Identifier
Values
[1,0] => [[1],[]] => [1] => 1
[1,0,1,0] => [[1,1],[]] => [1,1] => 2
[1,1,0,0] => [[2],[]] => [2] => 4
[1,0,1,0,1,0] => [[1,1,1],[]] => [1,1,1] => 3
[1,0,1,1,0,0] => [[2,1],[]] => [2,1] => 5
[1,1,0,0,1,0] => [[2,2],[1]] => [2,1] => 5
[1,1,0,1,0,0] => [[3],[]] => [3] => 9
[1,1,1,0,0,0] => [[2,2],[]] => [2,2] => 8
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => [1,1,1,1] => 4
[1,0,1,0,1,1,0,0] => [[2,1,1],[]] => [2,1,1] => 6
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [2,2] => 8
[1,0,1,1,0,1,0,0] => [[3,1],[]] => [3,1] => 10
[1,0,1,1,1,0,0,0] => [[2,2,1],[]] => [2,2,1] => 9
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [2,1,1] => 6
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => [3,1] => 10
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => [3,1] => 10
[1,1,0,1,0,1,0,0] => [[4],[]] => [4] => 16
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => [3,2] => 13
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [2,2,1] => 9
[1,1,1,0,0,1,0,0] => [[3,2],[]] => [3,2] => 13
[1,1,1,0,1,0,0,0] => [[2,2,2],[]] => [2,2,2] => 12
[1,1,1,1,0,0,0,0] => [[3,3],[]] => [3,3] => 18
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => [1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => [2,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [2,2,1] => 9
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => [3,1,1] => 11
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => [2,2,1,1] => 10
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [2,2,1] => 9
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [3,2] => 13
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [3,2] => 13
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => [4,1] => 17
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [3,3] => 18
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [2,2,2] => 12
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => [3,2,1] => 14
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => [2,2,2,1] => 13
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => [3,3,1] => 19
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [2,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [3,1,1] => 11
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [3,2] => 13
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [4,1] => 17
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [3,2,1] => 14
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [3,1,1] => 11
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [4,1] => 17
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [4,1] => 17
[1,1,0,1,0,1,0,1,0,0] => [[5],[]] => [5] => 25
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [4,2] => 20
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [3,2,1] => 14
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [4,2] => 20
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [3,2,2] => 17
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [4,3] => 25
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [2,2,1,1] => 10
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [3,2,1] => 14
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [3,3] => 18
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => [4,2] => 20
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [3,3,1] => 19
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [2,2,2,1] => 13
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => [3,2,2] => 17
[1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]] => [2,2,2,2] => 16
[1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]] => [3,3,2] => 22
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [3,3,1] => 19
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => [4,3] => 25
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => [3,3,2] => 22
[1,1,1,1,0,1,0,0,0,0] => [[4,4],[]] => [4,4] => 32
[1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]] => [3,3,3] => 27
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => [2,1,1,1,1] => 8
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [2,2,1,1] => 10
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => [3,1,1,1] => 12
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => [2,2,1,1,1] => 11
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [2,2,2] => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [3,2,1] => 14
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [3,2,1] => 14
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => [4,1,1] => 18
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [3,3,1] => 19
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [2,2,2,1] => 13
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => [3,2,1,1] => 15
[1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]] => [2,2,2,1,1] => 14
[1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]] => [3,3,1,1] => 20
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [2,2,1,1] => 10
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [3,2,1] => 14
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [3,3] => 18
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [4,2] => 20
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [3,3,1] => 19
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [3,2,1] => 14
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [4,2] => 20
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [4,2] => 20
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => [5,1] => 26
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [4,3] => 25
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [3,3,1] => 19
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [4,3] => 25
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [3,3,2] => 22
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => [4,4] => 32
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [2,2,2,1] => 13
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [3,2,2] => 17
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [3,3,1] => 19
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => [4,2,1] => 21
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => [3,3,2] => 22
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => [2,2,2,2] => 16
[1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]] => [3,2,2,1] => 18
[1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]] => [2,2,2,2,1] => 17
[1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]] => [3,3,2,1] => 23
>>> Load all 453 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => [3,3,2] => 22
[1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]] => [4,3,1] => 26
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => [3,3,3] => 27
[1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]] => [4,4,1] => 33
[1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1],[]] => [3,3,3,1] => 28
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [2,1,1,1,1] => 8
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [3,1,1,1] => 12
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [3,2,1] => 14
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [4,1,1] => 18
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [3,2,1,1] => 15
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [3,2,1] => 14
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [4,2] => 20
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [4,2] => 20
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [5,1] => 26
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [4,3] => 25
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [3,2,2] => 17
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [4,2,1] => 21
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [3,2,2,1] => 18
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [4,3,1] => 26
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [3,1,1,1] => 12
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [4,1,1] => 18
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [4,2] => 20
