Identifier
Mp00201: Dyck paths RingelPermutations
Mp00151: Permutations to cycle typeSet partitions
Mp00164: Set partitions Chen Deng Du Stanley Yan Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[1,0]=>[2,1]=>{{1,2}}=>{{1,2}} [1,0,1,0]=>[3,1,2]=>{{1,2,3}}=>{{1,2,3}} [1,1,0,0]=>[2,3,1]=>{{1,2,3}}=>{{1,2,3}} [1,0,1,0,1,0]=>[4,1,2,3]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,0,1,1,0,0]=>[3,1,4,2]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,0,1,0,0]=>[4,3,1,2]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,1,0,0,0]=>[2,3,4,1]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>{{1,3,5},{2,4}}=>{{1,5},{2,3,4}} [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}}=>{{1,2,6},{3,4,5}} [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}=>{{1,5,6},{2,3,4}} [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}=>{{1,6},{2,3,4,5}} [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}=>{{1,5,6},{2,3,4}} [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>{{1,3,6},{2,4,5}}=>{{1,5},{2,3,4,6}} [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>{{1,2,4,6},{3,5}}=>{{1,2,6},{3,4,5}} [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>{{1,4,6},{2,3,5}}=>{{1,3,4,5},{2,6}} [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}=>{{1,4,5},{2,3,6}} [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>{{1,2,4,7},{3,5,6}}=>{{1,2,6},{3,4,5,7}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>{{1,2,5,7},{3,4,6}}=>{{1,2,4,5,6},{3,7}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}=>{{1,7},{2,3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>{{1,3,5},{2,4,6,7}}=>{{1,6,7},{2,3,4,5}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>{{1,3,5,6},{2,4,7}}=>{{1,6},{2,3,4,5,7}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}}=>{{1,5,6,7},{2,3,4}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>{{1,3,6,7},{2,4,5}}=>{{1,5},{2,3,4,6,7}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>{{1,3,6},{2,4,5,7}}=>{{1,5,6},{2,3,4,7}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>{{1,3,6,7},{2,4,5}}=>{{1,5},{2,3,4,6,7}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>{{1,3,7},{2,4,5,6}}=>{{1,5,7},{2,3,4,6}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>{{1,2,4,6},{3,5,7}}=>{{1,2,7},{3,4,5,6}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>{{1,2,4,6,7},{3,5}}=>{{1,2,6,7},{3,4,5}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>{{1,2,4,7},{3,5,6}}=>{{1,2,6},{3,4,5,7}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>{{1,4,6,7},{2,3,5}}=>{{1,3,4,5},{2,6,7}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>{{1,4,6},{2,3,5,7}}=>{{1,3,4,5,6},{2,7}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>{{1,4,6,7},{2,3,5}}=>{{1,3,4,5},{2,6,7}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>{{1,3,4,6},{2,5,7}}=>{{1,4,5,6},{2,3,7}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}}=>{{1,4,5},{2,3,6,7}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>{{1,4,7},{2,3,5,6}}=>{{1,3,4,5,7},{2,6}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>{{1,3,4,7},{2,5,6}}=>{{1,4,5,7},{2,3,6}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>{{1,2,3,5,7},{4,6}}=>{{1,2,3,7},{4,5,6}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>{{1,2,5,7},{3,4,6}}=>{{1,2,4,5,6},{3,7}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>{{1,2,4,5,7},{3,6}}=>{{1,2,5,6},{3,4,7}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>{{1,5,7},{2,3,4,6}}=>{{1,3,7},{2,4,5,6}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>{{1,4,5,7},{2,3,6}}=>{{1,3,4,7},{2,5,6}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>{{1,3,4,5,7},{2,6}}=>{{1,4,7},{2,3,5,6}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>{{1,2,3,8},{4,5,6,7}} [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>{{1,2,3,5,8},{4,6,7}}=>{{1,2,3,7},{4,5,6,8}} [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>{{1,2,3,5,6,8},{4,7}}=>{{1,2,3,6,7},{4,5,8}} [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