1,2,6,7],[3,4],[5],[8]]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100
[[1,2,4,6],[3,8],[5],[7]]=>[[1,2,6,8],[3,4],[5],[7]]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101
[[1,2,3,6],[4,8],[5],[7]]=>[[1,2,7,8],[3,4],[5],[6]]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110
[[1,3,4,5],[2,8],[6],[7]]=>[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000
[[1,2,4,5],[3,8],[6],[7]]=>[[1,2,6,8],[3,5],[4],[7]]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001
[[1,2,3,5],[4,8],[6],[7]]=>[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010
[[1,2,3,4],[5,8],[6],[7]]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100
[[1,4,6,7],[2,5],[3],[8]]=>[[1,3,4,6],[2,7],[5],[8]]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101
[[1,3,6,7],[2,5],[4],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010
[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011
[[1,3,6,7],[2,4],[5],[8]]=>[[1,3,4,7],[2,8],[5],[6]]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110
[[1,2,6,7],[3,4],[5],[8]]=>[[1,3,4,6],[2,8],[5],[7]]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101
[[1,4,5,7],[2,6],[3],[8]]=>[[1,3,5,6],[2,7],[4],[8]]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001
[[1,3,5,7],[2,6],[4],[8]]=>[[1,3,5,7],[2,6],[4],[8]]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010
[[1,2,5,7],[3,6],[4],[8]]=>[[1,3,5,8],[2,6],[4],[7]]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011
[[1,3,4,7],[2,6],[5],[8]]=>[[1,3,4,7],[2,6],[5],[8]]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100
[[1,2,4,7],[3,6],[5],[8]]=>[[1,3,4,8],[2,6],[5],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101
[[1,2,3,7],[4,6],[5],[8]]=>[[1,3,4,8],[2,7],[5],[6]]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110
[[1,3,5,7],[2,4],[6],[8]]=>[[1,3,5,7],[2,8],[4],[6]]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010
[[1,2,5,7],[3,4],[6],[8]]=>[[1,3,5,6],[2,8],[4],[7]]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001
[[1,3,4,7],[2,5],[6],[8]]=>[[1,3,6,7],[2,8],[4],[5]]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100
[[1,2,4,7],[3,5],[6],[8]]=>[[1,3,6,8],[2,7],[4],[5]]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101
[[1,2,3,7],[4,5],[6],[8]]=>[[1,3,5,8],[2,7],[4],[6]]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010
[[1,4,5,6],[2,7],[3],[8]]=>[[1,4,5,6],[2,7],[3],[8]]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001
[[1,3,5,6],[2,7],[4],[8]]=>[[1,4,5,7],[2,6],[3],[8]]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010
[[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011
[[1,3,4,6],[2,7],[5],[8]]=>[[1,4,6,7],[2,5],[3],[8]]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100
[[1,2,4,6],[3,7],[5],[8]]=>[[1,4,6,8],[2,5],[3],[7]]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101
[[1,2,3,6],[4,7],[5],[8]]=>[[1,4,7,8],[2,5],[3],[6]]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110
[[1,3,4,5],[2,7],[6],[8]]=>[[1,3,6,7],[2,5],[4],[8]]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000
[[1,2,4,5],[3,7],[6],[8]]=>[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001
[[1,2,3,5],[4,7],[6],[8]]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010
[[1,2,3,4],[5,7],[6],[8]]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100
[[1,3,5,6],[2,4],[7],[8]]=>[[1,4,5,7],[2,8],[3],[6]]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010
[[1,2,5,6],[3,4],[7],[8]]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001
[[1,3,4,6],[2,5],[7],[8]]=>[[1,4,6,7],[2,8],[3],[5]]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100
[[1,2,4,6],[3,5],[7],[8]]=>[[1,4,6,8],[2,7],[3],[5]]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101
[[1,2,3,6],[4,5],[7],[8]]=>[[1,4,5,8],[2,7],[3],[6]]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010
[[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000
[[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001
[[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010
[[1,2,3,4],[5,6],[7],[8]]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100
[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111
[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011
[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101
[[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110
[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111
[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011
[[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101
[[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110
[[1,2,6,8],[3],[4],[5],[7]]=>[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111
[[1,4,5,8],[2],[3],[6],[7]]=>[[1,2,5,6],[3],[4],[7],[8]]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001
[[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,5,7],[3],[4],[6],[8]]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010
[[1,2,5,8],[3],[4],[6],[7]]=>[[1,2,5,8],[3],[4],[6],[7]]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011
[[1,3,4,8],[2],[5],[6],[7]]=>[[1,2,6,7],[3],[4],[5],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100
[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,6,8],[3],[4],[5],[7]]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101
[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110
[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011
[[1,4,6,7],[2],[3],[5],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101
[[1,3,6,7],[2],[4],[5],[8]]=>[[1,3,4,7],[2],[5],[6],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110
[[1,2,6,7],[3],[4],[5],[8]]=>[[1,3,4,8],[2],[5],[6],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111
[[1,4,5,7],[2],[3],[6],[8]]=>[[1,3,5,6],[2],[4],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001
[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010
[[1,2,5,7],[3],[4],[6],[8]]=>[[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011
[[1,3,4,7],[2],[5],[6],[8]]=>[[1,3,6,7],[2],[4],[5],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100
[[1,2,4,7],[3],[5],[6],[8]]=>[[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101
[[1,2,3,7],[4],[5],[6],[8]]=>[[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110
[[1,4,5,6],[2],[3],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001
[[1,3,5,6],[2],[4],[7],[8]]=>[[1,4,5,7],[2],[3],[6],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010
[[1,2,5,6],[3],[4],[7],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011
[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100
[[1,2,4,6],[3],[5],[7],[8]]=>[[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101
[[1,2,3,6],[4],[5],[7],[8]]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110
[[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000
[[1,2,4,5],[3],[6],[7],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001
[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010
[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100
[[1,4,7],[2,5,8],[3,6]]=>[[1,3,6],[2,4,7],[5,8]]=>[[1,4,7],[2,5,8],[3,6]]=>1101101
[[1,3,7],[2,5,8],[4,6]]=>[[1,3,5],[2,4,7],[6,8]]=>[[1,4,6],[2,5,8],[3,7]]=>1101010
[[1,2,7],[3,5,8],[4,6]]=>[[1,3,5],[2,4,6],[7,8]]=>[[1,4,6],[2,5,7],[3,8]]=>1101011
[[1,3,7],[2,4,8],[5,6]]=>[[1,3,4],[2,5,7],[6,8]]=>[[1,4,5],[2,6,8],[3,7]]=>1100110
[[1,2,7],[3,4,8],[5,6]]=>[[1,3,4],[2,5,6],[7,8]]=>[[1,4,5],[2,6,7],[3,8]]=>1100101
[[1,4,6],[2,5,8],[3,7]]=>[[1,2,6],[3,4,7],[5,8]]=>[[1,3,7],[2,5,8],[4,6]]=>1010101
[[1,3,6],[2,5,8],[4,7]]=>[[1,2,5],[3,4,7],[6,8]]=>[[1,3,6],[2,5,8],[4,7]]=>1010010
[[1,2,6],[3,5,8],[4,7]]=>[[1,2,5],[3,4,6],[7,8]]=>[[1,3,6],[2,5,7],[4,8]]=>1010011
[[1,3,6],[2,4,8],[5,7]]=>[[1,2,4],[3,5,7],[6,8]]=>[[1,3,5],[2,6,8],[4,7]]=>1010110
[[1,2,6],[3,4,8],[5,7]]=>[[1,2,4],[3,5,6],[7,8]]=>[[1,3,5],[2,6,7],[4,8]]=>1010101
[[1,4,5],[2,6,8],[3,7]]=>[[1,2,6],[3,5,7],[4,8]]=>[[1,3,7],[2,4,8],[5,6]]=>1011001
[[1,3,5],[2,6,8],[4,7]]=>[[1,2,5],[3,6,7],[4,8]]=>[[1,3,6],[2,4,8],[5,7]]=>1011010
[[1,2,5],[3,6,8],[4,7]]=>[[1,2,5],[3,6,8],[4,7]]=>[[1,3,6],[2,4,7],[5,8]]=>1011011
[[1,3,4],[2,6,8],[5,7]]=>[[1,2,4],[3,6,7],[5,8]]=>[[1,3,5],[2,4,8],[6,7]]=>1010100
[[1,2,4],[3,6,8],[5,7]]=>[[1,2,4],[3,6,8],[5,7]]=>[[1,3,5],[2,4,7],[6,8]]=>1010101
[[1,2,3],[4,6,8],[5,7]]=>[[1,2,4],[3,5,8],[6,7]]=>[[1,3,5],[2,4,6],[7,8]]=>1010110
[[1,3,5],[2,4,8],[6,7]]=>[[1,2,3],[4,5,7],[6,8]]=>[[1,3,4],[2,6,8],[5,7]]=>1001010
