Identifier
Mp00033:
Dyck paths
—to two-row standard tableau⟶
Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
[1,0] => [[1],[2]] => 1
[1,0,1,0] => [[1,3],[2,4]] => 101
[1,1,0,0] => [[1,2],[3,4]] => 010
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 10101
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 10010
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 01001
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 01010
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 00100
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 1010101
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 1010010
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 1001001
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 1001010
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 1000100
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 0100101
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 0100010
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 0101001
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 0101010
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 0100100
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 0010001
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 0010010
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 0010100
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 0001000
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 101010010
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 101001001
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 101001010
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 101000100
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 100100101
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 100100010
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 100101001
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 100101010
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 100100100
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 100010001
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 100010010
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 100010100
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => 100001000
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 010010101
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 010010010
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 010001001
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => 010001010
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => 010000100
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 010100101
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => 010100010
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 010101001
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => 010101010
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => 010100100
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 010010001
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => 010010010
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => 010010100
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => 010001000
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => 001000101
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => 001000010
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => 001001001
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => 001001010
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => 001000100
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => 001010001
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => 001010010
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => 001010100
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => 001001000
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => 000100001
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => 000100010
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => 000100100
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => 000101000
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 10101010101
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => 10101010010
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => 10101001001
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => 10101001010
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 10101000100
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => 10100100101
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => 10100100010
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => 10100101001
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 10100101010
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => 10100100100
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 10100010001
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => 10100010010
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 10100010100
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 10100001000
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => 10010010101
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 10010010010
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => 10010001001
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 10010001010
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => 10010000100
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 10010100101
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 10010100010
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 10010101001
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 10010101010
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 10010100100
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 10010010001
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 10010010010
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 10010010100
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 10010001000
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 10001000101
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => 10001000010
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 10001001001
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 10001001010
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 10001000100
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 10001010001
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 10001010010
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 10001010100
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 10001001000
>>> Load all 1165 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 10000100001
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 10000100010
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 10000100100
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 10000101000
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 10000010000
[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => 01001010101
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => 01001010010
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => 01001001001
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 01001001010
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => 01001000100
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => 01000100101
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 01000100010
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 01000101001
[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => 01000101010
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 01000100100
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => 01000010001
[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 01000010010
[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 01000010100
[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => 01000001000
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => 01010010101
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 01010010010
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 01010001001
[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => 01010001010
[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 01010000100
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 01010100101
[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => 01010100010
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => 01010101001
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => 01010101010
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => 01010100100
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 01010010001
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => 01010010010
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => 01010010100
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => 01010001000
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 01001000101
[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 01001000010
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 01001001001
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => 01001001010
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => 01001000100
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 01001010001
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => 01001010010
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => 01001010100
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => 01001001000
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 01000100001
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => 01000100010
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => 01000100100
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => 01000101000
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => 01000010000
[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 00100010101
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => 00100010010
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => 00100001001
[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 00100001010
[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => 00100000100
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => 00100100101
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 00100100010
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 00100101001
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => 00100101010
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => 00100100100
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 00100010001
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => 00100010010
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => 00100010100
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => 00100001000
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 00101000101
[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 00101000010
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 00101001001
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => 00101001010
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => 00101000100
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 00101010001
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => 00101010010
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => 00101010100
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => 00101001000
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 00100100001
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => 00100100010
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => 00100100100
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => 00100101000
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => 00100010000
[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 00010000101
[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => 00010000010
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 00010001001
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => 00010001010
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => 00010000100
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 00010010001
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => 00010010010
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => 00010010100
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => 00010001000
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 00010100001
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => 00010100010
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => 00010100100
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => 00010101000
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => 00010010000
[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 00001000001
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => 00001000010
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => 00001000100
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => 00001001000
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => 00001010000
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13],[2,4,6,8,10,12,14]] => 1010101010101
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,12],[2,4,6,8,10,13,14]] => 1010101010010
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,9,10,13],[2,4,6,8,11,12,14]] => 1010101001001
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,10,12],[2,4,6,8,11,13,14]] => 1010101001010
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,10,11],[2,4,6,8,12,13,14]] => 1010101000100
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,7,8,11,13],[2,4,6,9,10,12,14]] => 1010100100101
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,7,8,11,12],[2,4,6,9,10,13,14]] => 1010100100010
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,7,8,10,13],[2,4,6,9,11,12,14]] => 1010100101001
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12],[2,4,6,9,11,13,14]] => 1010100101010
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,7,8,10,11],[2,4,6,9,12,13,14]] => 1010100100100
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,7,8,9,13],[2,4,6,10,11,12,14]] => 1010100010001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,8,9,12],[2,4,6,10,11,13,14]] => 1010100010010
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,7,8,9,11],[2,4,6,10,12,13,14]] => 1010100010100
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,7,8,9,10],[2,4,6,11,12,13,14]] => 1010100001000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,5,6,9,11,13],[2,4,7,8,10,12,14]] => 1010010010101
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,5,6,9,11,12],[2,4,7,8,10,13,14]] => 1010010010010
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,5,6,9,10,13],[2,4,7,8,11,12,14]] => 1010010001001
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,5,6,9,10,12],[2,4,7,8,11,13,14]] => 1010010001010