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [5,1] => 26
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [4,2,1] => 21
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [4,1,1] => 18
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [5,1] => 26
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [5,1] => 26
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => [6] => 36
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [5,2] => 29
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [4,2,1] => 21
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [5,2] => 29
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [4,2,2] => 24
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => [5,3] => 34
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [3,2,1,1] => 15
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [4,2,1] => 21
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [4,3] => 25
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [5,2] => 29
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [4,3,1] => 26
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [3,2,2,1] => 18
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [4,2,2] => 24
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [3,2,2,2] => 21
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [4,3,2] => 29
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [4,3,1] => 26
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => [5,3] => 34
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [4,3,2] => 29
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => [5,4] => 41
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => [4,3,3] => 34
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [2,2,1,1,1] => 11
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [3,2,1,1] => 15
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [3,3,1] => 19
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [4,2,1] => 21
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [3,3,1,1] => 20
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [3,3,1] => 19
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [4,3] => 25
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [4,3] => 25
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => [5,2] => 29
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => [4,4] => 32
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [3,3,2] => 22
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => [4,3,1] => 26
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [3,3,2,1] => 23
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => [4,4,1] => 33
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [2,2,2,1,1] => 14
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => [3,2,2,1] => 18
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => [3,3,2] => 22
[1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]] => [4,2,2] => 24
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => [3,3,2,1] => 23
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => [2,2,2,2,1] => 17
[1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]] => [3,2,2,2] => 21
[1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2],[]] => [2,2,2,2,2] => 20
[1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2],[]] => [3,3,2,2] => 26
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => [3,3,3] => 27
[1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]] => [4,3,2] => 29
[1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]] => [3,3,3,1] => 28
[1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2],[]] => [4,4,2] => 36
[1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2],[]] => [3,3,3,2] => 31
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [3,3,1,1] => 20
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => [4,3,1] => 26
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => [4,4] => 32
[1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]] => [5,3] => 34
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => [4,4,1] => 33
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [3,3,2,1] => 23
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => [4,3,2] => 29
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => [3,3,2,2] => 26
[1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]] => [4,4,2] => 36
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => [4,4,1] => 33
[1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]] => [5,4] => 41
[1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]] => [4,4,2] => 36
[1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5],[]] => [5,5] => 50
[1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]] => [4,4,3] => 41
[1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]] => [3,3,3,1] => 28
[1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3],[]] => [4,3,3] => 34
[1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]] => [3,3,3,2] => 31
[1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3],[]] => [4,4,3] => 41
[1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3],[]] => [3,3,3,3] => 36
[1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4],[]] => [4,4,4] => 48
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [2,2,1,1,1] => 11
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => [3,1,1,1,1] => 13
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => 12
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [2,2,2,1] => 13
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [3,2,1,1] => 15
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [3,2,1,1] => 15
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => [4,1,1,1] => 19
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]] => [3,2,1,1,1] => 16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => 15
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]] => [3,3,1,1,1] => 21
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [2,2,2,1] => 13
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [3,2,2] => 17
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [3,3,1] => 19
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [4,2,1] => 21
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [3,2,2] => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [4,2,1] => 21
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [4,2,1] => 21
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => [5,1,1] => 27
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]] => [4,2,1,1] => 22
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]] => [3,2,2,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1],[]] => [2,2,2,2,1,1] => 18
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1],[]] => [3,3,2,1,1] => 24
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]] => [4,3,1,1] => 27
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1],[]] => [4,4,1,1] => 34
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [2,2,1,1,1] => 11
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [3,2,1,1] => 15
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [3,3,1] => 19
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [4,2,1] => 21
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [3,3,1] => 19
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [4,3] => 25
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [4,3] => 25
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [5,2] => 29
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [3,2,1,1] => 15
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [4,2,1] => 21
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [4,3] => 25
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [5,2] => 29
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [4,2,1] => 21
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [5,2] => 29
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [5,2] => 29
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => [6,1] => 37
