Identifier
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
[1,0] => [2,1] => [2,1] => 1
[1,0,1,0] => [3,1,2] => [3,1,2] => 01
[1,1,0,0] => [2,3,1] => [3,2,1] => 11
[1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => 001
[1,0,1,1,0,0] => [3,1,4,2] => [4,3,1,2] => 011
[1,1,0,0,1,0] => [2,4,1,3] => [4,2,1,3] => 101
[1,1,0,1,0,0] => [4,3,1,2] => [3,1,4,2] => 011
[1,1,1,0,0,0] => [2,3,4,1] => [4,3,2,1] => 111
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,1,2,3,4] => 0001
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,4,1,2,3] => 0011
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5,3,1,2,4] => 0101
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,1,2,5,3] => 0011
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,4,3,1,2] => 0111
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,2,1,3,4] => 1001
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5,4,2,1,3] => 1011
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,5,2,4] => 0101
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,1,5,2,3] => 0011
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,1,5,4,2] => 0111
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,3,2,1,4] => 1101
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,2,1,5,3] => 1011
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,3,1,5,2] => 0111
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,4,3,2,1] => 1111
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 00001
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,5,1,2,3,4] => 00011
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [6,4,1,2,3,5] => 00101
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [5,1,2,3,6,4] => 00011
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,5,4,1,2,3] => 00111
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [6,3,1,2,4,5] => 01001
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [6,5,3,1,2,4] => 01011
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [4,1,2,6,3,5] => 00101
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,1,2,6,3,4] => 00011
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,1,2,6,5,3] => 00111
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [6,4,3,1,2,5] => 01101
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,3,1,2,6,4] => 01011
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,4,1,2,6,3] => 00111
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,5,4,3,1,2] => 01111
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => 10001
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,5,2,1,3,4] => 10011
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [6,4,2,1,3,5] => 10101
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [5,2,1,3,6,4] => 10011
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [6,5,4,2,1,3] => 10111
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => 01001
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,1,6,5,2,4] => 01011
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,1,6,2,3,5] => 00101
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,1,5,2,3,4] => 00011
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,1,6,5,2,3] => 00111
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,1,6,4,2,5] => 01101
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,1,5,2,6,4] => 01011
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,4,1,6,2,3] => 00111
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,1,6,5,4,2] => 01111
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,3,2,1,4,5] => 11001
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,5,3,2,1,4] => 11011
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,2,1,6,3,5] => 10101
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [5,2,1,6,3,4] => 10011
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,2,1,6,5,3] => 10111
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,3,1,6,2,5] => 01101
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,3,1,6,2,4] => 01011
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,1,5,2,6,3] => 00111
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,3,1,6,5,2] => 01111
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,4,3,2,1,5] => 11101
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,3,2,1,6,4] => 11011
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,4,2,1,6,3] => 10111
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,4,3,1,6,2] => 01111
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,5,4,3,2,1] => 11111
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 000001
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,6,1,2,3,4,5] => 000011
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [7,5,1,2,3,4,6] => 000101
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [6,1,2,3,4,7,5] => 000011
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,6,5,1,2,3,4] => 000111
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [7,4,1,2,3,5,6] => 001001
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [7,6,4,1,2,3,5] => 001011
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [5,1,2,3,7,4,6] => 000101
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [6,1,2,3,7,4,5] => 000011
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [5,1,2,3,7,6,4] => 000111
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [7,5,4,1,2,3,6] => 001101
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [6,4,1,2,3,7,5] => 001011
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [6,5,1,2,3,7,4] => 000111
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,6,5,4,1,2,3] => 001111
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [7,3,1,2,4,5,6] => 010001
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [7,6,3,1,2,4,5] => 010011
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [7,5,3,1,2,4,6] => 010101
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [6,3,1,2,4,7,5] => 010011
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [7,6,5,3,1,2,4] => 010111
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [4,1,2,7,3,5,6] => 001001
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [4,1,2,7,6,3,5] => 001011
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [5,1,2,7,3,4,6] => 000101
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [7,1,2,6,3,4,5] => 000011
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [5,1,2,7,6,3,4] => 000111
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [4,1,2,7,5,3,6] => 001101
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [4,1,2,6,3,7,5] => 001011
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [6,5,1,2,7,3,4] => 000111
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [4,1,2,7,6,5,3] => 001111
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [7,4,3,1,2,5,6] => 011001
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [7,6,4,3,1,2,5] => 011011
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [5,3,1,2,7,4,6] => 010101
