Identifier
Values
[2] => [1,0,1,0] => [2,1] => 0 => 1
[1,1] => [1,1,0,0] => [1,2] => 1 => 1
[3] => [1,0,1,0,1,0] => [3,2,1] => 00 => 2
[2,1] => [1,0,1,1,0,0] => [2,3,1] => 00 => 2
[1,1,1] => [1,1,0,1,0,0] => [2,1,3] => 01 => 2
[4] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 000 => 3
[3,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 000 => 3
[2,2] => [1,1,1,0,0,0] => [1,2,3] => 11 => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 000 => 3
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => 001 => 3
[5] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 0000 => 4
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 0000 => 4
[3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 000 => 3
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 0000 => 4
[2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => 001 => 3
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 0000 => 4
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 0001 => 4
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 00000 => 5
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 00000 => 5
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 0000 => 4
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 00000 => 5
[3,3] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => 011 => 3
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 0000 => 4
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 00000 => 5
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 111 => 3
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 0001 => 4
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 00000 => 5
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => 00001 => 5
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 000000 => 6
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => 000000 => 6
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 00000 => 5
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => 000000 => 6
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 0000 => 4
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 00000 => 5
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => 000000 => 6
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 0001 => 4
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0000 => 4
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 00000 => 5
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => 000000 => 6
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 0001 => 4
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => 00001 => 5
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => 000000 => 6
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => 000001 => 6
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 0000000 => 7
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => 0000000 => 7
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => 000000 => 6
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => 0000000 => 7
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 00000 => 5
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => 000000 => 6
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => 0000000 => 7
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 0011 => 4
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 00000 => 5
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 00000 => 5
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => 000000 => 6
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => 0000000 => 7
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 0011 => 4
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => 00001 => 5
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 00000 => 5
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => 000000 => 6
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => 0000000 => 7
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 0111 => 4
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => 00001 => 5
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => 000001 => 6
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => 0000000 => 7
[1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => 0000001 => 7
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => 00000000 => 8
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => 00000000 => 8
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => 0000000 => 7
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => 00000000 => 8
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => 000000 => 6
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => 0000000 => 7
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => 00000000 => 8
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 00000 => 5
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => 000000 => 6
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => 000000 => 6
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => 0000000 => 7
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => 00000000 => 8
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => 00001 => 5
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 00000 => 5
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => 000000 => 6
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => 000000 => 6
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => 0000000 => 7
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => 00000000 => 8
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 1111 => 4
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => 00001 => 5
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => 000001 => 6
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 00000 => 5
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => 000000 => 6
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => 0000000 => 7
[3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => 00000000 => 8
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => 00001 => 5
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => 000001 => 6
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => 0000001 => 7
[2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => 00000000 => 8
[1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => 00000001 => 8
[10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => 000000000 => 9
[9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => 000000000 => 9
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => 00000000 => 8
[8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => 000000000 => 9
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => 0000000 => 7
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => 00000000 => 8
>>> Load all 314 entries. <<<
[7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => 000000000 => 9
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => 000000 => 6
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => 0000000 => 7
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => 0000000 => 7
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => 00000000 => 8
[6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => 000000000 => 9
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => 00011 => 5
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => 000000 => 6
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => 000000 => 6
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => 0000000 => 7
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => 0000000 => 7
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => 00000000 => 8
[5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => 000000000 => 9
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => 00011 => 5
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => 000001 => 6
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 00000 => 5
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => 000000 => 6
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => 0000000 => 7
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => 000000 => 6
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => 0000000 => 7
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => 00000000 => 8
[4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => 000000000 => 9
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => 00001 => 5
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => 00011 => 5
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => 000001 => 6
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => 0000001 => 7
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => 000000 => 6
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => 0000000 => 7
[3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => 00000000 => 8
[3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => 000000000 => 9
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => 00111 => 5
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => 000001 => 6
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => 0000001 => 7
[2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => 00000001 => 8
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => 000000000 => 9
[1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => 000000001 => 9
[11] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => 0000000000 => 10
[10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => 0000000000 => 10
[9,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => 000000000 => 9
[9,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => 0000000000 => 10
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => 0000000 => 7
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => 00000000 => 8
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => 000000 => 6
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => 0000000 => 7
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => 0000000 => 7
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => 000001 => 6
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => 000000 => 6
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => 000000 => 6
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => 0000000 => 7
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => 00011 => 5
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => 000001 => 6
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => 0000001 => 7
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 000000 => 6
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 000000 => 6
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => 00111 => 5
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => 000001 => 6
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => 000001 => 6
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => 0000001 => 7
[3,3,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => 00000001 => 8
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 000000 => 6
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => 000001 => 6
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => 0000001 => 7
[2,2,2,1,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => 00000001 => 8
[2,2,1,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => 000000001 => 9