]=>{{1,2,4,6,7,8},{3,5}}=>{{1,2,6,7,8},{3,4,5}} [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>{{1,2,4,6},{3,5,7,8}}=>{{1,2,7,8},{3,4,5,6}} [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}=>{{1,2,7,8},{3,4,5,6}} [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>{{1,2,4,6,7,8},{3,5}}=>{{1,2,6,7,8},{3,4,5}} [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,1,8,2,3,7,4,5]=>{{1,2,4,6,7},{3,5,8}}=>{{1,2,7},{3,4,5,6,8}} [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>{{1,2,4,6,7,8},{3,5}}=>{{1,2,6,7,8},{3,4,5}} [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]=>{{1,2,4,7,8},{3,5,6}}=>{{1,2,6},{3,4,5,7,8}} [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]=>{{1,2,4,7},{3,5,6,8}}=>{{1,2,6,7},{3,4,5,8}} [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>{{1,2,4,7,8},{3,5,6}}=>{{1,2,6},{3,4,5,7,8}} [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>{{1,2,4,8},{3,5,6,7}}=>{{1,2,6,8},{3,4,5,7}} [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>{{1,2,3,5,7,8},{4,6}}=>{{1,2,3,7,8},{4,5,6}} [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>{{1,2,3,8},{4,5,6,7}} [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>{{1,2,3,5,8},{4,6,7}}=>{{1,2,3,7},{4,5,6,8}} [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,1,8,5,2,3,4,6]=>{{1,2,4,5,7},{3,6,8}}=>{{1,2,5,6,7},{3,4,8}} [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>{{1,2,5,6},{3,4,7,8}} [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]=>{{1,2,3,6,8},{4,5,7}}=>{{1,2,3,5,6,7},{4,8}} [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]=>{{1,2,6,8},{3,4,5,7}}=>{{1,2,4,8},{3,5,6,7}} [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>{{1,2,5,6,8},{3,4,7}}=>{{1,2,4,5,8},{3,6,7}} [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>{{1,2,3,5,7},{4,6,8}}=>{{1,2,3,8},{4,5,6,7}} [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>{{1,2,3,5,6,8},{4,7}}=>{{1,2,3,6,7},{4,5,8}} [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,8,7,3,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]=>{{1,3,5,6,7,8},{2,4}}=>{{1,5,6,7,8},{2,3,4}} [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>{{1,3,5,7,8},{2,4,6}}=>{{1,7,8},{2,3,4,5,6}} [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>{{1,3,5},{2,4,6,7,8}}=>{{1,6,7,8},{2,3,4,5}} [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]=>{{1,3,5,8},{2,4,6,7}}=>{{1,7},{2,3,4,5,6,8}} [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>{{1,3,5},{2,4,6,7,8}}=>{{1,6,7,8},{2,3,4,5}} [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>{{1,3,5,6,7,8},{2,4}}=>{{1,5,6,7,8},{2,3,4}} [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>{{1,3,5,6,7,8},{2,4}}=>{{1,5,6,7,8},{2,3,4}} [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>{{1,3,5,6,8},{2,4,7}}=>{{1,6,7},{2,3,4,5,8}} [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>{{1,3,5,6},{2,4,7,8}}=>{{1,6},{2,3,4,5,7,8}} [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>{{1,3,5,6,7,8},{2,4}}=>{{1,5,6,7,8},{2,3,4}} [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>{{1,3,5,6,7},{2,4,8}}=>{{1,6,8},{2,3,4,5,7}} [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>{{1,3,5,6,7,8},{2,4}}=>{{1,5,6,7,8},{2,3,4}} [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,3,1,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>{{1,2,3,5,7,8},{4,6}}=>{{1,2,3,7,8},{4,5,6}} [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>{{1,2,3,5,7,8},{4,6}}=>{{1,2,3,7,8},{4,5,6}} [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]=>{{1,2,3,5,8},{4,6,7}}=>{{1,2,3,7},{4,5,6,8}} [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>{{1,3,6,7,8},{2,4,5}}=>{{1,5},{2,3,4,6,7,8}} [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]=>{{1,3,6},{2,4,5,7,8}}=>{{1,5,6},{2,3,4,7,8}} [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]=>{{1,3,6,7,8},{2,4,5}}=>{{1,5},{2,3,4,6,7,8}} [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>{{1,3,6,7},{2,4,5,8}}=>{{1,5,6,8},{2,3,4,7}} [