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [6,3,1,2,7,4,5] => 010011
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [5,3,1,2,7,6,4] => 010111
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [5,4,1,2,7,3,6] => 001101
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [6,4,1,2,7,3,5] => 001011
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [5,1,2,6,3,7,4] => 000111
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [5,4,1,2,7,6,3] => 001111
>>> Load all 674 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [7,5,4,3,1,2,6] => 011101
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [6,4,3,1,2,7,5] => 011011
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [6,5,3,1,2,7,4] => 010111
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [6,5,4,1,2,7,3] => 001111
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,6,5,4,3,1,2] => 011111
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => 100001
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [7,6,2,1,3,4,5] => 100011
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [7,5,2,1,3,4,6] => 100101
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [6,2,1,3,4,7,5] => 100011
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [7,6,5,2,1,3,4] => 100111
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [7,4,2,1,3,5,6] => 101001
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [7,6,4,2,1,3,5] => 101011
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [5,2,1,3,7,4,6] => 100101
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [6,2,1,3,7,4,5] => 100011
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [5,2,1,3,7,6,4] => 100111
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [7,5,4,2,1,3,6] => 101101
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [6,4,2,1,3,7,5] => 101011
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [6,5,2,1,3,7,4] => 100111
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [7,6,5,4,2,1,3] => 101111
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [3,1,7,2,4,5,6] => 010001
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [3,1,7,6,2,4,5] => 010011
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [3,1,7,5,2,4,6] => 010101
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [3,1,6,2,4,7,5] => 010011
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [3,1,7,6,5,2,4] => 010111
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [4,1,7,2,3,5,6] => 001001
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [4,1,7,6,2,3,5] => 001011
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [7,1,5,2,3,4,6] => 000101
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [6,1,7,2,3,4,5] => 000011
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [7,6,1,5,2,3,4] => 000111
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [4,1,7,5,2,3,6] => 001101
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [4,1,6,2,3,7,5] => 001011
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [6,1,7,5,2,3,4] => 000111
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [4,1,7,6,5,2,3] => 001111
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [3,1,7,4,2,5,6] => 011001
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [3,1,7,6,4,2,5] => 011011
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [3,1,5,2,7,4,6] => 010101
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [3,1,6,2,7,4,5] => 010011
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [3,1,5,2,7,6,4] => 010111
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [5,4,1,7,2,3,6] => 001101
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [6,4,1,7,2,3,5] => 001011
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [5,1,7,2,3,6,4] => 000111
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [5,4,1,7,6,2,3] => 001111
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [3,1,7,5,4,2,6] => 011101
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [3,1,6,4,2,7,5] => 011011
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [3,1,6,5,2,7,4] => 010111
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [6,5,4,1,7,2,3] => 001111
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [3,1,7,6,5,4,2] => 011111
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [7,3,2,1,4,5,6] => 110001
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [7,6,3,2,1,4,5] => 110011
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [7,5,3,2,1,4,6] => 110101
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [6,3,2,1,4,7,5] => 110011
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [7,6,5,3,2,1,4] => 110111
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [4,2,1,7,3,5,6] => 101001
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [4,2,1,7,6,3,5] => 101011
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [5,2,1,7,3,4,6] => 100101
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [7,2,1,6,3,4,5] => 100011
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [5,2,1,7,6,3,4] => 100111
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [4,2,1,7,5,3,6] => 101101
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [4,2,1,6,3,7,5] => 101011
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [6,5,2,1,7,3,4] => 100111
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [4,2,1,7,6,5,3] => 101111
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [4,3,1,7,2,5,6] => 011001
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [4,3,1,7,6,2,5] => 011011
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [5,3,1,7,2,4,6] => 010101
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [7,3,1,6,2,4,5] => 010011
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [5,3,1,7,6,2,4] => 010111
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [4,1,5,2,7,3,6] => 001101
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,1,7,2,6,3,5] => 001011
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [5,1,7,2,6,3,4] => 000111
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [4,1,5,2,7,6,3] => 001111
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [4,3,1,7,5,2,6] => 011101
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [4,3,1,6,2,7,5] => 011011
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [6,5,3,1,7,2,4] => 010111
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,1,6,5,2,7,3] => 001111
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [4,3,1,7,6,5,2] => 011111
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [7,4,3,2,1,5,6] => 111001
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [7,6,4,3,2,1,5] => 111011
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [5,3,2,1,7,4,6] => 110101
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [6,3,2,1,7,4,5] => 110011
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [5,3,2,1,7,6,4] => 110111
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [5,4,2,1,7,3,6] => 101101
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [6,4,2,1,7,3,5] => 101011