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,5,6,9,10,11],[2,4,7,8,12,13,14]] => 1010010000100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,5,6,8,11,13],[2,4,7,9,10,12,14]] => 1010010100101
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,5,6,8,11,12],[2,4,7,9,10,13,14]] => 1010010100010
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,5,6,8,10,13],[2,4,7,9,11,12,14]] => 1010010101001
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12],[2,4,7,9,11,13,14]] => 1010010101010
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,5,6,8,10,11],[2,4,7,9,12,13,14]] => 1010010100100
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,5,6,8,9,13],[2,4,7,10,11,12,14]] => 1010010010001
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,5,6,8,9,12],[2,4,7,10,11,13,14]] => 1010010010010
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,5,6,8,9,11],[2,4,7,10,12,13,14]] => 1010010010100
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,5,6,8,9,10],[2,4,7,11,12,13,14]] => 1010010001000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,5,6,7,11,13],[2,4,8,9,10,12,14]] => 1010001000101
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,5,6,7,11,12],[2,4,8,9,10,13,14]] => 1010001000010
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,5,6,7,10,13],[2,4,8,9,11,12,14]] => 1010001001001
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,6,7,10,12],[2,4,8,9,11,13,14]] => 1010001001010
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,5,6,7,10,11],[2,4,8,9,12,13,14]] => 1010001000100
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,5,6,7,9,13],[2,4,8,10,11,12,14]] => 1010001010001
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,5,6,7,9,12],[2,4,8,10,11,13,14]] => 1010001010010
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,5,6,7,9,11],[2,4,8,10,12,13,14]] => 1010001010100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,5,6,7,9,10],[2,4,8,11,12,13,14]] => 1010001001000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,5,6,7,8,13],[2,4,9,10,11,12,14]] => 1010000100001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,5,6,7,8,12],[2,4,9,10,11,13,14]] => 1010000100010
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,5,6,7,8,11],[2,4,9,10,12,13,14]] => 1010000100100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,5,6,7,8,10],[2,4,9,11,12,13,14]] => 1010000101000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,5,6,7,8,9],[2,4,10,11,12,13,14]] => 1010000010000
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[1,3,4,7,9,11,13],[2,5,6,8,10,12,14]] => 1001001010101
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[1,3,4,7,9,11,12],[2,5,6,8,10,13,14]] => 1001001010010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[1,3,4,7,9,10,13],[2,5,6,8,11,12,14]] => 1001001001001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[1,3,4,7,9,10,12],[2,5,6,8,11,13,14]] => 1001001001010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[1,3,4,7,9,10,11],[2,5,6,8,12,13,14]] => 1001001000100
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,8,11,13],[2,5,6,9,10,12,14]] => 1001000100101
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8,11,12],[2,5,6,9,10,13,14]] => 1001000100010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[1,3,4,7,8,10,13],[2,5,6,9,11,12,14]] => 1001000101001
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[1,3,4,7,8,10,12],[2,5,6,9,11,13,14]] => 1001000101010
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[1,3,4,7,8,10,11],[2,5,6,9,12,13,14]] => 1001000100100
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[1,3,4,7,8,9,13],[2,5,6,10,11,12,14]] => 1001000010001
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[1,3,4,7,8,9,12],[2,5,6,10,11,13,14]] => 1001000010010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[1,3,4,7,8,9,11],[2,5,6,10,12,13,14]] => 1001000010100
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[1,3,4,7,8,9,10],[2,5,6,11,12,13,14]] => 1001000001000
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[1,3,4,6,9,11,13],[2,5,7,8,10,12,14]] => 1001010010101
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[1,3,4,6,9,11,12],[2,5,7,8,10,13,14]] => 1001010010010
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[1,3,4,6,9,10,13],[2,5,7,8,11,12,14]] => 1001010001001
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[1,3,4,6,9,10,12],[2,5,7,8,11,13,14]] => 1001010001010
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[1,3,4,6,9,10,11],[2,5,7,8,12,13,14]] => 1001010000100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,8,11,13],[2,5,7,9,10,12,14]] => 1001010100101
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,8,11,12],[2,5,7,9,10,13,14]] => 1001010100010
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,10,13],[2,5,7,9,11,12,14]] => 1001010101001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12],[2,5,7,9,11,13,14]] => 1001010101010
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,10,11],[2,5,7,9,12,13,14]] => 1001010100100
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,8,9,13],[2,5,7,10,11,12,14]] => 1001010010001
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,8,9,12],[2,5,7,10,11,13,14]] => 1001010010010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,8,9,11],[2,5,7,10,12,13,14]] => 1001010010100
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,8,9,10],[2,5,7,11,12,13,14]] => 1001010001000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[1,3,4,6,7,11,13],[2,5,8,9,10,12,14]] => 1001001000101
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[1,3,4,6,7,11,12],[2,5,8,9,10,13,14]] => 1001001000010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[1,3,4,6,7,10,13],[2,5,8,9,11,12,14]] => 1001001001001
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[1,3,4,6,7,10,12],[2,5,8,9,11,13,14]] => 1001001001010
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[1,3,4,6,7,10,11],[2,5,8,9,12,13,14]] => 1001001000100
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[1,3,4,6,7,9,13],[2,5,8,10,11,12,14]] => 1001001010001
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[1,3,4,6,7,9,12],[2,5,8,10,11,13,14]] => 1001001010010
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[1,3,4,6,7,9,11],[2,5,8,10,12,13,14]] => 1001001010100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[1,3,4,6,7,9,10],[2,5,8,11,12,13,14]] => 1001001001000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[1,3,4,6,7,8,13],[2,5,9,10,11,12,14]] => 1001000100001
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[1,3,4,6,7,8,12],[2,5,9,10,11,13,14]] => 1001000100010
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[1,3,4,6,7,8,11],[2,5,9,10,12,13,14]] => 1001000100100
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[1,3,4,6,7,8,10],[2,5,9,11,12,13,14]] => 1001000101000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 1001000010000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[1,3,4,5,9,11,13],[2,6,7,8,10,12,14]] => 1000100010101
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[1,3,4,5,9,11,12],[2,6,7,8,10,13,14]] => 1000100010010
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[1,3,4,5,9,10,13],[2,6,7,8,11,12,14]] => 1000100001001
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[1,3,4,5,9,10,12],[2,6,7,8,11,13,14]] => 1000100001010
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[1,3,4,5,9,10,11],[2,6,7,8,12,13,14]] => 1000100000100
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[1,3,4,5,8,11,13],[2,6,7,9,10,12,14]] => 1000100100101
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[1,3,4,5,8,11,12],[2,6,7,9,10,13,14]] => 1000100100010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[1,3,4,5,8,10,13],[2,6,7,9,11,12,14]] => 1000100101001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12],[2,6,7,9,11,13,14]] => 1000100101010
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[1,3,4,5,8,10,11],[2,6,7,9,12,13,14]] => 1000100100100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[1,3,4,5,8,9,13],[2,6,7,10,11,12,14]] => 1000100010001
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[1,3,4,5,8,9,12],[2,6,7,10,11,13,14]] => 1000100010010
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[1,3,4,5,8,9,11],[2,6,7,10,12,13,14]] => 1000100010100
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[1,3,4,5,8,9,10],[2,6,7,11,12,13,14]] => 1000100001000
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[1,3,4,5,7,11,13],[2,6,8,9,10,12,14]] => 1000101000101
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[1,3,4,5,7,11,12],[2,6,8,9,10,13,14]] => 1000101000010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[1,3,4,5,7,10,13],[2,6,8,9,11,12,14]] => 1000101001001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[1,3,4,5,7,10,12],[2,6,8,9,11,13,14]] => 1000101001010
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[1,3,4,5,7,10,11],[2,6,8,9,12,13,14]] => 1000101000100
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,9,13],[2,6,8,10,11,12,14]] => 1000101010001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,9,12],[2,6,8,10,11,13,14]] => 1000101010010
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9,11],[2,6,8,10,12,13,14]] => 1000101010100
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,9,10],[2,6,8,11,12,13,14]] => 1000101001000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[1,3,4,5,7,8,13],[2,6,9,10,11,12,14]] => 1000100100001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[1,3,4,5,7,8,12],[2,6,9,10,11,13,14]] => 1000100100010
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[1,3,4,5,7,8,11],[2,6,9,10,12,13,14]] => 1000100100100
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 1000100101000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 1000100010000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[1,3,4,5,6,11,13],[2,7,8,9,10,12,14]] => 1000010000101
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[1,3,4,5,6,11,12],[2,7,8,9,10,13,14]] => 1000010000010
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[1,3,4,5,6,10,13],[2,7,8,9,11,12,14]] => 1000010001001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[1,3,4,5,6,10,12],[2,7,8,9,11,13,14]] => 1000010001010
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[1,3,4,5,6,10,11],[2,7,8,9,12,13,14]] => 1000010000100
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[1,3,4,5,6,9,13],[2,7,8,10,11,12,14]] => 1000010010001
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[1,3,4,5,6,9,12],[2,7,8,10,11,13,14]] => 1000010010010
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[1,3,4,5,6,9,11],[2,7,8,10,12,13,14]] => 1000010010100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 1000010001000
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[1,3,4,5,6,8,13],[2,7,9,10,11,12,14]] => 1000010100001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[1,3,4,5,6,8,12],[2,7,9,10,11,13,14]] => 1000010100010
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 1000010100100
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 1000010101000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 1000010010000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[1,3,4,5,6,7,13],[2,8,9,10,11,12,14]] => 1000001000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 1000001000010
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 1000001000100
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 1000001001000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 1000001010000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]] => 1000000100000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11,13],[3,4,6,8,10,12,14]] => 0100101010101
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,11,12],[3,4,6,8,10,13,14]] => 0100101010010
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,9,10,13],[3,4,6,8,11,12,14]] => 0100101001001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,9,10,12],[3,4,6,8,11,13,14]] => 0100101001010
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,9,10,11],[3,4,6,8,12,13,14]] => 0100101000100
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[1,2,5,7,8,11,13],[3,4,6,9,10,12,14]] => 0100100100101
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[1,2,5,7,8,11,12],[3,4,6,9,10,13,14]] => 0100100100010
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[1,2,5,7,8,10,13],[3,4,6,9,11,12,14]] => 0100100101001
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[1,2,5,7,8,10,12],[3,4,6,9,11,13,14]] => 0100100101010
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[1,2,5,7,8,10,11],[3,4,6,9,12,13,14]] => 0100100100100
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[1,2,5,7,8,9,13],[3,4,6,10,11,12,14]] => 0100100010001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[1,2,5,7,8,9,12],[3,4,6,10,11,13,14]] => 0100100010010
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[1,2,5,7,8,9,11],[3,4,6,10,12,13,14]] => 0100100010100
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[1,2,5,7,8,9,10],[3,4,6,11,12,13,14]] => 0100100001000
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[1,2,5,6,9,11,13],[3,4,7,8,10,12,14]] => 0100010010101
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[1,2,5,6,9,11,12],[3,4,7,8,10,13,14]] => 0100010010010
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9,10,13],[3,4,7,8,11,12,14]] => 0100010001001
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,9,10,12],[3,4,7,8,11,13,14]] => 0100010001010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,9,10,11],[3,4,7,8,12,13,14]] => 0100010000100
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[1,2,5,6,8,11,13],[3,4,7,9,10,12,14]] => 0100010100101
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[1,2,5,6,8,11,12],[3,4,7,9,10,13,14]] => 0100010100010
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[1,2,5,6,8,10,13],[3,4,7,9,11,12,14]] => 0100010101001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[1,2,5,6,8,10,12],[3,4,7,9,11,13,14]] => 0100010101010
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[1,2,5,6,8,10,11],[3,4,7,9,12,13,14]] => 0100010100100
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[1,2,5,6,8,9,13],[3,4,7,10,11,12,14]] => 0100010010001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[1,2,5,6,8,9,12],[3,4,7,10,11,13,14]] => 0100010010010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[1,2,5,6,8,9,10],[3,4,7,11,12,13,14]] => 0100010001000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[1,2,5,6,7,11,13],[3,4,8,9,10,12,14]] => 0100001000101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[1,2,5,6,7,11,12],[3,4,8,9,10,13,14]] => 0100001000010