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]] => [4,4,3] => 41
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]] => [5,2,1] => 30
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]] => [4,2,2,1] => 25
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1],[]] => [3,2,2,2,1] => 22
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1],[]] => [4,3,2,1] => 30
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,1],[]] => [4,4,2,1] => 37
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,1],[]] => [3,3,3,2,1] => 32
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]] => [5,3,1] => 35
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => [4,4,3] => 41
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1],[]] => [5,4,1] => 42
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1],[2]] => [4,4,3] => 41
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1],[]] => [5,5,1] => 51
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1],[1]] => [4,4,4] => 48
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,1],[]] => [4,3,3,1] => 35
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1],[1]] => [3,3,3,3] => 36
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1],[]] => [4,4,3,1] => 42
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [2,1,1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [3,1,1,1,1] => 13
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [3,2,1,1] => 15
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [4,1,1,1] => 19
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [3,2,2] => 17
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [4,2,1] => 21
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [4,2,1] => 21
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [5,1,1] => 27
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [3,2,1,1] => 15
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [4,2,1] => 21
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [4,3] => 25
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [5,2] => 29
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [4,2,1] => 21
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [5,2] => 29
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [5,2] => 29
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [6,1] => 37
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1,1]] => [4,3,3,1] => 35
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [3,1,1,1,1] => 13
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [4,1,1,1] => 19
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [4,2,1] => 21
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [5,1,1] => 27
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [4,2,1] => 21
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [5,2] => 29
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [5,2] => 29
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [6,1] => 37
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [4,1,1,1] => 19
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [5,1,1] => 27
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [5,2] => 29
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [6,1] => 37
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [5,1,1] => 27
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [6,1] => 37
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [6,1] => 37
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => [7] => 49
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6],[4]] => [6,2] => 40
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5],[3]] => [6,2] => 40
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]] => [5,2,2] => 33
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6],[3]] => [6,3] => 45
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => [6,2] => 40
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => [5,3,1] => 35
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]] => [5,2,2] => 33
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]] => [4,2,2,2] => 28
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]] => [5,3,2] => 38
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5],[2]] => [6,3] => 45
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]] => [5,3,2] => 38
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6],[2]] => [6,4] => 52
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]] => [5,3,3] => 43
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3],[1]] => [6,2] => 40
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => [5,4] => 41
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => [5,3,1] => 35
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => [4,3,2,1] => 30
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => [5,4,1] => 42
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]] => [5,2,2] => 33
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => [4,3,2,1] => 30
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]] => [4,2,2,2] => 28
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1,1]] => [3,2,2,2,2] => 25
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1,1]] => [4,3,2,2] => 33
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => [5,3,2] => 38
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => [4,3,3,1] => 35
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]] => [5,4,2] => 45
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1,1]] => [4,3,3,2] => 38
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4],[1]] => [6,3] => 45
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => [5,4,1] => 42
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => [5,3,2] => 38
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]] => [4,3,2,2] => 33
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => [5,4,2] => 45
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5],[1]] => [6,4] => 52
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]] => [5,4,2] => 45
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6],[1]] => [6,5] => 61
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]] => [5,4,3] => 50
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]] => [4,3,3,1] => 35
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]] => [5,3,3] => 43
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1,1]] => [4,3,3,2] => 38
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]] => [5,4,3] => 50
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]] => [6,2] => 40
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => [5,4] => 41
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => [5,4] => 41
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => [4,4,2] => 36
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => [5,5] => 50
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => [5,3,1] => 35
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => [4,4,2] => 36
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => [4,3,2,1] => 30
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1]] => [3,3,2,2,1] => 27
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => [4,4,2,1] => 37
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => [5,4,1] => 42
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => [4,4,3] => 41
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1]] => [5,5,1] => 51
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]] => [4,4,3,1] => 42
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]] => [5,2,2] => 33
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => [4,4,2] => 36
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => [4,3,2,1] => 30
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => [3,3,3,1,1] => 29
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2],[1]] => [4,4,2,1] => 37
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2],[]] => [4,2,2,2] => 28
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2],[1]] => [3,3,2,2,1] => 27