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [5,2,1,6,3,7,4] => 100111
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [5,4,2,1,7,6,3] => 101111
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [5,4,3,1,7,2,6] => 011101
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [6,4,3,1,7,2,5] => 011011
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [5,3,1,6,2,7,4] => 010111
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [5,4,1,6,2,7,3] => 001111
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [5,4,3,1,7,6,2] => 011111
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [7,5,4,3,2,1,6] => 111101
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [6,4,3,2,1,7,5] => 111011
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [6,5,3,2,1,7,4] => 110111
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [6,5,4,2,1,7,3] => 101111
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [6,5,4,3,1,7,2] => 011111
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,6,5,4,3,2,1] => 111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 0000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,7,1,2,3,4,5,6] => 0000011
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [8,6,1,2,3,4,5,7] => 0000101
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [7,1,2,3,4,5,8,6] => 0000011
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,7,6,1,2,3,4,5] => 0000111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [8,5,1,2,3,4,6,7] => 0001001
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [8,7,5,1,2,3,4,6] => 0001011
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [6,1,2,3,4,8,5,7] => 0000101
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [7,1,2,3,4,8,5,6] => 0000011
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [6,1,2,3,4,8,7,5] => 0000111
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [8,6,5,1,2,3,4,7] => 0001101
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [7,5,1,2,3,4,8,6] => 0001011
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [7,6,1,2,3,4,8,5] => 0000111
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,7,6,5,1,2,3,4] => 0001111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [8,4,1,2,3,5,6,7] => 0010001
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [8,7,4,1,2,3,5,6] => 0010011
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [7,4,1,2,3,5,8,6] => 0010011
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [8,7,6,4,1,2,3,5] => 0010111
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [5,1,2,3,8,4,6,7] => 0001001
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [5,1,2,3,8,7,4,6] => 0001011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [6,1,2,3,8,4,5,7] => 0000101
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [8,1,2,3,7,4,5,6] => 0000011
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [6,1,2,3,8,7,4,5] => 0000111
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [5,1,2,3,8,6,4,7] => 0001101
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [5,1,2,3,7,4,8,6] => 0001011
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [7,6,1,2,3,8,4,5] => 0000111
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [5,1,2,3,8,7,6,4] => 0001111
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [8,5,4,1,2,3,6,7] => 0011001
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [8,7,5,4,1,2,3,6] => 0011011
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [6,4,1,2,3,8,5,7] => 0010101
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [7,4,1,2,3,8,5,6] => 0010011
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [6,4,1,2,3,8,7,5] => 0010111
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [6,5,1,2,3,8,4,7] => 0001101
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [7,5,1,2,3,8,4,6] => 0001011
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [6,1,2,3,7,4,8,5] => 0000111
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [6,5,1,2,3,8,7,4] => 0001111
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [8,6,5,4,1,2,3,7] => 0011101
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [7,5,4,1,2,3,8,6] => 0011011
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [7,6,4,1,2,3,8,5] => 0010111
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,6,5,1,2,3,8,4] => 0001111
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,7,6,5,4,1,2,3] => 0011111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [8,3,1,2,4,5,6,7] => 0100001
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [7,3,1,2,4,5,8,6] => 0100011
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [8,7,6,3,1,2,4,5] => 0100111
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [8,5,3,1,2,4,6,7] => 0101001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [8,7,5,3,1,2,4,6] => 0101011
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [6,3,1,2,4,8,5,7] => 0100101
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [6,3,1,2,4,8,7,5] => 0100111
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [7,5,3,1,2,4,8,6] => 0101011
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => [7,6,3,1,2,4,8,5] => 0100111
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [8,7,6,5,3,1,2,4] => 0101111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [4,1,2,8,3,5,6,7] => 0010001
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [4,1,2,8,7,3,5,6] => 0010011
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [4,1,2,8,6,3,5,7] => 0010101
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [4,1,2,7,3,5,8,6] => 0010011
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [5,1,2,8,3,4,6,7] => 0001001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [8,1,2,6,3,4,5,7] => 0000101
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [7,1,2,8,3,4,5,6] => 0000011
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [8,7,1,2,6,3,4,5] => 0000111
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [5,1,2,8,6,3,4,7] => 0001101
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => [5,1,2,7,3,4,8,6] => 0001011
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [5,1,2,8,7,6,3,4] => 0001111
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [4,1,2,8,5,3,6,7] => 0011001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [4,1,2,8,7,5,3,6] => 0011011
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [4,1,2,6,3,8,5,7] => 0010101
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [4,1,2,6,3,8,7,5] => 0010111
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [6,5,1,2,8,3,4,7] => 0001101
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [7,5,1,2,8,3,4,6] => 0001011
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [6,1,2,8,3,4,7,5] => 0000111
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [6,5,1,2,8,7,3,4] => 0001111
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [4,1,2,7,6,3,8,5] => 0010111
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [7,6,5,1,2,8,3,4] => 0001111
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [4,1,2,8,7,6,5,3] => 0011111