[[1,2,5],[3,4,8],[6,7]]=>[[1,2,3],[4,5,6],[7,8]]=>[[1,3,4],[2,6,7],[5,8]]=>1001001
[[1,3,4],[2,5,8],[6,7]]=>[[1,2,3],[4,6,7],[5,8]]=>[[1,3,4],[2,5,8],[6,7]]=>1001100
[[1,2,4],[3,5,8],[6,7]]=>[[1,2,3],[4,6,8],[5,7]]=>[[1,3,4],[2,5,7],[6,8]]=>1001101
[[1,2,3],[4,5,8],[6,7]]=>[[1,2,3],[4,5,8],[6,7]]=>[[1,3,4],[2,5,6],[7,8]]=>1001010
[[1,4,6],[2,5,7],[3,8]]=>[[1,4,6],[2,5,7],[3,8]]=>[[1,2,7],[3,5,8],[4,6]]=>0110101
[[1,3,6],[2,5,7],[4,8]]=>[[1,4,5],[2,6,7],[3,8]]=>[[1,2,6],[3,5,8],[4,7]]=>0110010
[[1,2,6],[3,5,7],[4,8]]=>[[1,4,5],[2,6,8],[3,7]]=>[[1,2,6],[3,5,7],[4,8]]=>0110011
[[1,3,6],[2,4,7],[5,8]]=>[[1,4,7],[2,5,8],[3,6]]=>[[1,2,5],[3,6,8],[4,7]]=>0110110
[[1,2,6],[3,4,7],[5,8]]=>[[1,4,6],[2,5,8],[3,7]]=>[[1,2,5],[3,6,7],[4,8]]=>0110101
[[1,4,5],[2,6,7],[3,8]]=>[[1,3,6],[2,5,7],[4,8]]=>[[1,2,7],[3,4,8],[5,6]]=>0101001
[[1,3,5],[2,6,7],[4,8]]=>[[1,3,5],[2,6,7],[4,8]]=>[[1,2,6],[3,4,8],[5,7]]=>0101010
[[1,2,5],[3,6,7],[4,8]]=>[[1,3,5],[2,6,8],[4,7]]=>[[1,2,6],[3,4,7],[5,8]]=>0101011
[[1,3,4],[2,6,7],[5,8]]=>[[1,3,4],[2,6,7],[5,8]]=>[[1,2,5],[3,4,8],[6,7]]=>0100100
[[1,2,4],[3,6,7],[5,8]]=>[[1,3,4],[2,6,8],[5,7]]=>[[1,2,5],[3,4,7],[6,8]]=>0100101
[[1,2,3],[4,6,7],[5,8]]=>[[1,3,4],[2,5,8],[6,7]]=>[[1,2,5],[3,4,6],[7,8]]=>0100110
[[1,3,5],[2,4,7],[6,8]]=>[[1,3,7],[2,5,8],[4,6]]=>[[1,2,4],[3,6,8],[5,7]]=>0101010
[[1,2,5],[3,4,7],[6,8]]=>[[1,3,6],[2,5,8],[4,7]]=>[[1,2,4],[3,6,7],[5,8]]=>0101001
[[1,3,4],[2,5,7],[6,8]]=>[[1,3,7],[2,4,8],[5,6]]=>[[1,2,4],[3,5,8],[6,7]]=>0101100
[[1,2,4],[3,5,7],[6,8]]=>[[1,3,6],[2,4,8],[5,7]]=>[[1,2,4],[3,5,7],[6,8]]=>0101101
[[1,2,3],[4,5,7],[6,8]]=>[[1,3,5],[2,4,8],[6,7]]=>[[1,2,4],[3,5,6],[7,8]]=>0101010
[[1,3,5],[2,4,6],[7,8]]=>[[1,2,7],[3,5,8],[4,6]]=>[[1,2,3],[4,6,8],[5,7]]=>0011010
[[1,2,5],[3,4,6],[7,8]]=>[[1,2,6],[3,5,8],[4,7]]=>[[1,2,3],[4,6,7],[5,8]]=>0011001
[[1,3,4],[2,5,6],[7,8]]=>[[1,2,7],[3,4,8],[5,6]]=>[[1,2,3],[4,5,8],[6,7]]=>0010100
[[1,2,4],[3,5,6],[7,8]]=>[[1,2,6],[3,4,8],[5,7]]=>[[1,2,3],[4,5,7],[6,8]]=>0010101
[[1,2,3],[4,5,6],[7,8]]=>[[1,2,5],[3,4,8],[6,7]]=>[[1,2,3],[4,5,6],[7,8]]=>0010010
[[1,5,7],[2,6,8],[3],[4]]=>[[1,3,5],[2,4,6],[7],[8]]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011
[[1,4,7],[2,6,8],[3],[5]]=>[[1,3,4],[2,5,6],[7],[8]]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101
[[1,3,7],[2,6,8],[4],[5]]=>[[1,3,4],[2,5,7],[6],[8]]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110
[[1,2,7],[3,6,8],[4],[5]]=>[[1,3,4],[2,5,8],[6],[7]]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111
[[1,4,7],[2,5,8],[3],[6]]=>[[1,3,6],[2,4,7],[5],[8]]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101
[[1,3,7],[2,5,8],[4],[6]]=>[[1,3,5],[2,4,7],[6],[8]]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010
[[1,2,7],[3,5,8],[4],[6]]=>[[1,3,5],[2,4,8],[6],[7]]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011
[[1,3,7],[2,4,8],[5],[6]]=>[[1,3,7],[2,4,8],[5],[6]]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110
[[1,2,7],[3,4,8],[5],[6]]=>[[1,3,6],[2,4,8],[5],[7]]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101
[[1,5,6],[2,7,8],[3],[4]]=>[[1,2,5],[3,4,6],[7],[8]]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011
[[1,4,6],[2,7,8],[3],[5]]=>[[1,2,4],[3,5,6],[7],[8]]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101
[[1,3,6],[2,7,8],[4],[5]]=>[[1,2,4],[3,5,7],[6],[8]]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110
[[1,2,6],[3,7,8],[4],[5]]=>[[1,2,4],[3,5,8],[6],[7]]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111
[[1,4,5],[2,7,8],[3],[6]]=>[[1,2,3],[4,5,6],[7],[8]]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001
[[1,3,5],[2,7,8],[4],[6]]=>[[1,2,3],[4,5,7],[6],[8]]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010
[[1,2,5],[3,7,8],[4],[6]]=>[[1,2,3],[4,5,8],[6],[7]]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011
[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100
[[1,2,4],[3,7,8],[5],[6]]=>[[1,2,3],[4,6,8],[5],[7]]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101
[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110
[[1,4,6],[2,5,8],[3],[7]]=>[[1,2,6],[3,4,7],[5],[8]]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101
[[1,3,6],[2,5,8],[4],[7]]=>[[1,2,5],[3,4,7],[6],[8]]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010
[[1,2,6],[3,5,8],[4],[7]]=>[[1,2,5],[3,4,8],[6],[7]]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011
[[1,3,6],[2,4,8],[5],[7]]=>[[1,2,7],[3,4,8],[5],[6]]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110
[[1,2,6],[3,4,8],[5],[7]]=>[[1,2,6],[3,4,8],[5],[7]]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101
[[1,4,5],[2,6,8],[3],[7]]=>[[1,2,6],[3,5,7],[4],[8]]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001
[[1,3,5],[2,6,8],[4],[7]]=>[[1,2,5],[3,6,7],[4],[8]]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010
[[1,2,5],[3,6,8],[4],[7]]=>[[1,2,5],[3,6,8],[4],[7]]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011
[[1,3,4],[2,6,8],[5],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100
[[1,2,4],[3,6,8],[5],[7]]=>[[1,2,4],[3,6,8],[5],[7]]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101
[[1,2,3],[4,6,8],[5],[7]]=>[[1,2,4],[3,7,8],[5],[6]]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110
[[1,3,5],[2,4,8],[6],[7]]=>[[1,2,7],[3,5,8],[4],[6]]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010
[[1,2,5],[3,4,8],[6],[7]]=>[[1,2,6],[3,5,8],[4],[7]]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001
[[1,3,4],[2,5,8],[6],[7]]=>[[1,2,7],[3,6,8],[4],[5]]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100
[[1,2,4],[3,5,8],[6],[7]]=>[[1,2,6],[3,7,8],[4],[5]]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101
[[1,2,3],[4,5,8],[6],[7]]=>[[1,2,5],[3,7,8],[4],[6]]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010
[[1,4,6],[2,5,7],[3],[8]]=>[[1,4,6],[2,5,7],[3],[8]]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101
[[1,3,6],[2,5,7],[4],[8]]=>[[1,4,5],[2,6,7],[3],[8]]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010
[[1,2,6],[3,5,7],[4],[8]]=>[[1,4,5],[2,6,8],[3],[7]]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011
[[1,3,6],[2,4,7],[5],[8]]=>[[1,4,7],[2,5,8],[3],[6]]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110
[[1,2,6],[3,4,7],[5],[8]]=>[[1,4,6],[2,5,8],[3],[7]]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101
[[1,4,5],[2,6,7],[3],[8]]=>[[1,3,6],[2,5,7],[4],[8]]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001
[[1,3,5],[2,6,7],[4],[8]]=>[[1,3,5],[2,6,7],[4],[8]]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010
[[1,2,5],[3,6,7],[4],[8]]=>[[1,3,5],[2,6,8],[4],[7]]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011
[[1,3,4],[2,6,7],[5],[8]]=>[[1,3,4],[2,6,7],[5],[8]]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100
[[1,2,4],[3,6,7],[5],[8]]=>[[1,3,4],[2,6,8],[5],[7]]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101
[[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110
[[1,3,5],[2,4,7],[6],[8]]=>[[1,3,7],[2,5,8],[4],[6]]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010
[[1,2,5],[3,4,7],[6],[8]]=>[[1,3,6],[2,5,8],[4],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001
[[1,3,4],[2,5,7],[6],[8]]=>[[1,3,7],[2,6,8],[4],[5]]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100
[[1,2,4],[3,5,7],[6],[8]]=>[[1,3,6],[2,7,8],[4],[5]]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101
[[1,2,3],[4,5,7],[6],[8]]=>[[1,3,5],[2,7,8],[4],[6]]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010
[[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010
[[1,2,5],[3,4,6],[7],[8]]=>[[1,5,6],[2,7,8],[3],[4]]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001
[[1,3,4],[2,5,6],[7],[8]]=>[[1,4,7],[2,6,8],[3],[5]]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100
[[1,2,4],[3,5,6],[7],[8]]=>[[1,4,6],[2,7,8],[3],[5]]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101
[[1,2,3],[4,5,6],[7],[8]]=>[[1,4,5],[2,7,8],[3],[6]]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010
[[1,5,8],[2,6],[3,7],[4]]=>[[1,2,5],[3,6],[4,7],[8]]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011
[[1,4,8],[2,6],[3,7],[5]]=>[[1,2,4],[3,6],[5,7],[8]]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101
[[1,3,8],[2,6],[4,7],[5]]=>[[1,2,4],[3,5],[6,7],[8]]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110