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>{{1,3,6,7,8},{2,4,5}}=>{{1,5},{2,3,4,6,7,8}} [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,1,7,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>{{1,2,3,6,8},{4,5,7}}=>{{1,2,3,5,6,7},{4,8}} [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>{{1,2,3,5,6,8},{4,7}}=>{{1,2,3,6,7},{4,5,8}} [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]=>{{1,3,7},{2,4,5,6,8}}=>{{1,5,8},{2,3,4,6,7}} [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>{{1,2,4,6},{3,5,7,8}}=>{{1,2,7,8},{3,4,5,6}} [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>{{1,2,4,6,7,8},{3,5}}=>{{1,2,6,7,8},{3,4,5}} [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>{{1,2,4,7,8},{3,5,6}}=>{{1,2,6},{3,4,5,7,8}} [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>{{1,4,6,7,8},{2,3,5}}=>{{1,3,4,5},{2,6,7,8}} [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>{{1,4,6,7,8},{2,3,5}}=>{{1,3,4,5},{2,6,7,8}} [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>{{1,4,6},{2,3,5,7,8}}=>{{1,3,4,5,6},{2,7,8}} [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]=>{{1,4,6,7,8},{2,3,5}}=>{{1,3,4,5},{2,6,7,8}} [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>{{1,4,6,7},{2,3,5,8}}=>{{1,3,4,5,6,8},{2,7}} [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]=>{{1,3,4,6},{2,5,7,8}}=>{{1,4,5,6},{2,3,7,8}} [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>{{1,3,4,6,7,8},{2,5}}=>{{1,4,5},{2,3,6,7,8}} [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]=>{{1,3,4,6,7},{2,5,8}}=>{{1,4,5,6,8},{2,3,7}} [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>{{1,4,7,8},{2,3,5,6}}=>{{1,3,4,5,7,8},{2,6}} [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>{{1,4,7},{2,3,5,6,8}}=>{{1,3,4,5,8},{2,6,7}} [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>{{1,4,7,8},{2,3,5,6}}=>{{1,3,4,5,7,8},{2,6}} [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]=>{{1,3,4,7,8},{2,5,6}}=>{{1,4,5,7,8},{2,3,6}} [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>{{1,3,4,7},{2,5,6,8}}=>{{1,4,5,8},{2,3,6,7}} [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,5,4,1,6,2,8,3]=>{{1,3,4,7,8},{2,5,6}}=>{{1,4,5,7,8},{2,3,6}} [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>{{1,2,3,5,7,8},{4,6}}=>{{1,2,3,7,8},{4,5,6}} [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>{{1,2,5,7},{3,4,6,8}}=>{{1,2,4,5,6,7},{3,8}} [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]=>{{1,2,5,7,8},{3,4,6}}=>{{1,2,4,5,6},{3,7,8}} [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>{{1,2,4,5,7,8},{3,6}}=>{{1,2,5,6},{3,4,7,8}} [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,7,8,5,1,3,4,6]=>{{1,2,4,5,7},{3,6,8}}=>{{1,2,5,6,7},{3,4,8}} [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>{{1,2,4,5,7,8},{3,6}}=>{{1,2,5,6},{3,4,7,8}} [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,6,4,5,1,8,3,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>{{1,2,5,8},{3,4,6,7}}=>{{1,2,4,5,6,8},{3,7}} [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>{{1,4,5,7},{2,3,6,8}}=>{{1,3,4,8},{2,5,6,7}} [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>{{1,3,4,5,8},{2,6,7}}=>{{1,4,7},{2,3,5,6,8}} [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>{{1,2,3,4,6,8},{5,7}}=>{{1,2,3,4,8},{5,6,7}} [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>{{1,2,3,6,8},{4,5,7}}=>{{1,2,3,5,6,7},{4,8}} [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>{{1,2,5,6,8},{3,4,7}}=>{{1,2,4,5,8},{3,6,7}} [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>{{1,2,4,5,6,8},{3,7}}=>{{1,2,5,8},{3,4,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,3,4,7,6,1,2,5]=>{{1,5,6,8},{2,3,4,7}}=>{{1,3,6,7},{2,4,5,8}} [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>{{1,4,5,6,8},{2,3,7}}=>{{1,3,4,6,7},{2,5,8}} [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}}
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
Chen Deng Du Stanley Yan
Description
A map that swaps the crossing number and the nesting number of a set partition.