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [8,6,4,3,1,2,5,7] => 0110101
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [8,7,6,4,3,1,2,5] => 0110111
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => [5,3,1,2,8,4,6,7] => 0101001
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [5,3,1,2,8,7,4,6] => 0101011
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [6,3,1,2,8,4,5,7] => 0100101
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [8,3,1,2,7,4,5,6] => 0100011
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => [6,3,1,2,8,7,4,5] => 0100111
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [5,3,1,2,8,6,4,7] => 0101101
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [5,3,1,2,7,4,8,6] => 0101011
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [7,6,3,1,2,8,4,5] => 0100111
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [5,4,1,2,8,3,6,7] => 0011001
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [5,4,1,2,8,7,3,6] => 0011011
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [6,4,1,2,8,3,5,7] => 0010101
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [8,4,1,2,7,3,5,6] => 0010011
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [6,4,1,2,8,7,3,5] => 0010111
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [5,1,2,6,3,8,4,7] => 0001101
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [6,1,2,8,3,7,4,5] => 0000111
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [5,1,2,6,3,8,7,4] => 0001111
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [5,4,1,2,7,3,8,6] => 0011011
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [5,4,1,2,8,7,6,3] => 0011111
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [8,7,5,4,3,1,2,6] => 0111011
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => [6,4,3,1,2,8,5,7] => 0110101
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [7,4,3,1,2,8,5,6] => 0110011
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [6,4,3,1,2,8,7,5] => 0110111
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [6,5,3,1,2,8,4,7] => 0101101
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [7,5,3,1,2,8,4,6] => 0101011
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [6,3,1,2,7,4,8,5] => 0100111
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [6,5,4,1,2,8,3,7] => 0011101
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [7,5,4,1,2,8,3,6] => 0011011
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [6,4,1,2,7,3,8,5] => 0010111
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [6,5,1,2,7,3,8,4] => 0001111
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [8,6,5,4,3,1,2,7] => 0111101
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [7,6,4,3,1,2,8,5] => 0110111
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [7,6,5,3,1,2,8,4] => 0101111
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [7,6,5,4,1,2,8,3] => 0011111
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,7,6,5,4,3,1,2] => 0111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => 1000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [8,7,2,1,3,4,5,6] => 1000011
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [7,2,1,3,4,5,8,6] => 1000011
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [8,7,6,2,1,3,4,5] => 1000111
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [8,5,2,1,3,4,6,7] => 1001001
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [8,7,5,2,1,3,4,6] => 1001011
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [7,2,1,3,4,8,5,6] => 1000011
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => [6,2,1,3,4,8,7,5] => 1000111
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [8,6,5,2,1,3,4,7] => 1001101
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [8,7,6,5,2,1,3,4] => 1001111
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [8,4,2,1,3,5,6,7] => 1010001
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [8,7,4,2,1,3,5,6] => 1010011
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [8,6,4,2,1,3,5,7] => 1010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [8,7,6,4,2,1,3,5] => 1010111
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [5,2,1,3,8,4,6,7] => 1001001
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [5,2,1,3,8,7,4,6] => 1001011
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [6,2,1,3,8,4,5,7] => 1000101
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => [5,2,1,3,8,7,6,4] => 1001111
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [8,5,4,2,1,3,6,7] => 1011001
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [6,4,2,1,3,8,5,7] => 1010101
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [7,4,2,1,3,8,5,6] => 1010011
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [6,4,2,1,3,8,7,5] => 1010111
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [6,5,2,1,3,8,4,7] => 1001101
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [7,5,2,1,3,8,4,6] => 1001011
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [6,2,1,3,7,4,8,5] => 1000111
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => [6,5,2,1,3,8,7,4] => 1001111
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [8,6,5,4,2,1,3,7] => 1011101
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [7,6,4,2,1,3,8,5] => 1010111
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [8,7,6,5,4,2,1,3] => 1011111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [3,1,8,2,4,5,6,7] => 0100001
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [3,1,8,7,2,4,5,6] => 0100011
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => [3,1,8,6,2,4,5,7] => 0100101
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [3,1,7,2,4,5,8,6] => 0100011
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5] => [3,1,8,7,6,2,4,5] => 0100111
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [3,1,8,5,2,4,6,7] => 0101001
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [3,1,8,7,5,2,4,6] => 0101011
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [3,1,6,2,4,8,5,7] => 0100101
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [3,1,6,2,4,8,7,5] => 0100111
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [3,1,7,5,2,4,8,6] => 0101011
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [3,1,7,6,2,4,8,5] => 0100111
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [3,1,8,7,6,5,2,4] => 0101111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [4,1,8,2,3,5,6,7] => 0010001
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [4,1,8,7,2,3,5,6] => 0010011
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [4,1,8,6,2,3,5,7] => 0010101
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [4,1,7,2,3,5,8,6] => 0010011
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => [4,1,8,7,6,2,3,5] => 0010111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [8,1,5,2,3,4,6,7] => 0001001
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [8,7,1,5,2,3,4,6] => 0001011
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [6,1,8,2,3,4,5,7] => 0000101