[[1,2,8],[3,6],[4,7],[5]]=>[[1,2,4],[3,5],[6,8],[7]]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111
[[1,4,8],[2,5],[3,7],[6]]=>[[1,2,3],[4,6],[5,7],[8]]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101
[[1,3,8],[2,5],[4,7],[6]]=>[[1,2,3],[4,5],[6,7],[8]]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010
[[1,2,8],[3,5],[4,7],[6]]=>[[1,2,3],[4,5],[6,8],[7]]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011
[[1,3,8],[2,4],[5,7],[6]]=>[[1,2,3],[4,7],[5,8],[6]]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110
[[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101
[[1,4,8],[2,5],[3,6],[7]]=>[[1,2,6],[3,7],[4,8],[5]]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101
[[1,3,8],[2,5],[4,6],[7]]=>[[1,2,5],[3,7],[4,8],[6]]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010
[[1,2,8],[3,5],[4,6],[7]]=>[[1,2,5],[3,6],[4,8],[7]]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011
[[1,3,8],[2,4],[5,6],[7]]=>[[1,2,4],[3,7],[5,8],[6]]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110
[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,4],[3,6],[5,8],[7]]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101
[[1,5,7],[2,6],[3,8],[4]]=>[[1,3,5],[2,6],[4,7],[8]]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011
[[1,4,7],[2,6],[3,8],[5]]=>[[1,3,4],[2,6],[5,7],[8]]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101
[[1,3,7],[2,6],[4,8],[5]]=>[[1,3,4],[2,5],[6,7],[8]]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110
[[1,2,7],[3,6],[4,8],[5]]=>[[1,3,4],[2,5],[6,8],[7]]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111
[[1,4,7],[2,5],[3,8],[6]]=>[[1,3,6],[2,4],[5,7],[8]]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101
[[1,3,7],[2,5],[4,8],[6]]=>[[1,3,5],[2,4],[6,7],[8]]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010
[[1,2,7],[3,5],[4,8],[6]]=>[[1,3,5],[2,4],[6,8],[7]]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011
[[1,3,7],[2,4],[5,8],[6]]=>[[1,3,7],[2,4],[5,8],[6]]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110
[[1,2,7],[3,4],[5,8],[6]]=>[[1,3,6],[2,4],[5,8],[7]]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101
[[1,5,6],[2,7],[3,8],[4]]=>[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011
[[1,4,6],[2,7],[3,8],[5]]=>[[1,4,6],[2,5],[3,7],[8]]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101
[[1,3,6],[2,7],[4,8],[5]]=>[[1,4,7],[2,5],[3,6],[8]]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110
[[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111
[[1,4,5],[2,7],[3,8],[6]]=>[[1,3,6],[2,5],[4,7],[8]]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001
[[1,3,5],[2,7],[4,8],[6]]=>[[1,3,7],[2,5],[4,6],[8]]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010
[[1,2,5],[3,7],[4,8],[6]]=>[[1,3,8],[2,5],[4,6],[7]]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011
[[1,3,4],[2,7],[5,8],[6]]=>[[1,3,7],[2,4],[5,6],[8]]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100
[[1,2,4],[3,7],[5,8],[6]]=>[[1,3,8],[2,4],[5,6],[7]]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101
[[1,2,3],[4,7],[5,8],[6]]=>[[1,3,8],[2,4],[5,7],[6]]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110
[[1,4,6],[2,5],[3,8],[7]]=>[[1,2,6],[3,4],[5,7],[8]]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101
[[1,3,6],[2,5],[4,8],[7]]=>[[1,2,5],[3,4],[6,7],[8]]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010
[[1,2,6],[3,5],[4,8],[7]]=>[[1,2,5],[3,4],[6,8],[7]]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011
[[1,3,6],[2,4],[5,8],[7]]=>[[1,2,7],[3,4],[5,8],[6]]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110
[[1,2,6],[3,4],[5,8],[7]]=>[[1,2,6],[3,4],[5,8],[7]]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101
[[1,4,5],[2,6],[3,8],[7]]=>[[1,2,6],[3,5],[4,7],[8]]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001
[[1,3,5],[2,6],[4,8],[7]]=>[[1,2,7],[3,5],[4,6],[8]]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010
[[1,2,5],[3,6],[4,8],[7]]=>[[1,2,8],[3,5],[4,6],[7]]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011
[[1,3,4],[2,6],[5,8],[7]]=>[[1,2,7],[3,4],[5,6],[8]]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100
[[1,2,4],[3,6],[5,8],[7]]=>[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101
[[1,2,3],[4,6],[5,8],[7]]=>[[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110
[[1,3,5],[2,4],[6,8],[7]]=>[[1,2,7],[3,5],[4,8],[6]]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010
[[1,2,5],[3,4],[6,8],[7]]=>[[1,2,6],[3,5],[4,8],[7]]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001
[[1,3,4],[2,5],[6,8],[7]]=>[[1,2,7],[3,6],[4,8],[5]]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100
[[1,2,4],[3,5],[6,8],[7]]=>[[1,2,8],[3,6],[4,7],[5]]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101
[[1,2,3],[4,5],[6,8],[7]]=>[[1,2,8],[3,5],[4,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010
[[1,4,7],[2,5],[3,6],[8]]=>[[1,3,6],[2,7],[4,8],[5]]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101
[[1,3,7],[2,5],[4,6],[8]]=>[[1,3,5],[2,7],[4,8],[6]]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010
[[1,2,7],[3,5],[4,6],[8]]=>[[1,3,5],[2,6],[4,8],[7]]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011
[[1,3,7],[2,4],[5,6],[8]]=>[[1,3,4],[2,7],[5,8],[6]]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110
[[1,2,7],[3,4],[5,6],[8]]=>[[1,3,4],[2,6],[5,8],[7]]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101
[[1,4,6],[2,5],[3,7],[8]]=>[[1,4,6],[2,7],[3,8],[5]]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101
[[1,3,6],[2,5],[4,7],[8]]=>[[1,4,5],[2,7],[3,8],[6]]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010
[[1,2,6],[3,5],[4,7],[8]]=>[[1,4,5],[2,6],[3,8],[7]]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011
[[1,3,6],[2,4],[5,7],[8]]=>[[1,4,7],[2,5],[3,8],[6]]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110
[[1,2,6],[3,4],[5,7],[8]]=>[[1,4,6],[2,5],[3,8],[7]]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101
[[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001
[[1,3,5],[2,6],[4,7],[8]]=>[[1,5,7],[2,6],[3,8],[4]]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010
[[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011
[[1,3,4],[2,6],[5,7],[8]]=>[[1,4,7],[2,6],[3,8],[5]]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100
[[1,2,4],[3,6],[5,7],[8]]=>[[1,4,8],[2,6],[3,7],[5]]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101
[[1,2,3],[4,6],[5,7],[8]]=>[[1,4,8],[2,5],[3,7],[6]]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110
[[1,3,5],[2,4],[6,7],[8]]=>[[1,3,7],[2,5],[4,8],[6]]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010
[[1,2,5],[3,4],[6,7],[8]]=>[[1,3,6],[2,5],[4,8],[7]]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001
[[1,3,4],[2,5],[6,7],[8]]=>[[1,3,7],[2,6],[4,8],[5]]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100
[[1,2,4],[3,5],[6,7],[8]]=>[[1,3,8],[2,6],[4,7],[5]]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101
[[1,2,3],[4,5],[6,7],[8]]=>[[1,3,8],[2,5],[4,7],[6]]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010
[[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111
[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011
[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101
[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110
[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111
[[1,5,8],[2,6],[3],[4],[7]]=>[[1,2,5],[3,6],[4],[7],[8]]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011
[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101
[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110
[[1,2,8],[3,6],[4],[5],[7]]=>[[1,2,4],[3,8],[5],[6],[7]]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111
[[1,4,8],[2,5],[3],[6],[7]]=>[[1,2,6],[3,7],[4],[5],[8]]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101
[[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,5],[3,7],[4],[6],[8]]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010
[[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,5],[3,8],[4],[6],[7]]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011
[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110
[[1,2,8],[3,4],[5],[6],[7]]=>[[1,2,6],[3,8],[4],[5],[7]]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101