[2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => 0000000000 => 10
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => 0000000001 => 10
[8,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => 000000000 => 9
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => 0000000 => 7
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => 000011 => 6
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => 0000000 => 7
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,6,9,2,1] => 00000000 => 8
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => 0000000 => 7
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => 000011 => 6
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => 0000001 => 7
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 000000 => 6
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => 01111 => 5
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => 000001 => 6
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => 000011 => 6
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => 0000001 => 7
[4,4,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => 00000001 => 8
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 000000 => 6
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => 0000000 => 7
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => 0000000 => 7
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => 0000000 => 7
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 11111 => 5
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => 000001 => 6
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => 0000001 => 7
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => 000011 => 6
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => 0000001 => 7
[3,3,2,1,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => 00000001 => 8
[3,3,1,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => 000000001 => 9
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => 0000000 => 7
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => 000111 => 6
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => 0000001 => 7
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => 0000000 => 7
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => 00000000 => 8
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => 0000001 => 7
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => 000011 => 6
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => 0000001 => 7
[5,5,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => 00000001 => 8
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 000000 => 6
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => 0000000 => 7
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => 0000000 => 7
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => 000001 => 6
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => 000011 => 6
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => 0000001 => 7
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => 0000001 => 7
[4,4,2,1,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => 00000001 => 8
[4,4,1,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => 000000001 => 9
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 000000 => 6
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => 0000000 => 7
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => 000001 => 6
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => 000111 => 6
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => 0000000 => 7
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => 0000001 => 7
[8,3,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => 000000000 => 9
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => 0000011 => 7
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => 00000000 => 8
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => 0000011 => 7
[6,6,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => 00000001 => 8
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => 0000000 => 7
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => 000011 => 6
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => 0000001 => 7
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => 0000011 => 7
[5,5,2,1,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => 00000001 => 8
[5,5,1,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => 000000001 => 9
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => 0000000 => 7
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => 000111 => 6
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => 000011 => 6
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => 0000011 => 7
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => 0000000 => 7
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => 0000000 => 7
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => 000111 => 6
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => 0000001 => 7
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => 0000001 => 7
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => 0000011 => 7
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => 0000111 => 7
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => 00000000 => 8
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => 00000001 => 8
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => 0000011 => 7
[6,6,2,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => 00000001 => 8
[6,6,1,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => 000000001 => 9
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => 0000000 => 7
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => 00000000 => 8
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => 001111 => 6
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => 0000000 => 7
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => 0000000 => 7
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => 001111 => 6
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => 0000001 => 7
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => 0000000 => 7
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 011111 => 6
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => 0000001 => 7
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => 0000111 => 7
[3,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => 00000000 => 8
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => 00000011 => 8
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => 00000011 => 8
[7,7,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => 000000001 => 9
[7,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => 000000000 => 9
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => 0000000 => 7
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => 0000001 => 7
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => 0000011 => 7
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => 0000011 => 7
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => 0000000 => 7
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 111111 => 6
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => 0000001 => 7
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => 0000111 => 7
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => 0000011 => 7
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => 0000000 => 7
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => 00000000 => 8
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => 0000001 => 7
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => 0000111 => 7
[3,3,2,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => 00000011 => 8
[2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => 00000111 => 8
[9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => 000000000 => 9
[8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => 000000001 => 9
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => 0000011 => 7
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => 0000111 => 7
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => 0000011 => 7
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0000000 => 7
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => 0000001 => 7
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => 0000111 => 7
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => 0000011 => 7
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => 0000111 => 7
[3,3,3,2,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => 00000111 => 8
[3,2,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => 000000000 => 9
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => 00000001 => 8
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => 00000000 => 8
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => 0000111 => 7
[2,2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => 000000111 => 9
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => 0011111 => 7
[3,3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => 000011111 => 9
[3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => 00011111 => 8
[4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => 00000000 => 8
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 1111111 => 7
[4,4,4,3,3,3] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => 00001111 => 8
[4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => 01111111 => 8
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => 0111111 => 7
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => 00111111 => 8
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => 0001111 => 7
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => 00000000 => 8
[10,10] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => 0000000011 => 10
[6,6,6,6,6] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => 011111111 => 9
[5,5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 111111111 => 9
[7,7,7,7] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => 000111111 => 9
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => 00001111 => 8
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 11111111 => 8
[9,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => 000000011 => 9
[8,8,8] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => 000001111 => 9
[4,4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => 001111111 => 9
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => 00000000 => 8
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 00000000 => 8
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => 00000001 => 8
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => 00000001 => 8
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Description
The number of factors in the Catalan decomposition of a binary word.
Every binary word can be written in a unique way as $(\mathcal D 0)^\ell \mathcal D (1 \mathcal D)^m$, where $\mathcal D$ is the set of Dyck words. This is the Catalan factorisation, see [1, sec.9.1.2].
This statistic records the number of factors in the Catalan factorisation, that is, $\ell + m$ if the middle Dyck word is empty and $\ell + 1 + m$ otherwise.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].