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [7,1,8,2,3,4,5,6] => 0000011
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [6,1,8,7,2,3,4,5] => 0000111
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [8,6,1,5,2,3,4,7] => 0001101
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [7,1,5,2,3,4,8,6] => 0001011
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [7,6,1,8,2,3,4,5] => 0000111
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [8,7,6,1,5,2,3,4] => 0001111
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [4,1,8,5,2,3,6,7] => 0011001
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [4,1,8,7,5,2,3,6] => 0011011
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7] => [4,1,6,2,3,8,5,7] => 0010101
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [4,1,7,2,3,8,5,6] => 0010011
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [4,1,6,2,3,8,7,5] => 0010111
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [6,1,8,5,2,3,4,7] => 0001101
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [7,1,8,5,2,3,4,6] => 0001011
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [6,1,7,2,3,4,8,5] => 0000111
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [6,1,8,7,5,2,3,4] => 0001111
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [4,1,7,5,2,3,8,6] => 0011011
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [4,1,7,6,2,3,8,5] => 0010111
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [7,6,1,8,5,2,3,4] => 0001111
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [4,1,8,7,6,5,2,3] => 0011111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [3,1,8,4,2,5,6,7] => 0110001
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [3,1,7,4,2,5,8,6] => 0110011
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => [3,1,8,7,6,4,2,5] => 0110111
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [3,1,5,2,8,4,6,7] => 0101001
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [3,1,5,2,8,7,4,6] => 0101011
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [3,1,6,2,8,4,5,7] => 0100101
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [3,1,8,2,7,4,5,6] => 0100011
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [3,1,6,2,8,7,4,5] => 0100111
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [3,1,5,2,7,4,8,6] => 0101011
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [3,1,5,2,8,7,6,4] => 0101111
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [5,4,1,8,2,3,6,7] => 0011001
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [5,4,1,8,7,2,3,6] => 0011011
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [6,4,1,8,2,3,5,7] => 0010101
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [8,4,1,7,2,3,5,6] => 0010011
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [5,1,7,2,3,8,4,6] => 0001011
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [6,1,7,2,3,8,4,5] => 0000111
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [5,1,8,7,2,3,6,4] => 0001111
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [7,6,4,1,8,2,3,5] => 0010111
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [5,1,7,2,3,8,6,4] => 0001111
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [5,4,1,8,7,6,2,3] => 0011111
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [3,1,8,5,4,2,6,7] => 0111001
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => [3,1,8,7,5,4,2,6] => 0111011
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [3,1,6,4,2,8,5,7] => 0110101
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [3,1,6,5,2,8,4,7] => 0101101
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [3,1,7,5,2,8,4,6] => 0101011
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [3,1,6,2,7,4,8,5] => 0100111
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [3,1,6,5,2,8,7,4] => 0101111
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [7,5,4,1,8,2,3,6] => 0011011
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [6,4,1,7,2,3,8,5] => 0010111
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [6,5,4,1,8,7,2,3] => 0011111
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [3,1,8,6,5,4,2,7] => 0111101
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [3,1,7,5,4,2,8,6] => 0111011
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [3,1,7,6,4,2,8,5] => 0110111
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [3,1,7,6,5,2,8,4] => 0101111
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [7,6,5,4,1,8,2,3] => 0011111
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [3,1,8,7,6,5,4,2] => 0111111
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [8,3,2,1,4,5,6,7] => 1100001
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [8,7,3,2,1,4,5,6] => 1100011
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [8,6,3,2,1,4,5,7] => 1100101
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => [7,3,2,1,4,5,8,6] => 1100011
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [8,7,6,3,2,1,4,5] => 1100111
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [8,5,3,2,1,4,6,7] => 1101001
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [8,7,5,3,2,1,4,6] => 1101011
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => [6,3,2,1,4,8,5,7] => 1100101
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [6,3,2,1,4,8,7,5] => 1100111
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [8,6,5,3,2,1,4,7] => 1101101
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [8,7,6,5,3,2,1,4] => 1101111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [4,2,1,8,3,5,6,7] => 1010001
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [4,2,1,8,7,3,5,6] => 1010011
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [4,2,1,8,6,3,5,7] => 1010101
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [4,2,1,7,3,5,8,6] => 1010011
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [4,2,1,8,7,6,3,5] => 1010111
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [5,2,1,8,3,4,6,7] => 1001001
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [5,2,1,8,7,3,4,6] => 1001011
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [8,2,1,6,3,4,5,7] => 1000101
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [7,2,1,8,3,4,5,6] => 1000011
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [8,7,2,1,6,3,4,5] => 1000111
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [5,2,1,7,3,4,8,6] => 1001011
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [7,2,1,8,6,3,4,5] => 1000111
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [5,2,1,8,7,6,3,4] => 1001111
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [4,2,1,8,5,3,6,7] => 1011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [4,2,1,6,3,8,5,7] => 1010101
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [4,2,1,7,3,8,5,6] => 1010011
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [4,2,1,6,3,8,7,5] => 1010111
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [6,5,2,1,8,3,4,7] => 1001101
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [7,5,2,1,8,3,4,6] => 1001011
