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
=>
Cc0005;cc-rep-0Cc0007;cc-rep-1
[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
[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
Sorry, this map was not found in the database.