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[1,2,5,6,7,10,13],[3,4,8,9,11,12,14]] => 0100001001001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[1,2,5,6,7,10,12],[3,4,8,9,11,13,14]] => 0100001001010
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[1,2,5,6,7,10,11],[3,4,8,9,12,13,14]] => 0100001000100
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[1,2,5,6,7,9,13],[3,4,8,10,11,12,14]] => 0100001010001
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[1,2,5,6,7,9,12],[3,4,8,10,11,13,14]] => 0100001010010
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[1,2,5,6,7,9,11],[3,4,8,10,12,13,14]] => 0100001010100
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[1,2,5,6,7,9,10],[3,4,8,11,12,13,14]] => 0100001001000
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[1,2,5,6,7,8,13],[3,4,9,10,11,12,14]] => 0100000100001
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[1,2,5,6,7,8,12],[3,4,9,10,11,13,14]] => 0100000100010
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[1,2,5,6,7,8,11],[3,4,9,10,12,13,14]] => 0100000100100
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,5,6,7,8,10],[3,4,9,11,12,13,14]] => 0100000101000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]] => 0100000010000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,7,9,11,13],[3,5,6,8,10,12,14]] => 0101001010101
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,4,7,9,11,12],[3,5,6,8,10,13,14]] => 0101001010010
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,4,7,9,10,13],[3,5,6,8,11,12,14]] => 0101001001001
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,4,7,9,10,12],[3,5,6,8,11,13,14]] => 0101001001010
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,4,7,9,10,11],[3,5,6,8,12,13,14]] => 0101001000100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,4,7,8,11,13],[3,5,6,9,10,12,14]] => 0101000100101
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,4,7,8,11,12],[3,5,6,9,10,13,14]] => 0101000100010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,4,7,8,10,13],[3,5,6,9,11,12,14]] => 0101000101001
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,4,7,8,10,12],[3,5,6,9,11,13,14]] => 0101000101010
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,4,7,8,10,11],[3,5,6,9,12,13,14]] => 0101000100100
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,4,7,8,9,13],[3,5,6,10,11,12,14]] => 0101000010001
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,4,7,8,9,12],[3,5,6,10,11,13,14]] => 0101000010010
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,4,7,8,9,11],[3,5,6,10,12,13,14]] => 0101000010100
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,4,7,8,9,10],[3,5,6,11,12,13,14]] => 0101000001000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,6,9,11,13],[3,5,7,8,10,12,14]] => 0101010010101
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,6,9,11,12],[3,5,7,8,10,13,14]] => 0101010010010
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,6,9,10,13],[3,5,7,8,11,12,14]] => 0101010001001
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,6,9,10,12],[3,5,7,8,11,13,14]] => 0101010001010
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,6,9,10,11],[3,5,7,8,12,13,14]] => 0101010000100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,8,11,13],[3,5,7,9,10,12,14]] => 0101010100101
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,8,11,12],[3,5,7,9,10,13,14]] => 0101010100010
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,10,13],[3,5,7,9,11,12,14]] => 0101010101001
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12],[3,5,7,9,11,13,14]] => 0101010101010
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,10,11],[3,5,7,9,12,13,14]] => 0101010100100
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,8,9,13],[3,5,7,10,11,12,14]] => 0101010010001
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,8,9,12],[3,5,7,10,11,13,14]] => 0101010010010
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,8,9,11],[3,5,7,10,12,13,14]] => 0101010010100
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,8,9,10],[3,5,7,11,12,13,14]] => 0101010001000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,6,7,11,13],[3,5,8,9,10,12,14]] => 0101001000101
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,6,7,11,12],[3,5,8,9,10,13,14]] => 0101001000010
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,6,7,10,13],[3,5,8,9,11,12,14]] => 0101001001001
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,6,7,10,12],[3,5,8,9,11,13,14]] => 0101001001010
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,6,7,10,11],[3,5,8,9,12,13,14]] => 0101001000100
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,6,7,9,13],[3,5,8,10,11,12,14]] => 0101001010001
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,6,7,9,12],[3,5,8,10,11,13,14]] => 0101001010010
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,6,7,9,11],[3,5,8,10,12,13,14]] => 0101001010100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,6,7,9,10],[3,5,8,11,12,13,14]] => 0101001001000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,6,7,8,13],[3,5,9,10,11,12,14]] => 0101000100001
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,6,7,8,12],[3,5,9,10,11,13,14]] => 0101000100010
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,6,7,8,11],[3,5,9,10,12,13,14]] => 0101000100100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,7,8,10],[3,5,9,11,12,13,14]] => 0101000101000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,6,7,8,9],[3,5,10,11,12,13,14]] => 0101000010000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,4,5,9,11,13],[3,6,7,8,10,12,14]] => 0100100010101
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,4,5,9,11,12],[3,6,7,8,10,13,14]] => 0100100010010
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,4,5,9,10,13],[3,6,7,8,11,12,14]] => 0100100001001
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,4,5,9,10,12],[3,6,7,8,11,13,14]] => 0100100001010
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,4,5,9,10,11],[3,6,7,8,12,13,14]] => 0100100000100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,4,5,8,11,13],[3,6,7,9,10,12,14]] => 0100100100101
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,4,5,8,11,12],[3,6,7,9,10,13,14]] => 0100100100010
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,4,5,8,10,13],[3,6,7,9,11,12,14]] => 0100100101001
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,4,5,8,10,12],[3,6,7,9,11,13,14]] => 0100100101010
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,4,5,8,10,11],[3,6,7,9,12,13,14]] => 0100100100100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,4,5,8,9,13],[3,6,7,10,11,12,14]] => 0100100010001
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,4,5,8,9,12],[3,6,7,10,11,13,14]] => 0100100010010
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,4,5,8,9,11],[3,6,7,10,12,13,14]] => 0100100010100
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,4,5,8,9,10],[3,6,7,11,12,13,14]] => 0100100001000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,4,5,7,11,13],[3,6,8,9,10,12,14]] => 0100101000101
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,4,5,7,11,12],[3,6,8,9,10,13,14]] => 0100101000010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,4,5,7,10,13],[3,6,8,9,11,12,14]] => 0100101001001
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,4,5,7,10,12],[3,6,8,9,11,13,14]] => 0100101001010
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,4,5,7,10,11],[3,6,8,9,12,13,14]] => 0100101000100
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,9,13],[3,6,8,10,11,12,14]] => 0100101010001
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,9,12],[3,6,8,10,11,13,14]] => 0100101010010
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9,11],[3,6,8,10,12,13,14]] => 0100101010100
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,9,10],[3,6,8,11,12,13,14]] => 0100101001000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,4,5,7,8,13],[3,6,9,10,11,12,14]] => 0100100100001
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,4,5,7,8,12],[3,6,9,10,11,13,14]] => 0100100100010
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,4,5,7,8,11],[3,6,9,10,12,13,14]] => 0100100100100
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,4,5,7,8,10],[3,6,9,11,12,13,14]] => 0100100101000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,4,5,7,8,9],[3,6,10,11,12,13,14]] => 0100100010000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,4,5,6,11,13],[3,7,8,9,10,12,14]] => 0100010000101
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,4,5,6,11,12],[3,7,8,9,10,13,14]] => 0100010000010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,4,5,6,10,13],[3,7,8,9,11,12,14]] => 0100010001001
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,4,5,6,10,12],[3,7,8,9,11,13,14]] => 0100010001010
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,4,5,6,10,11],[3,7,8,9,12,13,14]] => 0100010000100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,4,5,6,9,13],[3,7,8,10,11,12,14]] => 0100010010001
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,4,5,6,9,12],[3,7,8,10,11,13,14]] => 0100010010010
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,4,5,6,9,11],[3,7,8,10,12,13,14]] => 0100010010100
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,4,5,6,9,10],[3,7,8,11,12,13,14]] => 0100010001000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,4,5,6,8,13],[3,7,9,10,11,12,14]] => 0100010100001
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,4,5,6,8,12],[3,7,9,10,11,13,14]] => 0100010100010
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,4,5,6,8,11],[3,7,9,10,12,13,14]] => 0100010100100
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,6,8,10],[3,7,9,11,12,13,14]] => 0100010101000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]] => 0100010010000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 0100001000001
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,4,5,6,7,12],[3,8,9,10,11,13,14]] => 0100001000010
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,4,5,6,7,11],[3,8,9,10,12,13,14]] => 0100001000100
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,4,5,6,7,10],[3,8,9,11,12,13,14]] => 0100001001000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,4,5,6,7,9],[3,8,10,11,12,13,14]] => 0100001010000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,4,5,6,7,8],[3,9,10,11,12,13,14]] => 0100000100000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,7,9,11,13],[4,5,6,8,10,12,14]] => 0010001010101
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[1,2,3,7,9,11,12],[4,5,6,8,10,13,14]] => 0010001010010
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[1,2,3,7,9,10,13],[4,5,6,8,11,12,14]] => 0010001001001
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[1,2,3,7,9,10,12],[4,5,6,8,11,13,14]] => 0010001001010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[1,2,3,7,9,10,11],[4,5,6,8,12,13,14]] => 0010001000100
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[1,2,3,7,8,11,13],[4,5,6,9,10,12,14]] => 0010000100101
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[1,2,3,7,8,11,12],[4,5,6,9,10,13,14]] => 0010000100010
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[1,2,3,7,8,10,13],[4,5,6,9,11,12,14]] => 0010000101001
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[1,2,3,7,8,10,12],[4,5,6,9,11,13,14]] => 0010000101010
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[1,2,3,7,8,10,11],[4,5,6,9,12,13,14]] => 0010000100100
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[1,2,3,7,8,9,13],[4,5,6,10,11,12,14]] => 0010000010001
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[1,2,3,7,8,9,12],[4,5,6,10,11,13,14]] => 0010000010010
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[1,2,3,7,8,9,11],[4,5,6,10,12,13,14]] => 0010000010100
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,7,8,9,10],[4,5,6,11,12,13,14]] => 0010000001000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[1,2,3,6,9,11,13],[4,5,7,8,10,12,14]] => 0010010010101
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[1,2,3,6,9,11,12],[4,5,7,8,10,13,14]] => 0010010010010
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[1,2,3,6,9,10,13],[4,5,7,8,11,12,14]] => 0010010001001
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[1,2,3,6,9,10,12],[4,5,7,8,11,13,14]] => 0010010001010
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[1,2,3,6,9,10,11],[4,5,7,8,12,13,14]] => 0010010000100
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[1,2,3,6,8,11,13],[4,5,7,9,10,12,14]] => 0010010100101
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[1,2,3,6,8,11,12],[4,5,7,9,10,13,14]] => 0010010100010
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,10,13],[4,5,7,9,11,12,14]] => 0010010101001
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12],[4,5,7,9,11,13,14]] => 0010010101010
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,10,11],[4,5,7,9,12,13,14]] => 0010010100100
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[1,2,3,6,8,9,13],[4,5,7,10,11,12,14]] => 0010010010001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[1,2,3,6,8,9,12],[4,5,7,10,11,13,14]] => 0010010010010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[1,2,3,6,8,9,11],[4,5,7,10,12,13,14]] => 0010010010100
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[1,2,3,6,8,9,10],[4,5,7,11,12,13,14]] => 0010010001000
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[1,2,3,6,7,11,13],[4,5,8,9,10,12,14]] => 0010001000101
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[1,2,3,6,7,11,12],[4,5,8,9,10,13,14]] => 0010001000010
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,7,10,13],[4,5,8,9,11,12,14]] => 0010001001001
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,7,10,12],[4,5,8,9,11,13,14]] => 0010001001010
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7,10,11],[4,5,8,9,12,13,14]] => 0010001000100
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[1,2,3,6,7,9,13],[4,5,8,10,11,12,14]] => 0010001010001
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[1,2,3,6,7,9,12],[4,5,8,10,11,13,14]] => 0010001010010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[1,2,3,6,7,9,11],[4,5,8,10,12,13,14]] => 0010001010100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[1,2,3,6,7,9,10],[4,5,8,11,12,13,14]] => 0010001001000
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[1,2,3,6,7,8,13],[4,5,9,10,11,12,14]] => 0010000100001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[1,2,3,6,7,8,12],[4,5,9,10,11,13,14]] => 0010000100010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[1,2,3,6,7,8,11],[4,5,9,10,12,13,14]] => 0010000100100