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [6,2,1,8,3,4,7,5] => 1000111
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [6,5,2,1,8,7,3,4] => 1001111
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [4,2,1,8,6,5,3,7] => 1011101
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [4,2,1,8,7,6,5,3] => 1011111
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [4,3,1,8,2,5,6,7] => 0110001
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [4,3,1,8,7,2,5,6] => 0110011
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [4,3,1,8,6,2,5,7] => 0110101
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [4,3,1,7,2,5,8,6] => 0110011
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [5,3,1,8,2,4,6,7] => 0101001
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [5,3,1,8,7,2,4,6] => 0101011
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [8,3,1,6,2,4,5,7] => 0100101
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [7,3,1,8,2,4,5,6] => 0100011
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [8,7,3,1,6,2,4,5] => 0100111
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [5,3,1,8,6,2,4,7] => 0101101
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [7,3,1,8,6,2,4,5] => 0100111
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [4,1,5,2,8,3,6,7] => 0011001
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [4,1,5,2,8,7,3,6] => 0011011
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [4,1,8,2,6,3,5,7] => 0010101
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [4,1,7,2,8,3,5,6] => 0010011
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [4,1,8,7,2,6,3,5] => 0010111
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [5,1,8,2,6,3,4,7] => 0001101
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [5,1,7,2,8,3,4,6] => 0001011
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,1,7,2,6,3,4,5] => 0000111
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [5,1,8,7,2,6,3,4] => 0001111
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [4,1,5,2,7,3,8,6] => 0011011
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [5,1,7,2,8,6,3,4] => 0001111
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [4,1,5,2,8,7,6,3] => 0011111
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [4,3,1,8,5,2,6,7] => 0111001
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [4,3,1,8,7,5,2,6] => 0111011
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [4,3,1,6,2,8,5,7] => 0110101
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [4,3,1,7,2,8,5,6] => 0110011
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => [6,5,3,1,8,2,4,7] => 0101101
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [7,5,3,1,8,2,4,6] => 0101011
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [6,3,1,8,2,4,7,5] => 0100111
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [4,1,6,2,8,3,7,5] => 0010111
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [6,5,1,8,2,7,3,4] => 0001111
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [4,3,1,7,5,2,8,6] => 0111011
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [4,3,1,7,6,2,8,5] => 0110111
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [7,6,5,3,1,8,2,4] => 0101111
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [4,1,7,6,5,2,8,3] => 0011111
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [4,3,1,8,7,6,5,2] => 0111111
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [8,4,3,2,1,5,6,7] => 1110001
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [8,7,4,3,2,1,5,6] => 1110011
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [8,6,4,3,2,1,5,7] => 1110101
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [7,4,3,2,1,5,8,6] => 1110011
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [8,7,6,4,3,2,1,5] => 1110111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [5,3,2,1,8,4,6,7] => 1101001
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [6,3,2,1,8,4,5,7] => 1100101
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [8,3,2,1,7,4,5,6] => 1100011
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [6,3,2,1,8,7,4,5] => 1100111
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [5,3,2,1,8,6,4,7] => 1101101
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [5,3,2,1,7,4,8,6] => 1101011
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [7,6,3,2,1,8,4,5] => 1100111
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [5,3,2,1,8,7,6,4] => 1101111
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [5,4,2,1,8,3,6,7] => 1011001
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [5,4,2,1,8,7,3,6] => 1011011
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [6,4,2,1,8,3,5,7] => 1010101
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [8,4,2,1,7,3,5,6] => 1010011
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [5,2,1,6,3,8,4,7] => 1001101
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [6,2,1,8,3,7,4,5] => 1000111
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [5,2,1,6,3,8,7,4] => 1001111
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [7,6,4,2,1,8,3,5] => 1010111
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [5,2,1,7,6,3,8,4] => 1001111
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [5,4,2,1,8,7,6,3] => 1011111
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [5,4,3,1,8,7,2,6] => 0111011
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [6,4,3,1,8,2,5,7] => 0110101
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [5,3,1,6,2,8,4,7] => 0101101
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [5,3,1,8,2,7,4,6] => 0101011
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [6,3,1,8,2,7,4,5] => 0100111
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [5,4,1,6,2,8,3,7] => 0011101
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [5,1,6,2,8,3,7,4] => 0001111
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [5,4,3,1,7,2,8,6] => 0111011
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [7,6,4,3,1,8,2,5] => 0110111
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [5,4,1,7,6,2,8,3] => 0011111
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [5,4,3,1,8,7,6,2] => 0111111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [8,5,4,3,2,1,6,7] => 1111001
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [8,7,5,4,3,2,1,6] => 1111011
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [6,4,3,2,1,8,5,7] => 1110101
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [7,4,3,2,1,8,5,6] => 1110011
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [6,4,3,2,1,8,7,5] => 1110111
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [7,5,3,2,1,8,4,6] => 1101011
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [6,3,2,1,7,4,8,5] => 1100111
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [6,5,3,2,1,8,7,4] => 1101111
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [7,5,4,2,1,8,3,6] => 1011011
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [6,4,2,1,7,3,8,5] => 1010111