[[1,6,7],[2,8],[3],[4],[5]]=>[[1,3,4],[2,5],[6],[7],[8]]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111
[[1,5,7],[2,8],[3],[4],[6]]=>[[1,3,5],[2,4],[6],[7],[8]]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011
[[1,4,7],[2,8],[3],[5],[6]]=>[[1,3,6],[2,4],[5],[7],[8]]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101
[[1,3,7],[2,8],[4],[5],[6]]=>[[1,3,7],[2,4],[5],[6],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110
[[1,2,7],[3,8],[4],[5],[6]]=>[[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111
[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011
[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101
[[1,3,6],[2,8],[4],[5],[7]]=>[[1,2,7],[3,4],[5],[6],[8]]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110
[[1,2,6],[3,8],[4],[5],[7]]=>[[1,2,8],[3,4],[5],[6],[7]]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111
[[1,4,5],[2,8],[3],[6],[7]]=>[[1,2,6],[3,5],[4],[7],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001
[[1,3,5],[2,8],[4],[6],[7]]=>[[1,2,7],[3,5],[4],[6],[8]]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010
[[1,2,5],[3,8],[4],[6],[7]]=>[[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011
[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100
[[1,2,4],[3,8],[5],[6],[7]]=>[[1,2,8],[3,6],[4],[5],[7]]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101
[[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110
[[1,5,7],[2,6],[3],[4],[8]]=>[[1,3,5],[2,6],[4],[7],[8]]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011
[[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101
[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110
[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111
[[1,4,7],[2,5],[3],[6],[8]]=>[[1,3,6],[2,7],[4],[5],[8]]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101
[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010
[[1,2,7],[3,5],[4],[6],[8]]=>[[1,3,5],[2,8],[4],[6],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011
[[1,3,7],[2,4],[5],[6],[8]]=>[[1,3,7],[2,8],[4],[5],[6]]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110
[[1,2,7],[3,4],[5],[6],[8]]=>[[1,3,6],[2,8],[4],[5],[7]]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101
[[1,5,6],[2,7],[3],[4],[8]]=>[[1,4,5],[2,6],[3],[7],[8]]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011
[[1,4,6],[2,7],[3],[5],[8]]=>[[1,4,6],[2,5],[3],[7],[8]]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101
[[1,3,6],[2,7],[4],[5],[8]]=>[[1,4,7],[2,5],[3],[6],[8]]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110
[[1,2,6],[3,7],[4],[5],[8]]=>[[1,4,8],[2,5],[3],[6],[7]]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111
[[1,4,5],[2,7],[3],[6],[8]]=>[[1,3,6],[2,5],[4],[7],[8]]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001
[[1,3,5],[2,7],[4],[6],[8]]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010
[[1,2,5],[3,7],[4],[6],[8]]=>[[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011
[[1,3,4],[2,7],[5],[6],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100
[[1,2,4],[3,7],[5],[6],[8]]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101
[[1,2,3],[4,7],[5],[6],[8]]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110
[[1,4,6],[2,5],[3],[7],[8]]=>[[1,4,6],[2,7],[3],[5],[8]]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101
[[1,3,6],[2,5],[4],[7],[8]]=>[[1,4,5],[2,7],[3],[6],[8]]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010
[[1,2,6],[3,5],[4],[7],[8]]=>[[1,4,5],[2,8],[3],[6],[7]]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011
[[1,3,6],[2,4],[5],[7],[8]]=>[[1,4,7],[2,8],[3],[5],[6]]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110
[[1,2,6],[3,4],[5],[7],[8]]=>[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101
[[1,4,5],[2,6],[3],[7],[8]]=>[[1,5,6],[2,7],[3],[4],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001
[[1,3,5],[2,6],[4],[7],[8]]=>[[1,5,7],[2,6],[3],[4],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010
[[1,2,5],[3,6],[4],[7],[8]]=>[[1,5,8],[2,6],[3],[4],[7]]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011
[[1,3,4],[2,6],[5],[7],[8]]=>[[1,4,7],[2,6],[3],[5],[8]]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100
[[1,2,4],[3,6],[5],[7],[8]]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101
[[1,2,3],[4,6],[5],[7],[8]]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110
[[1,3,5],[2,4],[6],[7],[8]]=>[[1,5,7],[2,8],[3],[4],[6]]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010
[[1,2,5],[3,4],[6],[7],[8]]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001
[[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100
[[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101
[[1,2,3],[4,5],[6],[7],[8]]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010
[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111
[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111
[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011
[[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101
[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110
[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111
[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111
[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011
[[1,4,7],[2],[3],[5],[6],[8]]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101
[[1,3,7],[2],[4],[5],[6],[8]]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110
[[1,2,7],[3],[4],[5],[6],[8]]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111
[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011
[[1,4,6],[2],[3],[5],[7],[8]]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101
[[1,3,6],[2],[4],[5],[7],[8]]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110
[[1,2,6],[3],[4],[5],[7],[8]]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111
[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001
[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010
[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011
[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100
[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101
[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110
[[1,5],[2,6],[3,7],[4,8]]=>[[1,5],[2,6],[3,7],[4,8]]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011
[[1,4],[2,6],[3,7],[5,8]]=>[[1,4],[2,6],[3,7],[5,8]]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101
[[1,3],[2,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,7],[6,8]]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110
[[1,2],[3,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,6],[7,8]]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111
[[1,4],[2,5],[3,7],[6,8]]=>[[1,3],[2,6],[4,7],[5,8]]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101
[[1,3],[2,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,7],[6,8]]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010
[[1,2],[3,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,6],[7,8]]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011
[[1,3],[2,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,7],[6,8]]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110
[[1,2],[3,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,6],[7,8]]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101
[[1,4],[2,5],[3,6],[7,8]]=>[[1,2],[3,6],[4,7],[5,8]]=>[[1,3],[2,4],[5,7],[6,8]]=>1011101
[[1,3],[2,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,7],[6,8]]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010
[[1,2],[3,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,6],[7,8]]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011
[[1,3],[2,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,7],[6,8]]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110
[[1,2],[3,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,6],[7,8]]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101
[[1,6],[2,7],[3,8],[4],[5]]=>[[1,4],[2,5],[3,6],[7],[8]]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111
[[1,5],[2,7],[3,8],[4],[6]]=>[[1,3],[2,5],[4,6],[7],[8]]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011
[[1,4],[2,7],[3,8],[5],[6]]=>[[1,3],[2,4],[5,6],[7],[8]]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101
[[1,3],[2,7],[4,8],[5],[6]]=>[[1,3],[2,4],[5,7],[6],[8]]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110