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[1,2,3,6,7,8,10],[4,5,9,11,12,13,14]] => 0010000101000
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[1,2,3,6,7,8,9],[4,5,10,11,12,13,14]] => 0010000010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,5,9,11,13],[4,6,7,8,10,12,14]] => 0010100010101
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,5,9,11,12],[4,6,7,8,10,13,14]] => 0010100010010
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,5,9,10,13],[4,6,7,8,11,12,14]] => 0010100001001
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,5,9,10,12],[4,6,7,8,11,13,14]] => 0010100001010
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,5,9,10,11],[4,6,7,8,12,13,14]] => 0010100000100
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,5,8,11,13],[4,6,7,9,10,12,14]] => 0010100100101
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,5,8,11,12],[4,6,7,9,10,13,14]] => 0010100100010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,5,8,10,13],[4,6,7,9,11,12,14]] => 0010100101001
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,5,8,10,12],[4,6,7,9,11,13,14]] => 0010100101010
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,5,8,10,11],[4,6,7,9,12,13,14]] => 0010100100100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,5,8,9,13],[4,6,7,10,11,12,14]] => 0010100010001
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,5,8,9,12],[4,6,7,10,11,13,14]] => 0010100010010
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,5,8,9,11],[4,6,7,10,12,13,14]] => 0010100010100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,5,8,9,10],[4,6,7,11,12,13,14]] => 0010100001000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,7,11,13],[4,6,8,9,10,12,14]] => 0010101000101
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,7,11,12],[4,6,8,9,10,13,14]] => 0010101000010
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,7,10,13],[4,6,8,9,11,12,14]] => 0010101001001
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,7,10,12],[4,6,8,9,11,13,14]] => 0010101001010
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,7,10,11],[4,6,8,9,12,13,14]] => 0010101000100
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,9,13],[4,6,8,10,11,12,14]] => 0010101010001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,9,12],[4,6,8,10,11,13,14]] => 0010101010010
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9,11],[4,6,8,10,12,13,14]] => 0010101010100
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,9,10],[4,6,8,11,12,13,14]] => 0010101001000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,7,8,13],[4,6,9,10,11,12,14]] => 0010100100001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,7,8,12],[4,6,9,10,11,13,14]] => 0010100100010
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,7,8,11],[4,6,9,10,12,13,14]] => 0010100100100
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,7,8,10],[4,6,9,11,12,13,14]] => 0010100101000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,7,8,9],[4,6,10,11,12,13,14]] => 0010100010000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,5,6,11,13],[4,7,8,9,10,12,14]] => 0010010000101
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,5,6,11,12],[4,7,8,9,10,13,14]] => 0010010000010
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,5,6,10,13],[4,7,8,9,11,12,14]] => 0010010001001
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,5,6,10,12],[4,7,8,9,11,13,14]] => 0010010001010
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,5,6,10,11],[4,7,8,9,12,13,14]] => 0010010000100
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,5,6,9,13],[4,7,8,10,11,12,14]] => 0010010010001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,5,6,9,12],[4,7,8,10,11,13,14]] => 0010010010010
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,5,6,9,11],[4,7,8,10,12,13,14]] => 0010010010100
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,5,6,9,10],[4,7,8,11,12,13,14]] => 0010010001000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 0010010100001
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,5,6,8,12],[4,7,9,10,11,13,14]] => 0010010100010
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,5,6,8,11],[4,7,9,10,12,13,14]] => 0010010100100
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,5,6,8,10],[4,7,9,11,12,13,14]] => 0010010101000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,5,6,8,9],[4,7,10,11,12,13,14]] => 0010010010000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 0010001000001
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,5,6,7,12],[4,8,9,10,11,13,14]] => 0010001000010
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,5,6,7,11],[4,8,9,10,12,13,14]] => 0010001000100
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,5,6,7,10],[4,8,9,11,12,13,14]] => 0010001001000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,5,6,7,9],[4,8,10,11,12,13,14]] => 0010001010000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,5,6,7,8],[4,9,10,11,12,13,14]] => 0010000100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[1,2,3,4,9,11,13],[5,6,7,8,10,12,14]] => 0001000010101
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[1,2,3,4,9,11,12],[5,6,7,8,10,13,14]] => 0001000010010
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[1,2,3,4,9,10,13],[5,6,7,8,11,12,14]] => 0001000001001
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[1,2,3,4,9,10,12],[5,6,7,8,11,13,14]] => 0001000001010
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,9,10,11],[5,6,7,8,12,13,14]] => 0001000000100
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[1,2,3,4,8,11,13],[5,6,7,9,10,12,14]] => 0001000100101
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[1,2,3,4,8,11,12],[5,6,7,9,10,13,14]] => 0001000100010
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[1,2,3,4,8,10,13],[5,6,7,9,11,12,14]] => 0001000101001
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[1,2,3,4,8,10,12],[5,6,7,9,11,13,14]] => 0001000101010
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[1,2,3,4,8,10,11],[5,6,7,9,12,13,14]] => 0001000100100
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[1,2,3,4,8,9,13],[5,6,7,10,11,12,14]] => 0001000010001
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[1,2,3,4,8,9,12],[5,6,7,10,11,13,14]] => 0001000010010
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[1,2,3,4,8,9,11],[5,6,7,10,12,13,14]] => 0001000010100
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[1,2,3,4,8,9,10],[5,6,7,11,12,13,14]] => 0001000001000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[1,2,3,4,7,11,13],[5,6,8,9,10,12,14]] => 0001001000101
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[1,2,3,4,7,11,12],[5,6,8,9,10,13,14]] => 0001001000010
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[1,2,3,4,7,10,13],[5,6,8,9,11,12,14]] => 0001001001001
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[1,2,3,4,7,10,12],[5,6,8,9,11,13,14]] => 0001001001010
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[1,2,3,4,7,10,11],[5,6,8,9,12,13,14]] => 0001001000100
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[1,2,3,4,7,9,13],[5,6,8,10,11,12,14]] => 0001001010001
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[1,2,3,4,7,9,12],[5,6,8,10,11,13,14]] => 0001001010010
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[1,2,3,4,7,9,11],[5,6,8,10,12,13,14]] => 0001001010100
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[1,2,3,4,7,9,10],[5,6,8,11,12,13,14]] => 0001001001000
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 0001000100001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[1,2,3,4,7,8,12],[5,6,9,10,11,13,14]] => 0001000100010
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[1,2,3,4,7,8,11],[5,6,9,10,12,13,14]] => 0001000100100
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[1,2,3,4,7,8,10],[5,6,9,11,12,13,14]] => 0001000101000
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[1,2,3,4,7,8,9],[5,6,10,11,12,13,14]] => 0001000010000
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,6,11,13],[5,7,8,9,10,12,14]] => 0001010000101
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,6,11,12],[5,7,8,9,10,13,14]] => 0001010000010
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,6,10,13],[5,7,8,9,11,12,14]] => 0001010001001
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,6,10,12],[5,7,8,9,11,13,14]] => 0001010001010
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,6,10,11],[5,7,8,9,12,13,14]] => 0001010000100
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 0001010010001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,6,9,12],[5,7,8,10,11,13,14]] => 0001010010010
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,6,9,11],[5,7,8,10,12,13,14]] => 0001010010100
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,6,9,10],[5,7,8,11,12,13,14]] => 0001010001000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 0001010100001
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,8,12],[5,7,9,10,11,13,14]] => 0001010100010
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,8,11],[5,7,9,10,12,13,14]] => 0001010100100
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8,10],[5,7,9,11,12,13,14]] => 0001010101000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,9],[5,7,10,11,12,13,14]] => 0001010010000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 0001001000001
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,6,7,12],[5,8,9,10,11,13,14]] => 0001001000010
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,6,7,11],[5,8,9,10,12,13,14]] => 0001001000100
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,6,7,10],[5,8,9,11,12,13,14]] => 0001001001000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,6,7,9],[5,8,10,11,12,13,14]] => 0001001010000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,6,7,8],[5,9,10,11,12,13,14]] => 0001000100000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[1,2,3,4,5,11,13],[6,7,8,9,10,12,14]] => 0000100000101
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]] => 0000100000010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => 0000100001001
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[1,2,3,4,5,10,12],[6,7,8,9,11,13,14]] => 0000100001010
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[1,2,3,4,5,10,11],[6,7,8,9,12,13,14]] => 0000100000100
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => 0000100010001
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[1,2,3,4,5,9,12],[6,7,8,10,11,13,14]] => 0000100010010
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[1,2,3,4,5,9,11],[6,7,8,10,12,13,14]] => 0000100010100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[1,2,3,4,5,9,10],[6,7,8,11,12,13,14]] => 0000100001000
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => 0000100100001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]] => 0000100100010
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[1,2,3,4,5,8,11],[6,7,9,10,12,13,14]] => 0000100100100
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10],[6,7,9,11,12,13,14]] => 0000100101000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[1,2,3,4,5,8,9],[6,7,10,11,12,13,14]] => 0000100010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => 0000101000001
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,7,12],[6,8,9,10,11,13,14]] => 0000101000010
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,7,11],[6,8,9,10,12,13,14]] => 0000101000100
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,7,10],[6,8,9,11,12,13,14]] => 0000101001000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7,9],[6,8,10,11,12,13,14]] => 0000101010000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,8],[6,9,10,11,12,13,14]] => 0000100100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 0000010000001
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,12],[7,8,9,10,11,13,14]] => 0000010000010
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,11],[7,8,9,10,12,13,14]] => 0000010000100
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,10],[7,8,9,11,12,13,14]] => 0000010001000
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9],[7,8,10,11,12,13,14]] => 0000010010000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,8],[7,9,10,11,12,13,14]] => 0000010100000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 0000001000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15],[2,4,6,8,10,12,14,16]] => 101010101010101
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,14],[2,4,6,8,10,12,15,16]] => 101010101010010
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,12,14],[2,4,6,8,10,13,15,16]] => 101010101001010
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,11,12,13],[2,4,6,8,10,14,15,16]] => 101010101000100
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,7,9,10,13,15],[2,4,6,8,11,12,14,16]] => 101010100100101
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,7,9,10,13,14],[2,4,6,8,11,12,15,16]] => 101010100100010
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,7,9,10,12,15],[2,4,6,8,11,13,14,16]] => 101010100101001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14],[2,4,6,8,11,13,15,16]] => 101010100101010
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,7,9,10,12,13],[2,4,6,8,11,14,15,16]] => 101010100100100
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,7,9,10,11,15],[2,4,6,8,12,13,14,16]] => 101010100010001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,9,10,11,14],[2,4,6,8,12,13,15,16]] => 101010100010010
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,7,9,10,11,13],[2,4,6,8,12,14,15,16]] => 101010100010100
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,7,9,10,11,12],[2,4,6,8,13,14,15,16]] => 101010100001000
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,5,7,8,11,13,14],[2,4,6,9,10,12,15,16]] => 101010010010010
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14],[2,4,6,9,11,13,15,16]] => 101010010101010
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,7,8,9,12,14],[2,4,6,10,11,13,15,16]] => 101010001001010
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,5,7,8,9,11,14],[2,4,6,10,12,13,15,16]] => 101010001010010
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,5,7,8,9,10,14],[2,4,6,11,12,13,15,16]] => 101010000100010
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,5,7,8,9,10,11],[2,4,6,12,13,14,15,16]] => 101010000010000
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[1,3,5,6,9,11,13,14],[2,4,7,8,10,12,15,16]] => 101001001010010