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [6,5,2,1,7,3,8,4] => 1001111
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [6,5,4,3,1,8,2,7] => 0111101
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [7,5,4,3,1,8,2,6] => 0111011
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [6,4,3,1,7,2,8,5] => 0110111
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [6,5,3,1,7,2,8,4] => 0101111
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [6,5,4,1,7,2,8,3] => 0011111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [6,5,4,3,1,8,7,2] => 0111111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [8,6,5,4,3,2,1,7] => 1111101
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [7,5,4,3,2,1,8,6] => 1111011
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [7,6,4,3,2,1,8,5] => 1110111
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [7,6,5,3,2,1,8,4] => 1101111
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [7,6,5,4,2,1,8,3] => 1011111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [7,6,5,4,3,1,8,2] => 0111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,7,6,5,4,3,2,1] => 1111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 00000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,8,1,2,3,4,5,6,7] => 00000011
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [9,7,1,2,3,4,5,6,8] => 00000101
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [8,1,2,3,4,5,6,9,7] => 00000011
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,8,7,1,2,3,4,5,6] => 00000111
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [9,6,1,2,3,4,5,7,8] => 00001001
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7] => [9,8,6,1,2,3,4,5,7] => 00001011
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8] => [7,1,2,3,4,5,9,6,8] => 00000101
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => [8,1,2,3,4,5,9,6,7] => 00000011
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => [8,6,1,2,3,4,5,9,7] => 00001011
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => [8,7,1,2,3,4,5,9,6] => 00000111
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,8,7,6,1,2,3,4,5] => 00001111
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,1,2,3,6,4,5,7,8] => [6,1,2,3,4,9,5,7,8] => 00001001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [9,1,2,3,4,8,5,6,7] => 00000011
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [9,8,7,6,5,1,2,3,4] => 00011111
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7] => [9,8,4,1,2,3,5,6,7] => 00100011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,1,2,5,3,4,6,7,8] => [5,1,2,3,9,4,6,7,8] => 00010001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => [8,1,2,3,9,4,5,6,7] => 00000011
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => [9,8,1,2,3,7,4,5,6] => 00000111
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => [9,5,4,1,2,3,6,7,8] => 00110001
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [9,8,7,6,5,4,1,2,3] => 00111111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [9,3,1,2,4,5,6,7,8] => 01000001
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,9,2,4,5,8,6,7] => [8,3,1,2,4,5,6,9,7] => 01000011
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,9,6,8] => [9,7,5,3,1,2,4,6,8] => 01010101
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [9,1,4,2,3,5,8,6,7] => [4,1,2,8,3,5,6,9,7] => 00100011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => [8,1,2,9,3,4,5,6,7] => 00000011
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [9,1,4,5,2,3,6,7,8] => [5,4,1,2,9,3,6,7,8] => 00110001
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7] => [8,4,1,2,9,3,5,6,7] => 00100011
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8] => [9,7,6,5,4,3,1,2,8] => 01111101
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,8,7,6,5,4,3,1,2] => 01111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => 10000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7] => [8,2,1,3,4,5,6,9,7] => 10000011
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => [9,8,7,6,5,2,1,3,4] => 10011111
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [9,8,7,6,5,4,2,1,3] => 10111111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [3,1,9,2,4,5,6,7,8] => 01000001
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7] => [3,1,9,8,2,4,5,6,7] => 01000011
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [9,3,1,2,4,5,8,6,7] => [3,1,8,2,4,5,6,9,7] => 01000011
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [7,1,9,2,3,4,5,6,8] => 00000101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [9,1,8,2,3,4,5,6,7] => 00000011
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => [8,7,1,9,2,3,4,5,6] => 00000111
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,1,2,3,7,4,5,6] => [7,1,8,2,3,4,5,9,6] => 00000111
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,2] => [3,1,9,8,7,6,5,4,2] => 01111111
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [9,8,7,6,5,3,2,1,4] => 11011111
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,3,4,1,2,5,6,7,8] => [4,3,1,9,2,5,6,7,8] => 01100001
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => [9,8,7,6,4,3,2,1,5] => 11101111
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [7,3,4,5,1,2,8,9,6] => [5,4,3,1,9,8,7,2,6] => 01110111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [9,5,4,3,2,1,6,7,8] => 11110001
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,8,1,6,9,7] => [9,8,5,4,3,2,1,6,7] => 11110011
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [9,8,7,5,4,3,2,1,6] => 11110111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [9,6,5,4,3,2,1,7,8] => 11111001
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [9,8,6,5,4,3,2,1,7] => 11111011
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [9,7,6,5,4,3,2,1,8] => 11111101
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,9,8,1,7] => [8,6,5,4,3,2,1,9,7] => 11111011
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,5,9,7,8,1,6] => [8,7,5,4,3,2,1,9,6] => 11110111
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,9,6,7,8,1,5] => [8,7,6,4,3,2,1,9,5] => 11101111
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,9,5,6,7,8,1,4] => [8,7,6,5,3,2,1,9,4] => 11011111
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => [8,7,6,5,4,2,1,9,3] => 10111111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,2] => [8,7,6,5,4,3,1,9,2] => 01111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,8,7,6,5,4,3,2,1] => 11111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => [10,8,7,6,5,4,3,2,1,9] => 111111101
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,9,8,7,6,5,4,3,1,2] => 011111111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,11,1,10] => [11,9,8,7,6,5,4,3,2,1,10] => 1111111101
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,10,9,8,7,6,5,4,3,1,2] => 0111111111
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => [12,10,9,8,7,6,5,4,3,2,1,11] => 11111111101