[[1,2],[3,7],[4,8],[5],[6]]=>[[1,3],[2,4],[5,8],[6],[7]]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111
[[1,5],[2,6],[3,8],[4],[7]]=>[[1,2],[3,5],[4,6],[7],[8]]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011
[[1,4],[2,6],[3,8],[5],[7]]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101
[[1,3],[2,6],[4,8],[5],[7]]=>[[1,2],[3,4],[5,7],[6],[8]]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110
[[1,2],[3,6],[4,8],[5],[7]]=>[[1,2],[3,4],[5,8],[6],[7]]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111
[[1,4],[2,5],[3,8],[6],[7]]=>[[1,2],[3,6],[4,7],[5],[8]]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101
[[1,3],[2,5],[4,8],[6],[7]]=>[[1,2],[3,5],[4,7],[6],[8]]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010
[[1,2],[3,5],[4,8],[6],[7]]=>[[1,2],[3,5],[4,8],[6],[7]]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011
[[1,3],[2,4],[5,8],[6],[7]]=>[[1,2],[3,7],[4,8],[5],[6]]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110
[[1,2],[3,4],[5,8],[6],[7]]=>[[1,2],[3,6],[4,8],[5],[7]]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101
[[1,5],[2,6],[3,7],[4],[8]]=>[[1,5],[2,6],[3,7],[4],[8]]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011
[[1,4],[2,6],[3,7],[5],[8]]=>[[1,4],[2,6],[3,7],[5],[8]]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101
[[1,3],[2,6],[4,7],[5],[8]]=>[[1,4],[2,5],[3,7],[6],[8]]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110
[[1,2],[3,6],[4,7],[5],[8]]=>[[1,4],[2,5],[3,8],[6],[7]]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111
[[1,4],[2,5],[3,7],[6],[8]]=>[[1,3],[2,6],[4,7],[5],[8]]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101
[[1,3],[2,5],[4,7],[6],[8]]=>[[1,3],[2,5],[4,7],[6],[8]]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010
[[1,2],[3,5],[4,7],[6],[8]]=>[[1,3],[2,5],[4,8],[6],[7]]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011
[[1,3],[2,4],[5,7],[6],[8]]=>[[1,3],[2,7],[4,8],[5],[6]]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110
[[1,2],[3,4],[5,7],[6],[8]]=>[[1,3],[2,6],[4,8],[5],[7]]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101
[[1,4],[2,5],[3,6],[7],[8]]=>[[1,6],[2,7],[3,8],[4],[5]]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101
[[1,3],[2,5],[4,6],[7],[8]]=>[[1,5],[2,7],[3,8],[4],[6]]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010
[[1,2],[3,5],[4,6],[7],[8]]=>[[1,5],[2,6],[3,8],[4],[7]]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011
[[1,3],[2,4],[5,6],[7],[8]]=>[[1,4],[2,7],[3,8],[5],[6]]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110
[[1,2],[3,4],[5,6],[7],[8]]=>[[1,4],[2,6],[3,8],[5],[7]]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101
[[1,7],[2,8],[3],[4],[5],[6]]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111
[[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111
[[1,5],[2,8],[3],[4],[6],[7]]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011
[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101
[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110
[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111
[[1,6],[2,7],[3],[4],[5],[8]]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111
[[1,5],[2,7],[3],[4],[6],[8]]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011
[[1,4],[2,7],[3],[5],[6],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101
[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110
[[1,2],[3,7],[4],[5],[6],[8]]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111
[[1,5],[2,6],[3],[4],[7],[8]]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011
[[1,4],[2,6],[3],[5],[7],[8]]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101
[[1,3],[2,6],[4],[5],[7],[8]]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110
[[1,2],[3,6],[4],[5],[7],[8]]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111
[[1,4],[2,5],[3],[6],[7],[8]]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101
[[1,3],[2,5],[4],[6],[7],[8]]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010
[[1,2],[3,5],[4],[6],[7],[8]]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011
[[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110
[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101
[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111
[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111
[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111
[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011
[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101
[[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110
[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>1111111
[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,2,4,6,8],[3,5,7,9,10]]=>010101010
[[1,3,5,7,8],[2,4,6,9,10]]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,2,3,6,8],[4,5,7,9,10]]=>001001010
[[1,3,5,6,9],[2,4,7,8,10]]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[[1,2,4,5,8],[3,6,7,9,10]]=>010010010
[[1,3,5,6,8],[2,4,7,9,10]]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[[1,2,3,5,8],[4,6,7,9,10]]=>001010010
[[1,3,5,6,7],[2,4,8,9,10]]=>[[1,2,3,7,9],[4,5,6,8,10]]=>[[1,2,3,4,8],[5,6,7,9,10]]=>000100010
[[1,3,4,7,9],[2,5,6,8,10]]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[[1,2,4,6,7],[3,5,8,9,10]]=>010100100
[[1,3,4,7,8],[2,5,6,9,10]]=>[[1,2,5,6,9],[3,4,7,8,10]]=>[[1,2,3,6,7],[4,5,8,9,10]]=>001000100
[[1,3,4,6,9],[2,5,7,8,10]]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[[1,2,4,5,7],[3,6,8,9,10]]=>010010100
[[1,3,4,6,8],[2,5,7,9,10]]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[[1,2,3,5,7],[4,6,8,9,10]]=>001010100
[[1,3,4,6,7],[2,5,8,9,10]]=>[[1,2,3,6,9],[4,5,7,8,10]]=>[[1,2,3,4,7],[5,6,8,9,10]]=>000100100
[[1,3,4,5,9],[2,6,7,8,10]]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[[1,2,4,5,6],[3,7,8,9,10]]=>010001000
[[1,3,4,5,8],[2,6,7,9,10]]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[[1,2,3,5,6],[4,7,8,9,10]]=>001001000
[[1,3,4,5,7],[2,6,8,9,10]]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[[1,2,3,4,6],[5,7,8,9,10]]=>000101000
[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000
[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[[1,2,4,6,9],[3,5,7,8,10]]=>010101001
[[1,2,5,7,8],[3,4,6,9,10]]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[[1,2,3,6,9],[4,5,7,8,10]]=>001001001
[[1,2,5,6,9],[3,4,7,8,10]]=>[[1,3,4,7,8],[2,5,6,9,10]]=>[[1,2,4,5,9],[3,6,7,8,10]]=>010010001
[[1,2,5,6,8],[3,4,7,9,10]]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[[1,2,3,5,9],[4,6,7,8,10]]=>001010001
[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,2,3,4,9],[5,6,7,8,10]]=>000100001
[[1,2,4,7,9],[3,5,6,8,10]]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[[1,2,4,7,9],[3,5,6,8,10]]=>010100101
[[1,2,4,7,8],[3,5,6,9,10]]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[[1,2,3,7,9],[4,5,6,8,10]]=>001000101
[[1,2,4,6,9],[3,5,7,8,10]]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[[1,2,5,7,9],[3,4,6,8,10]]=>010010101
[[1,2,4,6,8],[3,5,7,9,10]]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101
[[1,2,4,6,7],[3,5,8,9,10]]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[[1,3,4,7,9],[2,5,6,8,10]]=>100100101
[[1,2,4,5,9],[3,6,7,8,10]]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[[1,2,5,6,9],[3,4,7,8,10]]=>010001001
[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,3,5,6,9],[2,4,7,8,10]]=>101001001
[[1,2,4,5,7],[3,6,8,9,10]]=>[[1,2,3,5,8],[4,6,7,9,10]]=>[[1,3,4,6,9],[2,5,7,8,10]]=>100101001
[[1,2,4,5,6],[3,7,8,9,10]]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,3,4,5,9],[2,6,7,8,10]]=>100010001
[[1,2,3,7,9],[4,5,6,8,10]]=>[[1,3,5,6,7],[2,4,8,9,10]]=>[[1,2,4,7,8],[3,5,6,9,10]]=>010100010
[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,2,3,7,8],[4,5,6,9,10]]=>001000010
[[1,2,3,6,9],[4,5,7,8,10]]=>[[1,3,4,6,7],[2,5,8,9,10]]=>[[1,2,5,7,8],[3,4,6,9,10]]=>010010010
[[1,2,3,6,8],[4,5,7,9,10]]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[[1,3,5,7,8],[2,4,6,9,10]]=>101010010
[[1,2,3,6,7],[4,5,8,9,10]]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[[1,3,4,7,8],[2,5,6,9,10]]=>100100010
[[1,2,3,5,9],[4,6,7,8,10]]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[[1,2,5,6,8],[3,4,7,9,10]]=>010001010
[[1,2,3,5,8],[4,6,7,9,10]]=>[[1,2,4,5,7],[3,6,8,9,10]]=>[[1,3,5,6,8],[2,4,7,9,10]]=>101001010