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,9,11,12,14],[2,4,7,8,10,13,15,16]] => 101001001001010
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,9,10,12,14],[2,4,7,8,11,13,15,16]] => 101001000101010
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14],[2,4,7,9,11,13,15,16]] => 101001010101010
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[1,3,5,6,8,10,12,13],[2,4,7,9,11,14,15,16]] => 101001010100100
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[1,3,5,6,7,11,13,15],[2,4,8,9,10,12,14,16]] => 101000100010101
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,5,6,7,10,12,14],[2,4,8,9,11,13,15,16]] => 101000100101010
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[1,3,5,6,7,9,12,14],[2,4,8,10,11,13,15,16]] => 101000101001010
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[1,3,5,6,7,9,11,14],[2,4,8,10,12,13,15,16]] => 101000101010010
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[1,3,5,6,7,8,12,14],[2,4,9,10,11,13,15,16]] => 101000010001010
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,5,6,7,8,10,12],[2,4,9,11,13,14,15,16]] => 101000010101000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[1,3,5,6,7,8,9,15],[2,4,10,11,12,13,14,16]] => 101000001000001
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,5,6,7,8,9,12],[2,4,10,11,13,14,15,16]] => 101000001001000
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,5,6,7,8,9,11],[2,4,10,12,13,14,15,16]] => 101000001010000
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,3,5,6,7,8,9,10],[2,4,11,12,13,14,15,16]] => 101000000100000
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,4,7,9,11,13,14],[2,5,6,8,10,12,15,16]] => 100100101010010
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,4,7,9,11,12,14],[2,5,6,8,10,13,15,16]] => 100100101001010
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[1,3,4,6,9,11,13,14],[2,5,7,8,10,12,15,16]] => 100101001010010
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[1,3,4,6,9,11,12,14],[2,5,7,8,10,13,15,16]] => 100101001001010
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[1,3,4,6,9,10,11,12],[2,5,7,8,13,14,15,16]] => 100101000001000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14],[2,5,7,9,11,13,15,16]] => 100101010101010
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,10,12,13],[2,5,7,9,11,14,15,16]] => 100101010100100
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,3,4,5,9,11,13,15],[2,6,7,8,10,12,14,16]] => 100010001010101
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[1,3,4,5,9,11,12,14],[2,6,7,8,10,13,15,16]] => 100010001001010
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12,14],[2,6,7,9,11,13,15,16]] => 100010010101010
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[1,3,4,5,7,11,13,15],[2,6,8,9,10,12,14,16]] => 100010100010101
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[1,3,4,5,7,11,12,13],[2,6,8,9,10,14,15,16]] => 100010100000100
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[1,3,4,5,7,10,12,15],[2,6,8,9,11,13,14,16]] => 100010100101001
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,7,10,12,14],[2,6,8,9,11,13,15,16]] => 100010100101010
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[1,3,4,5,7,9,13,15],[2,6,8,10,11,12,14,16]] => 100010101000101
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,9,11,15],[2,6,8,10,12,13,14,16]] => 100010101010001
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,9,11,14],[2,6,8,10,12,13,15,16]] => 100010101010010
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9,11,13],[2,6,8,10,12,14,15,16]] => 100010101010100
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,6,10,12,14],[2,7,8,9,11,13,15,16]] => 100001000101010
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,6,9,11,13],[2,7,8,10,12,14,15,16]] => 100001001010100
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[1,3,4,5,6,8,13,14],[2,7,9,10,11,12,15,16]] => 100001010000010
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[1,3,4,5,6,8,11,13],[2,7,9,10,12,14,15,16]] => 100001010010100
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[1,3,4,5,6,8,10,14],[2,7,9,11,12,13,15,16]] => 100001010100010
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10,12],[2,7,9,11,13,14,15,16]] => 100001010101000
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 100001000100000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[1,3,4,5,6,7,13,15],[2,8,9,10,11,12,14,16]] => 100000100000101
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,3,4,5,6,7,13,14],[2,8,9,10,11,12,15,16]] => 100000100000010
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[1,3,4,5,6,7,11,13],[2,8,9,10,12,14,15,16]] => 100000100010100
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,7,10,12],[2,8,9,11,13,14,15,16]] => 100000100101000
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,3,4,5,6,7,9,15],[2,8,10,11,12,13,14,16]] => 100000101000001
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,9,12],[2,8,10,11,13,14,15,16]] => 100000101001000
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 100000101010000
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 100000100100000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,3,4,5,6,7,8,15],[2,9,10,11,12,13,14,16]] => 100000010000001
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 100000010001000
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 100000010010000
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 100000010100000
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]] => 100000001000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11,13,15],[3,4,6,8,10,12,14,16]] => 010010101010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,11,13,14],[3,4,6,8,10,12,15,16]] => 010010101010010
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,9,11,12,15],[3,4,6,8,10,13,14,16]] => 010010101001001
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,9,11,12,14],[3,4,6,8,10,13,15,16]] => 010010101001010
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,9,11,12,13],[3,4,6,8,10,14,15,16]] => 010010101000100
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[1,2,5,7,9,10,13,15],[3,4,6,8,11,12,14,16]] => 010010100100101
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,2,5,7,9,10,12,14],[3,4,6,8,11,13,15,16]] => 010010100101010
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,2,5,7,8,10,12,14],[3,4,6,9,11,13,15,16]] => 010010010101010
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[1,2,5,7,8,9,11,13],[3,4,6,10,12,14,15,16]] => 010010001010100
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,5,7,8,9,10,12],[3,4,6,11,13,14,15,16]] => 010010000101000
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,5,7,8,9,10,11],[3,4,6,12,13,14,15,16]] => 010010000010000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,5,6,8,10,12,14],[3,4,7,9,11,13,15,16]] => 010001010101010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,5,6,8,10,11,12],[3,4,7,9,13,14,15,16]] => 010001010001000
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,5,6,8,9,10,11],[3,4,7,12,13,14,15,16]] => 010001000010000
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,5,6,7,11,13,15],[3,4,8,9,10,12,14,16]] => 010000100010101
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,5,6,7,10,12,14],[3,4,8,9,11,13,15,16]] => 010000100101010
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,5,6,7,9,11,13],[3,4,8,10,12,14,15,16]] => 010000101010100
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,5,6,7,8,10,12],[3,4,9,11,13,14,15,16]] => 010000010101000
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,5,6,7,8,9,15],[3,4,10,11,12,13,14,16]] => 010000001000001
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,5,6,7,8,9,14],[3,4,10,11,12,13,15,16]] => 010000001000010
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,5,6,7,8,9,11],[3,4,10,12,13,14,15,16]] => 010000001010000
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,5,6,7,8,9,10],[3,4,11,12,13,14,15,16]] => 010000000100000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,7,9,11,13,15],[3,5,6,8,10,12,14,16]] => 010100101010101
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,4,7,9,11,13,14],[3,5,6,8,10,12,15,16]] => 010100101010010
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,4,7,9,11,12,14],[3,5,6,8,10,13,15,16]] => 010100101001010
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[1,2,4,7,9,10,11,12],[3,5,6,8,13,14,15,16]] => 010100100001000
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,4,7,8,9,10,12],[3,5,6,11,13,14,15,16]] => 010100000101000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,4,7,8,9,10,11],[3,5,6,12,13,14,15,16]] => 010100000010000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,9,11,13,15],[3,5,7,8,10,12,14,16]] => 010101001010101
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,4,6,9,11,12,13],[3,5,7,8,10,14,15,16]] => 010101001000100
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,4,6,9,10,11,12],[3,5,7,8,13,14,15,16]] => 010101000001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,6,8,11,13,15],[3,5,7,9,10,12,14,16]] => 010101010010101
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,6,8,11,13,14],[3,5,7,9,10,12,15,16]] => 010101010010010
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,6,8,11,12,13],[3,5,7,9,10,14,15,16]] => 010101010000100
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,8,10,13,15],[3,5,7,9,11,12,14,16]] => 010101010100101
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,8,10,13,14],[3,5,7,9,11,12,15,16]] => 010101010100010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,10,12,15],[3,5,7,9,11,13,14,16]] => 010101010101001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14],[3,5,7,9,11,13,15,16]] => 010101010101010
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,10,12,13],[3,5,7,9,11,14,15,16]] => 010101010100100
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,8,10,11,15],[3,5,7,9,12,13,14,16]] => 010101010010001
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,8,10,11,14],[3,5,7,9,12,13,15,16]] => 010101010010010
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,8,10,11,13],[3,5,7,9,12,14,15,16]] => 010101010010100
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,8,10,11,12],[3,5,7,9,13,14,15,16]] => 010101010001000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,6,8,9,13,15],[3,5,7,10,11,12,14,16]] => 010101001000101
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,6,8,9,12,14],[3,5,7,10,11,13,15,16]] => 010101001001010
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,6,8,9,11,15],[3,5,7,10,12,13,14,16]] => 010101001010001
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,6,8,9,11,13],[3,5,7,10,12,14,15,16]] => 010101001010100
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,6,8,9,11,12],[3,5,7,10,13,14,15,16]] => 010101001001000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,6,8,9,10,15],[3,5,7,11,12,13,14,16]] => 010101000100001
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,8,9,10,12],[3,5,7,11,13,14,15,16]] => 010101000101000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,4,6,7,11,13,15],[3,5,8,9,10,12,14,16]] => 010100100010101
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,4,6,7,10,12,14],[3,5,8,9,11,13,15,16]] => 010100100101010
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,4,6,7,9,13,15],[3,5,8,10,11,12,14,16]] => 010100101000101
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,4,6,7,9,10,12],[3,5,8,11,13,14,15,16]] => 010100100101000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,4,6,7,8,13,15],[3,5,9,10,11,12,14,16]] => 010100010000101
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,7,8,10,12],[3,5,9,11,13,14,15,16]] => 010100010101000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,6,7,8,9,15],[3,5,10,11,12,13,14,16]] => 010100001000001
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,5,9,11,13,15],[3,6,7,8,10,12,14,16]] => 010010001010101
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,5,8,10,12,14],[3,6,7,9,11,13,15,16]] => 010010010101010
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[1,2,4,5,7,11,13,15],[3,6,8,9,10,12,14,16]] => 010010100010101
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,2,4,5,7,10,12,14],[3,6,8,9,11,13,15,16]] => 010010100101010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[1,2,4,5,7,9,13,15],[3,6,8,10,11,12,14,16]] => 010010101000101
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,9,11,15],[3,6,8,10,12,13,14,16]] => 010010101010001
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9,11,13],[3,6,8,10,12,14,15,16]] => 010010101010100
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,9,11,12],[3,6,8,10,13,14,15,16]] => 010010101001000
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,7,8,10,12],[3,6,9,11,13,14,15,16]] => 010010010101000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[1,2,4,5,6,11,13,15],[3,7,8,9,10,12,14,16]] => 010001000010101
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,6,8,10,12],[3,7,9,11,13,14,15,16]] => 010001010101000
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,4,5,6,7,13,14],[3,8,9,10,11,12,15,16]] => 010000100000010
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[1,2,4,5,6,7,12,14],[3,8,9,10,11,13,15,16]] => 010000100001010
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[1,2,4,5,6,7,12,13],[3,8,9,10,11,14,15,16]] => 010000100000100
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,2,4,5,6,7,9,11],[3,8,10,12,13,14,15,16]] => 010000101010000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,8,15],[3,9,10,11,12,13,14,16]] => 010000010000001
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[1,2,4,5,6,7,8,14],[3,9,10,11,12,13,15,16]] => 010000010000010
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,2,4,5,6,7,8,11],[3,9,10,12,13,14,15,16]] => 010000010010000
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,10],[3,9,11,12,13,14,15,16]] => 010000010100000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,9],[3,10,11,12,13,14,15,16]] => 010000001000000
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,7,9,11,13,15],[4,5,6,8,10,12,14,16]] => 001000101010101
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,3,7,9,11,13,14],[4,5,6,8,10,12,15,16]] => 001000101010010
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,3,7,9,11,12,14],[4,5,6,8,10,13,15,16]] => 001000101001010
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[1,2,3,7,9,10,11,13],[4,5,6,8,12,14,15,16]] => 001000100010100
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[1,2,3,7,8,9,11,13],[4,5,6,10,12,14,15,16]] => 001000001010100