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2],[]] => [3,2,2,2,2] => 25
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2],[]] => [2,2,2,2,2,2] => 24
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2],[]] => [3,3,2,2,2] => 30
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,2],[]] => [4,3,2,2] => 33
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2],[1]] => [3,3,3,2,1] => 32
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,2],[]] => [4,4,2,2] => 40
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2],[]] => [5,3,2] => 38
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => [4,4,3] => 41
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => [4,3,3,1] => 35
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]] => [3,3,3,2,1] => 32
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => [4,4,3,1] => 42
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2],[3]] => [4,4,3] => 41
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[5,4,2],[]] => [5,4,2] => 45
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => [4,4,4] => 48
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[5,5,2],[]] => [5,5,2] => 54
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2],[2]] => [3,3,3,3] => 36
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,2],[]] => [4,3,3,2] => 38
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,2],[]] => [4,4,3,2] => 45
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]] => [6,3] => 45
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => [5,5] => 50
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => [5,4,1] => 42
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]] => [4,4,2,1] => 37
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => [5,5,1] => 51
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1]] => [5,3,2] => 38
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => [4,4,2,1] => 37
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]] => [4,3,2,2] => 33
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1]] => [3,3,2,2,2] => 30
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => [4,4,2,2] => 40
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => [4,4,3] => 41
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => [5,4,2] => 45
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => [4,4,3,1] => 42
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1]] => [5,5,2] => 54
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]] => [4,4,3,2] => 45
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4],[]] => [6,4] => 52
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3]] => [5,5,1] => 51
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]] => [4,4,2,1] => 37
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2]] => [5,4,2] => 45
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]] => [4,4,2,2] => 40
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2]] => [5,5,2] => 54
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4]] => [5,5,1] => 51
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5],[]] => [6,5] => 61
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3]] => [5,5,2] => 54
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6],[]] => [6,6] => 72
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]] => [4,4,3,1] => 42
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1]] => [5,4,3] => 50
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]] => [4,4,3,2] => 45
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3],[2]] => [4,3,3,1] => 35
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3],[3]] => [4,4,3] => 41
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[5,3,3],[]] => [5,3,3] => 43
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3],[2]] => [4,4,3,1] => 42
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]] => [3,3,3,2,1] => 32
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3],[1]] => [4,3,3,2] => 38
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3],[1]] => [4,4,3,2] => 45
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3],[3]] => [4,4,4] => 48
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[5,4,3],[]] => [5,4,3] => 50
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => 14
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]] => [2,2,1,1,1,1,1] => 13
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]] => [4,1,1,1,1] => 20
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => 17
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1,1],[]] => [2,2,2,1,1,1,1] => 16
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1,1],[]] => [3,3,1,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]] => [5,1,1,1] => 28
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]] => [4,2,1,1,1] => 23
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1,1],[]] => [3,2,2,1,1,1] => 20
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1,1],[]] => [4,3,1,1,1] => 28
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]] => [6,1,1] => 38
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]] => [5,2,1,1] => 31
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1,1],[]] => [4,2,2,1,1] => 26
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1,1],[]] => [5,3,1,1] => 36
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]] => [7,1] => 50
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]] => [6,2,1] => 41
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,1],[]] => [5,2,2,1] => 34
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3,1],[]] => [6,3,1] => 46
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8],[]] => [8] => 64
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[]] => [7,2] => 53
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,2],[]] => [6,2,2] => 44
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[7,3],[]] => [7,3] => 58
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9],[]] => [9] => 81
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,2],[]] => [8,2] => 68
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => 21
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1],[]] => [5,1,1,1,1] => 29
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1],[]] => [6,1,1,1] => 39
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1],[]] => [7,1,1] => 51
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1],[]] => [8,1] => 65
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1,1] => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1,1],[]] => [2,2,1,1,1,1,1,1] => 14
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1,1] => 16
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1,1],[]] => [3,2,1,1,1,1,1] => 18
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1,1],[]] => [4,1,1,1,1,1,1] => 22
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1,1],[]] => [4,2,1,1,1,1] => 24
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1,1],[]] => [5,1,1,1,1,1] => 30
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1,1],[]] => [5,2,1,1,1] => 32
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1,1],[]] => [6,1,1,1,1] => 40
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1,1],[]] => [6,2,1,1] => 42
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1,1],[]] => [7,1,1,1] => 52
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2,1],[]] => [7,2,1] => 54
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1,1],[]] => [8,1,1] => 66
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9,1],[]] => [9,1] => 82
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[10],[]] => [10] => 100
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Description
The sum of the squares of the parts of a partition.
Map
dominating partition
Description
The dominating partition in the Schur expansion.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$ s_{331/2} = s_{311} + s_{32}, $$
and the partition $32$ dominates $311$.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.