[[1,2,3,5,7],[4,6,8,9,10]]=>[[1,2,3,5,7],[4,6,8,9,10]]=>[[1,3,4,6,8],[2,5,7,9,10]]=>100101010
[[1,2,3,5,6],[4,7,8,9,10]]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,3,4,5,8],[2,6,7,9,10]]=>100010010
[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,5,6,7],[3,4,8,9,10]]=>010000100
[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[[1,3,5,6,7],[2,4,8,9,10]]=>101000100
[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[[1,3,4,6,7],[2,5,8,9,10]]=>100100100
[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,3,4,5,7],[2,6,8,9,10]]=>100010100
[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,3,4,5,6],[2,7,8,9,10]]=>100001000
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>01010101010
[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>00100101010
[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>01001001010
[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>00101001010
[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>00010001010
[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>01010010010
[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>00100010010
[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>01001010010
[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>00101010010
[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>00010010010
[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>01000100010
[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>00100100010
[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>00010100010
[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>00001000010
[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>01010100100
[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>00100100100
[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>01001000100
[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>00101000100
[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>00010000100
[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>01010010100
[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>00100010100
[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>01001010100
[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>00101010100
[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>00010010100
[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>01000100100
[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>00100100100
[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>00010100100
[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>00001000100
[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>01010001000
[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>00100001000
[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>01001001000
[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>00101001000
[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>00010001000
[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>01000101000
[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>00100101000
[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>00010101000
[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>00001001000
[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>01000010000
[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>00100010000
[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>00010010000
[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>00001010000
[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000
[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>01010101001
[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>00100101001
[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>01001001001
[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>00101001001
[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>00010001001
[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>01010010001
[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>00100010001
[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>01001010001
[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>00101010001
[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>00010010001
[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>01000100001
[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>00100100001
[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>00010100001
[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>00001000001
[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>01010100101
[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>00100100101
[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>01001000101
[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>00101000101
[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>00010000101
[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>01010010101
[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>00100010101
[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>01001010101
[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>10101010101
[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>10010010101
[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>01000100101
[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>10100100101
[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>10010100101
[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>10001000101
[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>01010001001
[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>00100001001
[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>01001001001
[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>10101001001
[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>10010001001
[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>01000101001
[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>10100101001
[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>10010101001
[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>10001001001
[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>01000010001
[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>10100010001
[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>10010010001
[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>10001010001
[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>10000100001
[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>01010100010
[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>00100100010
[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>01001000010
[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>00101000010
[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>00010000010
[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>01010010010
[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>00100010010
[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>01001010010
[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>10101010010
[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>10010010010
[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>01000100010
[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>10100100010
[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>10010100010
[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>10001000010
[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>01010001010
[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>00100001010
[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>01001001010
[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>10101001010
[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>10010001010
[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>01000101010
[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>10100101010
[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>10010101010
[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>10001001010
[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>01000010010
[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>10100010010
[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>10010010010
[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>10001010010
[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>10000100010
[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>01010000100
[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>00100000100