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[1,2,3,7,8,9,11,12],[4,5,6,10,13,14,15,16]] => 001000001001000
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[1,2,3,7,8,9,10,15],[4,5,6,11,12,13,14,16]] => 001000000100001
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,3,7,8,9,10,12],[4,5,6,11,13,14,15,16]] => 001000000101000
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,3,7,8,9,10,11],[4,5,6,12,13,14,15,16]] => 001000000010000
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,6,9,11,13,15],[4,5,7,8,10,12,14,16]] => 001001001010101
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,6,9,10,11,12],[4,5,7,8,13,14,15,16]] => 001001000001000
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,3,6,8,11,13,15],[4,5,7,9,10,12,14,16]] => 001001010010101
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,3,6,8,10,13,15],[4,5,7,9,11,12,14,16]] => 001001010100101
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,10,12,15],[4,5,7,9,11,13,14,16]] => 001001010101001
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12,14],[4,5,7,9,11,13,15,16]] => 001001010101010
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,7,10,12,14],[4,5,8,9,11,13,15,16]] => 001000100101010
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,6,7,9,11,13],[4,5,8,10,12,14,15,16]] => 001000101010100
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,6,7,8,9,11],[4,5,10,12,13,14,15,16]] => 001000001010000
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,5,9,11,13,15],[4,6,7,8,10,12,14,16]] => 001010001010101
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,5,9,10,11,12],[4,6,7,8,13,14,15,16]] => 001010000001000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[1,2,3,5,8,10,12,15],[4,6,7,9,11,13,14,16]] => 001010010101001
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,5,8,10,12,14],[4,6,7,9,11,13,15,16]] => 001010010101010
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,5,7,11,13,15],[4,6,8,9,10,12,14,16]] => 001010100010101
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,5,7,11,13,14],[4,6,8,9,10,12,15,16]] => 001010100010010
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,5,7,10,13,15],[4,6,8,9,11,12,14,16]] => 001010100100101
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,5,7,10,13,14],[4,6,8,9,11,12,15,16]] => 001010100100010
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,5,7,10,12,15],[4,6,8,9,11,13,14,16]] => 001010100101001
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,5,7,10,12,14],[4,6,8,9,11,13,15,16]] => 001010100101010
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,7,9,13,15],[4,6,8,10,11,12,14,16]] => 001010101000101
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,7,9,13,14],[4,6,8,10,11,12,15,16]] => 001010101000010
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,7,9,12,13],[4,6,8,10,11,14,15,16]] => 001010101000100
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,9,11,15],[4,6,8,10,12,13,14,16]] => 001010101010001
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,9,11,14],[4,6,8,10,12,13,15,16]] => 001010101010010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9,11,13],[4,6,8,10,12,14,15,16]] => 001010101010100
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,9,11,12],[4,6,8,10,13,14,15,16]] => 001010101001000
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,5,7,8,13,14],[4,6,9,10,11,12,15,16]] => 001010010000010
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,5,6,8,10,12],[4,7,9,11,13,14,15,16]] => 001001010101000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,5,6,8,10,11],[4,7,9,12,13,14,15,16]] => 001001010010000
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,5,6,7,13,14],[4,8,9,10,11,12,15,16]] => 001000100000010
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[1,2,3,5,6,7,11,13],[4,8,9,10,12,14,15,16]] => 001000100010100
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[1,2,3,5,6,7,11,12],[4,8,9,10,13,14,15,16]] => 001000100001000
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,5,6,7,9,10],[4,8,11,12,13,14,15,16]] => 001000100100000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[1,2,3,5,6,7,8,13],[4,9,10,11,12,14,15,16]] => 001000010000100
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,2,3,5,6,7,8,11],[4,9,10,12,13,14,15,16]] => 001000010010000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,2,3,5,6,7,8,10],[4,9,11,12,13,14,15,16]] => 001000010100000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,5,6,7,8,9],[4,10,11,12,13,14,15,16]] => 001000001000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,9,11,13,15],[5,6,7,8,10,12,14,16]] => 000100001010101
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[1,2,3,4,9,11,12,14],[5,6,7,8,10,13,15,16]] => 000100001001010
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[1,2,3,4,9,10,11,13],[5,6,7,8,12,14,15,16]] => 000100000010100
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,4,9,10,11,12],[5,6,7,8,13,14,15,16]] => 000100000001000
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[1,2,3,4,8,11,13,15],[5,6,7,9,10,12,14,16]] => 000100010010101
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[1,2,3,4,8,10,13,15],[5,6,7,9,11,12,14,16]] => 000100010100101
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[1,2,3,4,8,10,12,15],[5,6,7,9,11,13,14,16]] => 000100010101001
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,4,8,10,12,14],[5,6,7,9,11,13,15,16]] => 000100010101010
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,8,9,10,12],[5,6,7,11,13,14,15,16]] => 000100000101000
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,4,7,11,13,15],[5,6,8,9,10,12,14,16]] => 000100100010101
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,7,11,12,13],[5,6,8,9,10,14,15,16]] => 000100100000100
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,4,7,9,11,14],[5,6,8,10,12,13,15,16]] => 000100101010010
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,4,7,9,11,13],[5,6,8,10,12,14,15,16]] => 000100101010100
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,7,8,10,12],[5,6,9,11,13,14,15,16]] => 000100010101000
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,7,8,9,11],[5,6,10,12,13,14,15,16]] => 000100001010000
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,6,11,12,13],[5,7,8,9,10,14,15,16]] => 000101000000100
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[1,2,3,4,6,10,12,14],[5,7,8,9,11,13,15,16]] => 000101000101010
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,6,8,12,14],[5,7,9,10,11,13,15,16]] => 000101010001010
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,6,8,11,12],[5,7,9,10,13,14,15,16]] => 000101010001000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,8,10,14],[5,7,9,11,12,13,15,16]] => 000101010100010
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8,10,12],[5,7,9,11,13,14,15,16]] => 000101010101000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,10,11],[5,7,9,12,13,14,15,16]] => 000101010010000
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,7,10,12],[5,8,9,11,13,14,15,16]] => 000100100101000
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7,10,11],[5,8,9,12,13,14,15,16]] => 000100100010000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,6,7,9,10],[5,8,11,12,13,14,15,16]] => 000100100100000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 000100010000001
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,6,7,8,14],[5,9,10,11,12,13,15,16]] => 000100010000010
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[1,2,3,4,6,7,8,12],[5,9,10,11,13,14,15,16]] => 000100010001000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,6,7,8,9],[5,10,11,12,13,14,15,16]] => 000100001000000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[1,2,3,4,5,11,13,15],[6,7,8,9,10,12,14,16]] => 000010000010101
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[1,2,3,4,5,11,12,14],[6,7,8,9,10,13,15,16]] => 000010000001010
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,5,11,12,13],[6,7,8,9,10,14,15,16]] => 000010000000100
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[1,2,3,4,5,10,13,15],[6,7,8,9,11,12,14,16]] => 000010000100101
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[1,2,3,4,5,10,12,15],[6,7,8,9,11,13,14,16]] => 000010000101001
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[1,2,3,4,5,10,11,13],[6,7,8,9,12,14,15,16]] => 000010000010100
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[1,2,3,4,5,9,13,15],[6,7,8,10,11,12,14,16]] => 000010001000101
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,8,13,14],[6,7,9,10,11,12,15,16]] => 000010010000010
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,5,8,10,13],[6,7,9,11,12,14,15,16]] => 000010010100100
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10,12],[6,7,9,11,13,14,15,16]] => 000010010101000
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,8,9,11],[6,7,10,12,13,14,15,16]] => 000010001010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,7,13,14],[6,8,9,10,11,12,15,16]] => 000010100000010
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [[1,2,3,4,5,7,11,12],[6,8,9,10,13,14,15,16]] => 000010100001000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,7,10,12],[6,8,9,11,13,14,15,16]] => 000010100101000
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[1,2,3,4,5,7,10,11],[6,8,9,12,13,14,15,16]] => 000010100010000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 000010101000001
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,7,9,14],[6,8,10,11,12,13,15,16]] => 000010101000010
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7,9,11],[6,8,10,12,13,14,15,16]] => 000010101010000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,9,10],[6,8,11,12,13,14,15,16]] => 000010100100000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => 000010010000001
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,7,8,14],[6,9,10,11,12,13,15,16]] => 000010010000010
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,7,8,11],[6,9,10,12,13,14,15,16]] => 000010010010000
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,7,8,9],[6,10,11,12,13,14,15,16]] => 000010001000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[1,2,3,4,5,6,13,15],[7,8,9,10,11,12,14,16]] => 000001000000101
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,6,13,14],[7,8,9,10,11,12,15,16]] => 000001000000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,6,12,15],[7,8,9,10,11,13,14,16]] => 000001000001001
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[1,2,3,4,5,6,12,14],[7,8,9,10,11,13,15,16]] => 000001000001010
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,6,11,15],[7,8,9,10,12,13,14,16]] => 000001000010001
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]] => 000001000100001
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[1,2,3,4,5,6,10,14],[7,8,9,11,12,13,15,16]] => 000001000100010
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]] => 000001001000001
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,9,14],[7,8,10,11,12,13,15,16]] => 000001001000010
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,9,13],[7,8,10,11,12,14,15,16]] => 000001001000100
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,9,12],[7,8,10,11,13,14,15,16]] => 000001001001000
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9,11],[7,8,10,12,13,14,15,16]] => 000001001010000
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => 000001010000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,8,14],[7,9,10,11,12,13,15,16]] => 000001010000010
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,10],[7,9,11,12,13,14,15,16]] => 000001010100000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,9],[7,10,11,12,13,14,15,16]] => 000001001000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => 000000100000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,14],[8,9,10,11,12,13,15,16]] => 000000100000010
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,7,13],[8,9,10,11,12,14,15,16]] => 000000100000100
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,7,12],[8,9,10,11,13,14,15,16]] => 000000100001000
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,7,11],[8,9,10,12,13,14,15,16]] => 000000100010000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,10],[8,9,11,12,13,14,15,16]] => 000000100100000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9],[8,10,11,12,13,14,15,16]] => 000000101000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]] => 000000010000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => 00000001000000001
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]] => 10000000010000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => 0000000010000000001
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]] => 00000010100000001
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 10000000101000000
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]] => 1000000000100000000
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]] => 000000000100000000001
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]] => 0000000101000000001
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]] => 00000010010000001
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => 00000100100000001
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 10000000100100000
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 10000001001000000
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 1000000001010000000
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]] => 100000000001000000000
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,12],[2,9,11,13,14,15,16,17,18]] => 10000001010100000
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,13],[2,11,12,14,15,16,17,18,19,20]] => 1000000001001000000
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11,13],[2,10,12,14,15,16,17,18,19,20]] => 1000000010101000000
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11,13],[2,9,10,12,14,15,16,17,18]] => 10000001001010000
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,6,7,14,17],[8,9,10,11,12,13,15,16,18]] => 00000010000001001
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,8,9,17],[3,10,11,12,13,14,15,16,18]] => 01000000100000001
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,6,7,15,16],[8,9,10,11,12,13,14,17,18]] => 00000010000000010
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11,13],[2,8,10,12,14,15,16,17,18]] => 10000010101010000
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,5,6,7,8,9,10,11],[3,4,12,13,14,15,16,17,18]] => 01000000001000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[1,2,3,4,5,6,7,15,17],[8,9,10,11,12,13,14,16,18]] => 00000010000000101
