Identifier
Values
[1,0,1,0] => [1] => [[1]] => 1
[1,0,1,0,1,0] => [2,1] => [[1,2],[3]] => 2
[1,0,1,1,0,0] => [1,1] => [[1],[2]] => 1
[1,1,0,0,1,0] => [2] => [[1,2]] => 2
[1,1,0,1,0,0] => [1] => [[1]] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,0,1,1,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,0,1,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,0,0,1,0,1,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,0,0,1,1,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,0,1,0,1,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,0,1,1,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,0,0,0,1,0] => [3] => [[1,2,3]] => 3
[1,1,1,0,0,1,0,0] => [2] => [[1,2]] => 2
[1,1,1,0,1,0,0,0] => [1] => [[1]] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,0,0,0,1,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,0,0,1,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => [[1]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
>>> Load all 805 entries. <<<
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [[1]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13,14]] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [[1,2,3,4,5,6]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [[1]] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14],[15,16]] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13],[14,15]] => 3
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12],[13,14]] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15]] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14]] => 3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12,13]] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9,10],[11]] => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]] => 5
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]] => 5
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [[1,2,3],[4,5,6],[7,8,9],[10],[11]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10],[11]] => 5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13,14]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]] => 5
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]] => 5
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [[1,2,3,4],[5,6,7],[8,9],[10,11]] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [[1,2,3,4,5],[6,7,8],[9,10,11]] => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [[1,2,3,4,5,6,7]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [[1,2,3,4,5,6]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [[1]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [[1,2,3,4,5,6,7,8]] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 7
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]] => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]] => 2
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12],[13,14]] => 3
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11],[12,13]] => 3
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15]] => 3
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9],[10,11]] => 3
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12,13]] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [[1,2,3,4,5],[6,7],[8,9],[10,11]] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11]] => 4
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11]] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [[1,2,3,4,5],[6,7,8,9],[10,11]] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [[1,2,3,4,5,6,7]] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [[1,2,3,4,5,6]] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [[1]] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]] => 5
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [[1,2,3,4,5,6,7,8]] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [[1]] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [[1]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [[1,2,3,4,5,6,7]] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [[1,2,3,4,5,6]] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [[1,2,3,4,5]] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [[1,2,3,4]] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] => 4
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => 7
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[16,17,18]] => 3
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11]] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]] => 4
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [[1,2,3,4],[5,6,7],[8,9],[10],[11]] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 3
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
search for individual values
searching the database for the individual values of this statistic
Description
The last entry in the first row of a standard tableau.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.