[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>01001000100
[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>10101000100
[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>10010000100
[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>01000100100
[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>10100100100
[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>10010100100
[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>10001000100
[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>01000010100
[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>10100010100
[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>10010010100
[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>10001010100
[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>10000100100
[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>01000001000
[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>10100001000
[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>10010001000
[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>10001001000
[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>10000101000
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>10000010000
[[1,2,3,4,5,6,7,8,9]]=>[[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]]=>[[1,2,3,4,9],[5,6,7,8]]=>[[1,2,3,4,5],[6,7,8,9]]=>00001000
[[1,2,3],[4,5],[6,7],[8,9]]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[[1,2,3],[4,5],[6,7],[8,9]]=>00101010
[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>01010101
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>11111111
[[1,2,3,4,5,6,7,8,9,10]]=>[[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]]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>000100100
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,3],[2,5],[4,7],[6,9],[8,10]]=>101010101
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>10101010101
[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000
[[1,3,4,5],[2,7,8,9],[6]]=>[[1,2,3,4],[5,6,7,8],[9]]=>[[1,3,4,5],[2,7,8,9],[6]]=>10001000
[[1,3],[2,5],[4,7],[6,9],[8]]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>10101010
[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000
[[1,3,4],[2,6,7],[5,9,10],[8]]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>100100100
[[1,6],[2,7],[3,8],[4,9],[5]]=>[[1,5],[2,6],[3,7],[4,8],[9]]=>[[1,6],[2,7],[3,8],[4,9],[5]]=>11110111
[[1,4,6,8],[2,5,7,9],[3]]=>[[1,3,5,7],[2,4,6,8],[9]]=>[[1,4,6,8],[2,5,7,9],[3]]=>11010101
[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[[1,2],[3,7],[4,8],[5,9],[6,10]]=>011110111
[[1,5,8],[2,6,9],[3,7,10],[4]]=>[[1,4,7],[2,5,8],[3,6,9],[10]]=>[[1,5,8],[2,6,9],[3,7,10],[4]]=>111011011
[[1,2,6],[3,7],[4,8],[5,9]]=>[[1,5,9],[2,6],[3,7],[4,8]]=>[[1,2,6],[3,7],[4,8],[5,9]]=>01110111
[[1,2,4,6,8],[3,5,7,9]]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101
[[1,2,5,8],[3,6,9],[4,7,10]]=>[[1,4,7,10],[2,5,8],[3,6,9]]=>[[1,2,5,8],[3,6,9],[4,7,10]]=>011011011
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[[1,4],[2,5],[3,7],[6,9],[8,10]]=>110110101
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,6],[7,8],[9,10]]=>[[1,3],[2,6],[4,7],[5,9],[8,10]]=>101101101
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[[1,4],[2,6],[3,7],[5,9],[8,10]]=>110101101
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,6],[7,8],[9,10]]=>[[1,5],[2,6],[3,7],[4,9],[8,10]]=>111011101
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,7],[6,8],[9,10]]=>[[1,3],[2,5],[4,8],[6,9],[7,10]]=>101011011
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,7],[6,8],[9,10]]=>[[1,4],[2,5],[3,8],[6,9],[7,10]]=>110111011
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,7],[6,8],[9,10]]=>[[1,3],[2,6],[4,8],[5,9],[7,10]]=>101101011
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,7],[6,8],[9,10]]=>[[1,4],[2,6],[3,8],[5,9],[7,10]]=>110101011
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,7],[6,8],[9,10]]=>[[1,5],[2,6],[3,8],[4,9],[7,10]]=>111011011
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,7],[5,8],[9,10]]=>[[1,3],[2,7],[4,8],[5,9],[6,10]]=>101110111
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,7],[5,8],[9,10]]=>[[1,4],[2,7],[3,8],[5,9],[6,10]]=>110110111
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,7],[5,8],[9,10]]=>[[1,5],[2,7],[3,8],[4,9],[6,10]]=>111010111
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,7],[4,8],[9,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>111101111
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[[1,3],[2,5],[4,7],[6,8],[9,10]]=>101010110
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,6],[7,9],[8,10]]=>[[1,4],[2,5],[3,7],[6,8],[9,10]]=>110110110
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,6],[7,9],[8,10]]=>[[1,3],[2,6],[4,7],[5,8],[9,10]]=>101101110
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,6],[7,9],[8,10]]=>[[1,4],[2,6],[3,7],[5,8],[9,10]]=>110101110
[[1,3],[2,4],[5,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,6],[7,9],[8,10]]=>[[1,5],[2,6],[3,7],[4,8],[9,10]]=>111011110
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,6],[7,8],[9,10]]=>101011010
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,7],[6,9],[8,10]]=>[[1,4],[2,5],[3,6],[7,8],[9,10]]=>110111010
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,7],[6,9],[8,10]]=>[[1,3],[2,4],[5,6],[7,8],[9,10]]=>101101010
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,7],[6,9],[8,10]]=>[[1,2],[3,5],[4,6],[7,8],[9,10]]=>011011010
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,7],[5,9],[8,10]]=>[[1,3],[2,4],[5,7],[6,8],[9,10]]=>101110110
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,7],[5,9],[8,10]]=>[[1,2],[3,4],[5,7],[6,8],[9,10]]=>010110110
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,7],[5,9],[8,10]]=>[[1,2],[3,5],[4,7],[6,8],[9,10]]=>011010110
[[1,3],[2,7],[4,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,7],[4,9],[8,10]]=>[[1,2],[3,6],[4,7],[5,8],[9,10]]=>011101110
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[[1,3],[2,5],[4,6],[7,9],[8,10]]=>101011101
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,6],[7,9],[8,10]]=>110111101
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,8],[6,9],[7,10]]=>[[1,3],[2,4],[5,6],[7,9],[8,10]]=>101101101
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,8],[6,9],[7,10]]=>[[1,2],[3,4],[5,6],[7,9],[8,10]]=>010101101
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,8],[6,9],[7,10]]=>[[1,2],[3,5],[4,6],[7,9],[8,10]]=>011011101
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,8],[5,9],[7,10]]=>[[1,3],[2,4],[5,7],[6,9],[8,10]]=>101110101
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,8],[5,9],[7,10]]=>[[1,2],[3,4],[5,7],[6,9],[8,10]]=>010110101
[[1,4],[2,6],[3,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,8],[5,9],[7,10]]=>[[1,2],[3,5],[4,7],[6,9],[8,10]]=>011010101
[[1,4],[2,7],[3,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,8],[4,9],[7,10]]=>[[1,2],[3,6],[4,7],[5,9],[8,10]]=>011101101
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[[1,3],[2,4],[5,8],[6,9],[7,10]]=>101111011
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>[[1,3],[2,7],[4,8],[5,9],[6,10]]=>[[1,2],[3,4],[5,8],[6,9],[7,10]]=>010111011
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>[[1,4],[2,7],[3,8],[5,9],[6,10]]=>[[1,2],[3,5],[4,8],[6,9],[7,10]]=>011011011
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>[[1,5],[2,7],[3,8],[4,9],[6,10]]=>[[1,2],[3,6],[4,8],[5,9],[7,10]]=>011101011
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>11011010101
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>10110110101
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>11010110101
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>11101110101
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>10101101101
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>11011101101
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>10110101101
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>11010101101
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>11101101101
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>10111011101
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>11011011101
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>11101011101
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>11110111101