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,3,4,5,6,7,8,9,17],[2,10,11,12,13,14,15,16,18]] => 10000000100000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,6,8,15,16],[7,9,10,11,12,13,14,17,18]] => 00000101000000010
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,12,14],[2,9,11,13,15,16,17,18,19,20]] => 1000000101010100000
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,2,5,6,7,8,9,10,12],[3,4,11,13,14,15,16,17,18]] => 01000000010100000
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,3,5,6,7,8,9,10,11],[2,4,12,13,14,15,16,17,18]] => 10100000001000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,6,7,8,17,18],[9,10,11,12,13,14,15,16,19,20]] => 0000000100000000010
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,5,6,7,8,9,10,11,12],[3,4,13,14,15,16,17,18,19,20]] => 0100000000010000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[1,2,3,4,5,6,7,8,17,19],[9,10,11,12,13,14,15,16,18,20]] => 0000000100000000101
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[1,3,4,5,6,7,8,9,10,19],[2,11,12,13,14,15,16,17,18,20]] => 1000000001000000001
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,7,10,12,14],[2,8,9,11,13,15,16,17,18]] => 10000010010101000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14,16],[3,5,7,9,11,13,15,17,18]] => 01010101010101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,10,12,14,15],[3,5,7,9,11,13,16,17,18]] => 01010101010100100
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,8,10,12,13,16],[3,5,7,9,11,14,15,17,18]] => 01010101010010010
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,8,10,12,13,15],[3,5,7,9,11,14,16,17,18]] => 01010101010010100
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,8,10,12,13,14],[3,5,7,9,11,15,16,17,18]] => 01010101010001000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,6,8,10,11,14,16],[3,5,7,9,12,13,15,17,18]] => 01010101001001010
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,6,8,10,11,13,16],[3,5,7,9,12,14,15,17,18]] => 01010101001010010
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,6,8,10,11,13,15],[3,5,7,9,12,14,16,17,18]] => 01010101001010100
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,6,8,10,11,13,14],[3,5,7,9,12,15,16,17,18]] => 01010101001001000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,6,8,10,11,12,16],[3,5,7,9,13,14,15,17,18]] => 01010101000100010
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,8,10,11,12,14],[3,5,7,9,13,15,16,17,18]] => 01010101000101000
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,8,9,10,12,14],[3,5,7,11,13,15,16,17,18]] => 01010100010101000
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,7,8,10,12,14],[3,5,9,11,13,15,16,17,18]] => 01010001010101000
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,5,8,10,12,14,16],[3,6,7,9,11,13,15,17,18]] => 01001001010101010
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9,11,13,15],[3,6,8,10,12,14,16,17,18]] => 01001010101010100
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,6,8,10,12,14],[3,7,9,11,13,15,16,17,18]] => 01000101010101000
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[1,2,4,5,6,7,8,9,16],[3,10,11,12,13,14,15,17,18]] => 01000000100000010
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,9,12],[3,10,11,13,14,15,16,17,18]] => 01000000100100000
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,9,11],[3,10,12,13,14,15,16,17,18]] => 01000000101000000
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,9,10],[3,11,12,13,14,15,16,17,18]] => 01000000010000000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12,14,16],[4,5,7,9,11,13,15,17,18]] => 00100101010101010
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,5,8,10,12,14,16],[4,6,7,9,11,13,15,17,18]] => 00101001010101010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,9,11,13,16],[4,6,8,10,12,14,15,17,18]] => 00101010101010010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9,11,13,15],[4,6,8,10,12,14,16,17,18]] => 00101010101010100
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,5,6,8,10,12,13],[4,7,9,11,14,15,16,17,18]] => 00100101010010000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[1,2,3,5,6,7,8,9,15],[4,10,11,12,13,14,16,17,18]] => 00100000100000100
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,5,6,7,8,9,10],[4,11,12,13,14,15,16,17,18]] => 00100000010000000
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,7,8,10,12,14],[5,6,9,11,13,15,16,17,18]] => 00010001010101000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[1,2,3,4,6,8,11,13,15],[5,7,9,10,12,14,16,17,18]] => 00010101001010100
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,6,8,10,13,14],[5,7,9,11,12,15,16,17,18]] => 00010101010001000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8,10,12,14],[5,7,9,11,13,15,16,17,18]] => 00010101010101000
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,10,12,13],[5,7,9,11,14,15,16,17,18]] => 00010101010010000
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[1,2,3,4,6,7,8,9,14],[5,10,11,12,13,15,16,17,18]] => 00010000100001000
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,6,7,8,9,10],[5,11,12,13,14,15,16,17,18]] => 00010000010000000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,5,8,10,12,15],[6,7,9,11,13,14,16,17,18]] => 00001001010100100
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10,12,14],[6,7,9,11,13,15,16,17,18]] => 00001001010101000
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,9,11,12],[6,8,10,13,14,15,16,17,18]] => 00001010100100000
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,7,8,10,11],[6,9,12,13,14,15,16,17,18]] => 00001001001000000
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,7,8,9,13],[6,10,11,12,14,15,16,17,18]] => 00001000100010000
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,7,8,9,10],[6,11,12,13,14,15,16,17,18]] => 00001000010000000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9,11,13],[7,8,10,12,14,15,16,17,18]] => 00000100101010000
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,9,10,12],[7,8,11,13,14,15,16,17,18]] => 00000100010100000
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,11,12],[7,9,10,13,14,15,16,17,18]] => 00000101000100000
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,10,11],[7,9,12,13,14,15,16,17,18]] => 00000101001000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,8,9,16],[7,10,11,12,13,14,15,17,18]] => 00000100100000010
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,9,12],[7,10,11,13,14,15,16,17,18]] => 00000100100100000
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,9,10],[7,11,12,13,14,15,16,17,18]] => 00000100010000000
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,10,16],[8,9,11,12,13,14,15,17,18]] => 00000010010000010
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,7,10,13],[8,9,11,12,14,15,16,17,18]] => 00000010010010000
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,10,12],[8,9,11,13,14,15,16,17,18]] => 00000010010100000
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,9,16],[8,10,11,12,13,14,15,17,18]] => 00000010100000010
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9,11],[8,10,12,13,14,15,16,17,18]] => 00000010101000000
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9,10],[8,11,12,13,14,15,16,17,18]] => 00000010010000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,8,16],[9,10,11,12,13,14,15,17,18]] => 00000001000000010
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,7,8,15],[9,10,11,12,13,14,16,17,18]] => 00000001000000100
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,7,8,14],[9,10,11,12,13,15,16,17,18]] => 00000001000001000
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,13],[9,10,11,12,14,15,16,17,18]] => 00000001000010000
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,12],[9,10,11,13,14,15,16,17,18]] => 00000001000100000
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,11],[9,10,12,13,14,15,16,17,18]] => 00000001001000000
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,10],[9,11,12,13,14,15,16,17,18]] => 00000001010000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17,18]] => 00000000100000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15,17],[2,4,6,8,10,12,14,16,18]] => 10101010101010101
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,15,16],[2,4,6,8,10,12,14,17,18]] => 10101010101010010
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,13,14,16],[2,4,6,8,10,12,15,17,18]] => 10101010101001010
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,12,14,16],[2,4,6,8,10,13,15,17,18]] => 10101010100101010
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14,16],[2,4,6,8,11,13,15,17,18]] => 10101010010101010
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14,16],[2,4,6,9,11,13,15,17,18]] => 10101001010101010
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14,16],[2,4,7,9,11,13,15,17,18]] => 10100101010101010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14,16],[2,5,7,9,11,13,15,17,18]] => 10010101010101010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20]] => 1010101010101010101
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,15,17,18],[2,4,6,8,10,12,14,16,19,20]] => 1010101010101010010
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,11,13,14,15],[2,4,6,8,10,12,16,17,18]] => 10101010101000100
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,13,15,16,18],[2,4,6,8,10,12,14,17,19,20]] => 1010101010101001010
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,9,11,12,13,16],[2,4,6,8,10,14,15,17,18]] => 10101010100010010
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,13,14,16,18],[2,4,6,8,10,12,15,17,19,20]] => 1010101010100101010
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,7,9,10,11,14,16],[2,4,6,8,12,13,15,17,18]] => 10101010001001010
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,12,14,16,18],[2,4,6,8,10,13,15,17,19,20]] => 1010101010010101010
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,9,12,14,16],[2,4,6,10,11,13,15,17,18]] => 10101000100101010
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14,16,18],[2,4,6,8,11,13,15,17,19,20]] => 1010101001010101010
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,7,10,12,14,16],[2,4,8,9,11,13,15,17,18]] => 10100010010101010
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14,16,18],[2,4,6,9,11,13,15,17,19,20]] => 1010100101010101010
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12,14,16],[2,6,7,9,11,13,15,17,18]] => 10001001010101010
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14,16,18],[2,4,7,9,11,13,15,17,19,20]] => 1010010101010101010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14,16,18],[2,5,7,9,11,13,15,17,19,20]] => 1001010101010101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14,16,18],[3,5,7,9,11,13,15,17,19,20]] => 0101010101010101010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,15,17,19,20],[2,4,6,8,10,12,14,16,18,21,22]] => 101010101010101010010
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,13,15,17,18,20],[2,4,6,8,10,12,14,16,19,21,22]] => 101010101010101001010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12,14,16,18],[4,5,7,9,11,13,15,17,19,20]] => 0010010101010101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14,16,18,20],[3,5,7,9,11,13,15,17,19,21,22]] => 010101010101010101010
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[1,3,5,6,7,9,11,14,16],[2,4,8,10,12,13,15,17,18]] => 10100010101001010
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,9,11,13,16],[2,6,8,10,12,14,15,17,18]] => 10001010101010010
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,5,7,9,12,14,16,18],[4,6,8,10,11,13,15,17,19,20]] => 0010101010010101010
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9,11,13,15],[2,6,8,10,12,14,16,17,18]] => 10001010101010100
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10,12,14],[2,7,9,11,13,15,16,17,18]] => 10000101010101000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9,11,13,15,17],[2,6,8,10,12,14,16,18,19,20]] => 1000101010101010100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,9,11,13,15,18],[4,6,8,10,12,14,16,17,19,20]] => 0010101010101010010
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10,12,14,16],[2,7,9,11,13,15,17,18,19,20]] => 1000010101010101000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,7,9,11,12,15,16],[2,4,6,8,10,13,14,17,18]] => 10101010100100010
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,8,11,13,15,17],[2,4,6,9,10,12,14,16,18]] => 10101001001010101
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,6,9,11,13,15,17],[2,4,7,8,10,12,14,16,18]] => 10100100101010101
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,4,7,9,11,13,15,16],[2,5,6,8,10,12,14,17,18]] => 10010010101010010
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[1,3,4,7,8,11,13,15,17],[2,5,6,9,10,12,14,16,18]] => 10010001001010101
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,4,5,9,11,13,15,17],[2,6,7,8,10,12,14,16,18]] => 10001000101010101
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[1,3,4,5,6,7,8,15,16],[2,9,10,11,12,13,14,17,18]] => 10000001000000010
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11,13,15,17],[3,4,6,8,10,12,14,16,18]] => 01001010101010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,11,13,15,16],[3,4,6,8,10,12,14,17,18]] => 01001010101010010
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,9,11,13,14,17],[3,4,6,8,10,12,15,16,18]] => 01001010101001001
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,5,6,7,8,9,10,17],[3,4,11,12,13,14,15,16,18]] => 01000000010000001
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,7,9,11,13,15,17],[4,5,6,8,10,12,14,16,18]] => 00100010101010101
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,7,8,9,10,11,12],[4,5,6,13,14,15,16,17,18]] => 00100000000100000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,9,11,13,15,17],[5,6,7,8,10,12,14,16,18]] => 00010000101010101
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,9,10,11,12,13],[5,6,7,8,14,15,16,17,18]] => 00010000000010000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,5,11,13,15,17],[6,7,8,9,10,12,14,16,18]] => 00001000001010101
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,4,5,11,12,13,14],[6,7,8,9,10,15,16,17,18]] => 00001000000001000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[1,2,3,4,5,6,13,15,17],[7,8,9,10,11,12,14,16,18]] => 00000100000010101
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,5,6,13,14,15],[7,8,9,10,11,12,16,17,18]] => 00000100000000100