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => [10,9,7,6,5,4,3,2,1,8] => 111111011
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [10,9,8,7,6,5,4,2,1,3] => 101111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => [10,7,6,5,4,3,2,1,8,9] => 111111001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => [10,8,7,6,5,4,3,1,2,9] => 011111101
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => [10,9,8,7,6,5,4,1,2,3] => 001111111
[] => [1] => [1] =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [9,1,10,2,3,4,5,6,7,8] => 000000011
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10,3,1,5,2,7,4,9,6,8] => [3,1,5,2,7,4,9,6,10,8] => 010101011
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,2] => [3,1,10,9,8,7,6,5,4,2] => 011111111
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => [10,3,1,9,2,4,5,6,7,8] => 010000011
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [8,1,9,2,10,3,4,5,6,7] => 000000111
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [10,5,4,1,2,9,8,3,6,7] => [4,1,5,2,8,3,9,6,10,7] => 001100111
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,2] => [6,5,4,3,1,10,9,8,7,2] => 011111111
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => [8,7,6,5,4,3,1,10,9,2] => 011111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,10,9,1,8] => [9,7,6,5,4,3,2,1,10,8] => 111111011
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,10,8,9,1,7] => [9,8,6,5,4,3,2,1,10,7] => 111110111
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,1,6] => [9,8,7,5,4,3,2,1,10,6] => 111101111
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,10,6,7,8,9,1,5] => [9,8,7,6,4,3,2,1,10,5] => 111011111
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,10,5,6,7,8,9,1,4] => [9,8,7,6,5,3,2,1,10,4] => 110111111
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => [9,8,7,6,5,4,2,1,10,3] => 101111111
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,2] => [9,8,7,6,5,4,3,1,10,2] => 011111111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => 000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,9,1,2,3,4,5,6,7,8] => 000000011
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => [9,1,2,3,4,5,6,7,10,8] => 000000011
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => [9,1,2,3,4,5,6,10,7,8] => 000000011
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [10,1,2,3,4,5,9,6,7,8] => 000000011
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => [9,1,2,3,4,10,5,6,7,8] => 000000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => [9,1,2,3,10,4,5,6,7,8] => 000000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [10,1,2,9,3,4,5,6,7,8] => 000000011
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,2,3,4,5,6,7,8,9,10] => 0000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => [11,10,1,2,3,4,5,6,7,8,9] => 0000000011
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,9,8,1,2,3,4,5,6,7] => 000000111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,1,2,3,4,5,6,7,10,8,9] => [10,1,2,3,4,5,6,7,8,11,9] => 0000000011
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => [9,7,1,2,3,4,5,6,10,8] => 000001011
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [11,1,2,3,4,5,6,10,7,8,9] => [10,1,2,3,4,5,6,7,11,8,9] => 0000000011
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [10,1,2,3,4,5,11,6,7,8,9] => [11,1,2,3,4,5,6,10,7,8,9] => 0000000011
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,4,10,5,6,7,8,9] => [10,1,2,3,4,5,11,6,7,8,9] => 0000000011
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => [11,1,2,3,10,4,5,6,7,8,9] => 0000000011
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,10,2,3,4,5,6,7,8,9] => [10,1,2,11,3,4,5,6,7,8,9] => 0000000011
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,1,2,3,4,5,6,7,8,9] => [10,1,11,2,3,4,5,6,7,8,9] => 0000000011
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [12,1,2,3,4,5,6,7,8,9,10,11] => 00000000001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => [12,11,1,2,3,4,5,6,7,8,9,10] => 00000000011
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [12,1,2,3,4,5,6,7,8,11,9,10] => [11,1,2,3,4,5,6,7,8,9,12,10] => 00000000011
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [10,9,8,7,1,2,3,4,5,6] => 000001111
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [10,9,8,7,6,1,2,3,4,5] => 000011111
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [10,9,8,7,6,5,1,2,3,4] => 000111111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => [10,4,1,2,3,5,6,7,8,9] => 001000001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => [10,9,7,5,3,1,2,4,6,8] => 010101011
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => 100000001
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [10,8,6,4,2,1,3,5,7,9] => 101010101
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => [10,8,7,6,5,4,2,1,3,9] => 101111101
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => [10,9,8,7,6,5,3,2,1,4] => 110111111
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => [10,9,8,7,6,4,3,2,1,5] => 111011111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => [10,9,8,7,5,4,3,2,1,6] => 111101111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => [10,9,8,6,5,4,3,2,1,7] => 111110111
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => [11,7,1,2,3,4,5,6,8,9,10] => 0000010001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,2,1,3,4,5,6,7,8,9,10] => 1000000001
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,10,9,8,7,6,5,4,3,2,1] => 1111111111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => [10,1,5,2,3,4,6,7,8,9] => 000100001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => [12,2,1,3,4,5,6,7,8,9,10,11] => 10000000001
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,3,1,2,4,5,6,9,7,8] => [3,1,9,2,4,5,6,7,10,8] => 010000011
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,10,2,4,5,6,9,7,8] => [9,3,1,2,4,5,6,7,10,8] => 010000011
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,3,1,2,4,5,6,7,10,8] => [3,1,10,9,2,4,5,6,7,8] => 010000011
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,3,4,1,2,5,6,7,8,9] => [4,3,1,10,2,5,6,7,8,9] => 011000001
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,2] => [10,9,8,7,6,5,4,3,1,11,2] => 0111111111
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [12,3,4,5,6,7,8,9,10,11,1,2] => [11,10,9,8,7,6,5,4,3,1,12,2] => 01111111111
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,2,5,3,4,6,7,8,9] => [5,1,2,3,10,4,6,7,8,9] => 000100001
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,7,1,2,3,4,5,6,10,8] => [7,1,10,9,2,3,4,5,6,8] => 000001011
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,7,11,9,10,1,8] => [10,9,7,6,5,4,3,2,1,11,8] => 1111110111
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [2,3,4,11,6,7,8,9,10,1,5] => [10,9,8,7,6,4,3,2,1,11,5] => 1110111111
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,12,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => 11111111111
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.