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>10101011011
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>11011011011
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>10110111011
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>11010111011
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>11101111011
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>10101101011
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>11011101011
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>10110101011
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>11010101011
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>11101101011
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>10111011011
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>11011011011
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>11101011011
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>11110111011
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>10101110111
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>11011110111
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>10110110111
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>11010110111
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>11101110111
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>10111010111
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>11011010111
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>11101010111
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>11110110111
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>10111101111
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>11011101111
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>11101101111
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>11110101111
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>11111011111
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>10101010110
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>11011010110
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>10110110110
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>11010110110
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>11101110110
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>10101101110
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>11011101110
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>10110101110
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>11010101110
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>11101101110
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>10111011110
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>11011011110
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>11101011110
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>11110111110
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>10101011010
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>11011011010
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>10110111010
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>11010111010
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>11101111010
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>10101101010
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>11011101010
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>10110101010
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>01101101010
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>10111011010
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>01011011010
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>01101011010
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>01110111010
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>10101110110
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>11011110110
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>10110110110
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>01010110110
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>01101110110
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>10111010110
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>01011010110
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>01101010110
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>01110110110
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>10111101110
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>01011101110
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>01101101110
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>01110101110
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>01111011110
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>10101011101
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>11011011101
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>10110111101
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>11010111101
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>11101111101
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>10101101101
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>11011101101
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>10110101101
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>01010101101
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>01101101101
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>10111011101
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>01011011101
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>01101011101
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>01110111101
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>10101110101
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>11011110101
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>10110110101
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>01010110101
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>01101110101
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>10111010101
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>01011010101
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>01101010101
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>01110110101
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>10111101101
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>01011101101
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>01101101101
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>01110101101
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>01111011101
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>10101111011
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>11011111011
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>10110111011
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>01010111011
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>01101111011
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>10111011011
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>01011011011
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>01101011011
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>01110111011
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>10111101011
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>01011101011
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>01101101011
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>01110101011
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>01111011011
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>10111110111
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>01011110111
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>01101110111
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>01110110111
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>01111010111
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>01111101111
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
Map
promotion
Description
The promotion of a standard Young tableau.
This map replaces the largest entry of the tableau with a zero, uses the jeu de taquin to move it to the origin, and finally increases all entries by one.
This map replaces the largest entry of the tableau with a zero, uses the jeu de taquin to move it to the origin, and finally increases all entries by one.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
searching the database
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