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,12,15,17,19],[2,4,6,8,10,13,14,16,18,20]] => 1010101010010010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11,13,15,17,19],[3,4,6,8,10,12,14,16,18,20]] => 0100101010101010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,11,13,15,17,18],[3,4,6,8,10,12,14,16,19,20]] => 0100101010101010010
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,7,9,11,13,15,17,19],[4,5,6,8,10,12,14,16,18,20]] => 0010001010101010101
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,7,8,9,10,11,12,13],[4,5,6,14,15,16,17,18,19,20]] => 0010000000001000000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,9,11,13,15,17,19],[5,6,7,8,10,12,14,16,18,20]] => 0001000010101010101
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,9,10,11,12,13,14],[5,6,7,8,15,16,17,18,19,20]] => 0001000000000100000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,5,11,13,15,17,19],[6,7,8,9,10,12,14,16,18,20]] => 0000100000101010101
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5,11,12,13,14,15],[6,7,8,9,10,16,17,18,19,20]] => 0000100000000010000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,5,6,13,15,17,19],[7,8,9,10,11,12,14,16,18,20]] => 0000010000001010101
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,4,5,6,13,14,15,16],[7,8,9,10,11,12,17,18,19,20]] => 0000010000000001000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[1,2,3,4,5,6,7,15,17,19],[8,9,10,11,12,13,14,16,18,20]] => 0000001000000010101
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,5,6,7,15,16,17],[8,9,10,11,12,13,14,18,19,20]] => 0000001000000000100
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]] => 0000000001000000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,7,9,11,13,15,17],[3,5,6,8,10,12,14,16,18]] => 01010010101010101
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,9,11,13,15,17],[3,5,7,8,10,12,14,16,18]] => 01010100101010101
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,8,11,13,15,17],[3,5,7,9,10,12,14,16,18]] => 01010101001010101
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,6,8,10,13,15,17],[3,5,7,9,11,12,14,16,18]] => 01010101010010101
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,8,10,12,15,17],[3,5,7,9,11,13,14,16,18]] => 01010101010100101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,10,12,14,17],[3,5,7,9,11,13,15,16,18]] => 01010101010101001
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,7,9,11,13,15,17,19],[3,5,6,8,10,12,14,16,18,20]] => 0101001010101010101
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,5,9,11,13,15,17],[3,6,7,8,10,12,14,16,18]] => 01001000101010101
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,9,11,13,15,17,19],[3,5,7,8,10,12,14,16,18,20]] => 0101010010101010101
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,7,11,13,15,17],[3,5,8,9,10,12,14,16,18]] => 01010010001010101
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,8,11,13,15,17,19],[3,5,7,9,10,12,14,16,18,20]] => 0101010100101010101
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,4,6,8,9,13,15,17],[3,5,7,10,11,12,14,16,18]] => 01010100100010101
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,4,6,8,10,13,15,17,19],[3,5,7,9,11,12,14,16,18,20]] => 0101010101001010101
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,6,8,10,11,15,17],[3,5,7,9,12,13,14,16,18]] => 01010101001000101
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,6,8,10,12,15,17,19],[3,5,7,9,11,13,14,16,18,20]] => 0101010101010010101
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,8,10,12,13,17],[3,5,7,9,11,14,15,16,18]] => 01010101010010001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,8,10,12,14,17,19],[3,5,7,9,11,13,15,16,18,20]] => 0101010101010100101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,10,12,14,16,19],[3,5,7,9,11,13,15,17,18,20]] => 0101010101010101001
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,9,11,13,14],[6,8,10,12,15,16,17,18,19,20]] => 0000101010100100000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9,11,13,15],[7,8,10,12,14,16,17,18,19,20]] => 0000010010101010000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,9,11,13,15,16],[6,8,10,12,14,17,18,19,20,21,22]] => 000010101010100100000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,10,12,14,15],[5,7,9,11,13,16,17,18,19,20]] => 0001010101010010000
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10,12,14,16],[6,7,9,11,13,15,17,18,19,20]] => 0000100101010101000
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9,11,13,15,17],[7,8,10,12,14,16,18,19,20,21,22]] => 000001001010101010000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11,13,15,17,19,21],[3,4,6,8,10,12,14,16,18,20,22]] => 010010101010101010101
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,9,11,13,14,16],[3,4,6,8,10,12,15,17,18]] => 01001010101001010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,10,12,14,16,17],[3,5,7,9,11,13,15,18,19,20]] => 0101010101010100100
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,10,11],[9,12,13,14,15,16,17,18,19,20]] => 0000000100100000000
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,12],[10,11,13,14,15,16,17,18,19,20]] => 0000000010010000000
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,11,12],[10,13,14,15,16,17,18,19,20,21,22]] => 000000001001000000000
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9,11,12],[8,10,13,14,15,16,17,18,19,20]] => 0000001010010000000
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,11,13],[9,10,12,14,15,16,17,18,19,20]] => 0000000100101000000
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,10,13],[11,12,14,15,16,17,18,19,20,21,22]] => 000000000100100000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,9,11,13,15,16,18],[3,4,6,8,10,12,14,17,19,20]] => 0100101010101001010
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,4,7,9,11,13,14,16],[3,5,6,8,10,12,15,17,18]] => 01010010101001010
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,4,7,9,11,13,14,16],[2,5,6,8,10,12,15,17,18]] => 10010010101001010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,4,7,9,11,13,15,16],[3,5,6,8,10,12,14,17,18]] => 01010010101010010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,9,11,13,17],[4,6,8,10,12,14,15,16,18]] => 00101010101010001
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,7,9,11,15,17],[4,6,8,10,12,13,14,16,18]] => 00101010101000101
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,5,7,9,13,15,17],[4,6,8,10,11,12,14,16,18]] => 00101010100010101
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,5,7,11,13,15,17],[4,6,8,9,10,12,14,16,18]] => 00101010001010101
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,5,9,11,13,15,17],[4,6,7,8,10,12,14,16,18]] => 00101000101010101
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,4,5,6,7,8,9,10,11],[3,12,13,14,15,16,17,18,19,20]] => 0100000000100000000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,8,9,18],[10,11,12,13,14,15,16,17,19,20]] => 0000000010000000010
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,8,9,10,20],[11,12,13,14,15,16,17,18,19,21,22]] => 000000000100000000010
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,7,8,10,18],[9,11,12,13,14,15,16,17,19,20]] => 0000000101000000010
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[1,2,3,4,5,6,12,15,17],[7,8,9,10,11,13,14,16,18]] => 00000100000100101
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[1,2,3,4,5,10,13,15,17],[6,7,8,9,11,12,14,16,18]] => 00001000010010101
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,3,4,8,11,13,15,17],[5,6,7,9,10,12,14,16,18]] => 00010001001010101
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[1,2,3,6,9,11,13,15,17],[4,5,7,8,10,12,14,16,18]] => 00100100101010101
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,11],[10,12,13,14,15,16,17,18,19,20]] => 0000000010100000000
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,9,10,11],[8,12,13,14,15,16,17,18,19,20]] => 0000001000100000000
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,8,9,10,11],[7,12,13,14,15,16,17,18,19,20]] => 0000010000100000000
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,7,8,9,10,11],[6,12,13,14,15,16,17,18,19,20]] => 0000100000100000000
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,6,7,8,9,10,11],[5,12,13,14,15,16,17,18,19,20]] => 0001000000100000000
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,2,3,5,6,7,8,9,10,11],[4,12,13,14,15,16,17,18,19,20]] => 0010000000100000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,7,9,11,15,16],[4,6,8,10,12,13,14,17,18]] => 00101010101000010
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,5,6,7,9,11,13,15],[3,4,8,10,12,14,16,17,18]] => 01000010101010100
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,9,11,13,17],[3,6,8,10,12,14,15,16,18]] => 01001010101010001
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9,11,13,15,17],[3,6,8,10,12,14,16,18,19,20]] => 0100101010101010100
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,10,12],[11,13,14,15,16,17,18,19,20,21,22]] => 000000000101000000000
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,4,7,8,9,10,11,12],[3,5,6,13,14,15,16,17,18]] => 01010000000100000
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,3,5,9,10,11,12,13],[4,6,7,8,14,15,16,17,18]] => 00101000000010000
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[1,2,3,4,6,11,12,13,14],[5,7,8,9,10,15,16,17,18]] => 00010100000001000
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,5,7,13,14,15],[6,8,9,10,11,12,16,17,18]] => 00001010000000100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,3,4,6,8,11,13,15,17],[2,5,7,9,10,12,14,16,18]] => 10010101001010101
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,3,5,6,8,11,13,15,17],[2,4,7,9,10,12,14,16,18]] => 10100101001010101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,5,7,9,11,12,14,17,19],[2,4,6,8,10,13,15,16,18,20]] => 1010101010010100101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,5,7,9,11,12,14,16,19],[2,4,6,8,10,13,15,17,18,20]] => 1010101010010101001
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,4,6,8,11,13,15,16],[3,5,7,9,10,12,14,17,18]] => 01010101001010010
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,6,8,11,13,15,17],[3,4,7,9,10,12,14,16,18]] => 01000101001010101
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,5,7,9,12,14,16,18],[3,6,8,10,11,13,15,17,19,20]] => 0100101010010101010
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,7,9,12,14,16,18],[3,5,8,10,11,13,15,17,19,20]] => 0101001010010101010
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,9,12,14,16,18],[3,5,7,10,11,13,15,17,19,20]] => 0101010010010101010
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11,13,15],[2,8,10,12,14,16,17,18,19,20]] => 1000001010101010000
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[1,3,4,5,6,9,11,13,15],[2,7,8,10,12,14,16,17,18]] => 10000100101010100
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,10,12,14,17],[4,5,7,9,11,13,15,16,18]] => 00100101010101001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,10,12,14,15],[2,5,7,9,11,13,16,17,18]] => 10010101010100100
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,8,10,12,15,16],[3,5,7,9,11,13,14,17,18]] => 01010101010100010
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,5,6,8,10,12,14,16],[3,4,7,9,11,13,15,17,18]] => 01000101010101010
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,6,8,10,13,14,15],[3,5,7,9,11,12,16,17,18]] => 01010101010000100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,8,10,12,14,15,16],[3,5,7,9,11,13,17,18,19,20]] => 0101010101010001000
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,4,6,8,11,12,13,14],[3,5,7,9,10,15,16,17,18]] => 01010101000001000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,8,10,12,13,14,16],[3,5,7,9,11,15,17,18,19,20]] => 0101010101000101000
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,9,10,11,12,14],[3,5,7,8,13,15,16,17,18]] => 01010100000101000
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,8,10,11,12,14,16],[3,5,7,9,13,15,17,18,19,20]] => 0101010100010101000
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,7,8,9,10,12,14],[3,5,6,11,13,15,16,17,18]] => 01010000010101000
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,8,9,10,12,14,16],[3,5,7,11,13,15,17,18,19,20]] => 0101010001010101000
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,5,6,7,8,10,12,14],[3,4,9,11,13,15,16,17,18]] => 01000001010101000
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,6,7,8,10,12,14,16],[3,5,9,11,13,15,17,18,19,20]] => 0101000101010101000
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,6,8,10,12,14,16],[3,7,9,11,13,15,17,18,19,20]] => 0100010101010101000
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8,10,12,14,16],[5,7,9,11,13,15,17,18,19,20]] => 0001010101010101000
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,5,6,8,9,10,11,12],[3,4,7,13,14,15,16,17,18]] => 01000100000100000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[1,2,3,5,6,7,8,15,16],[4,9,10,11,12,13,14,17,18]] => 00100001000000010
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,7,8,9,11,12,13],[4,5,6,10,14,15,16,17,18]] => 00100000100010000
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[1,2,3,4,6,7,13,14,15],[5,8,9,10,11,12,16,17,18]] => 00010010000000100
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,9,10,11,12,14],[5,6,7,8,13,15,16,17,18]] => 00010000000101000
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[1,2,3,4,5,6,13,14,16],[7,8,9,10,11,12,15,17,18]] => 00000100000001010
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,7,8,9,17],[10,11,12,13,14,15,16,18,19,20]] => 0000000010000000100
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[1,2,3,4,5,11,12,13,15],[6,7,8,9,10,14,16,17,18]] => 00001000000010100
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,16],[10,11,12,13,14,15,17,18,19,20]] => 0000000010000001000
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,15],[10,11,12,13,14,16,17,18,19,20]] => 0000000010000010000
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,7,8,9,10,11,13],[4,5,6,12,14,15,16,17,18]] => 00100000001010000
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,14],[10,11,12,13,15,16,17,18,19,20]] => 0000000010000100000
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7,8,9,13],[10,11,12,14,15,16,17,18,19,20]] => 0000000010001000000
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,9,11,12,14,16],[2,4,7,8,10,13,15,17,18]] => 10100100100101010
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
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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