[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 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
[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
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => [5,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [4,4] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [[1,2],[3]] => [2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [[1,2,3,4]] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [[1,2,3]] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [[1,2]] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [[1]] => [1] => 1
[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]] => [2,2,2,1,1,1] => 3
[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]] => [3,2,1,1,1,1] => 1
[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]] => [2,2,1,1,1,1] => 2
[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]] => [4,1,1,1,1,1] => 1
[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]] => [3,1,1,1,1,1] => 1
[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]] => [2,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1] => 6
[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]] => [2,2,2,2,1] => 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]] => [3,2,2,1,1] => 1
[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]] => [2,2,2,1,1] => 3
[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]] => [3,3,1,1,1] => 2
[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]] => [4,2,1,1,1] => 1
[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]] => [3,2,1,1,1] => 1
[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]] => [2,2,1,1,1] => 2
[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]] => [5,1,1,1,1] => 1
[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]] => [4,1,1,1,1] => 1
[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]] => [3,1,1,1,1] => 1
[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]] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 5
[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]] => [3,2,2,2] => 1
[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]] => [2,2,2,2] => 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]] => [3,3,2,1] => 2
[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]] => [4,2,2,1] => 1
[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]] => [3,2,2,1] => 1
[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]] => [2,2,2,1] => 3
[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]] => [4,3,1,1] => 1
[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]] => [3,3,1,1] => 2
[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]] => [5,2,1,1] => 1
[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]] => [4,2,1,1] => 1
[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]] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 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]] => [3,3,3] => 3
[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]] => [4,3,2] => 1
[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]] => [3,3,2] => 2
[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]] => [5,2,2] => 1
[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]] => [4,2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 3
[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]] => [4,4,1] => 2
[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]] => [5,3,1] => 1
[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]] => [4,3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 2
[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]] => [6,2,1] => 1
[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]] => [5,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 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
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 3
[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]] => [5,4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [4,4] => 2
[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]] => [6,3] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [[1,2,3,4,5,6],[7,8]] => [6,2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [2,2] => 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
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [[1,2,3,4,5,6]] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [[1,2,3,4]] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [[1,2,3]] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [[1,2]] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [[1]] => [1] => 1
[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]] => [2,2,1,1,1,1,1] => 2
[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]] => [3,1,1,1,1,1,1] => 1
[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]] => [2,1,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1,1] => 7
[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]] => [2,2,2,1,1,1] => 3
[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]] => [3,2,1,1,1,1] => 1
[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]] => [2,2,1,1,1,1] => 2
[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]] => [4,1,1,1,1,1] => 1
[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]] => [3,1,1,1,1,1] => 1
[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]] => [2,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1] => 6
[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]] => [2,2,2,2,1] => 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]] => [3,2,2,1,1] => 1
[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]] => [2,2,2,1,1] => 3
[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]] => [3,3,1,1,1] => 2
[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]] => [4,2,1,1,1] => 1
[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]] => [3,2,1,1,1] => 1
[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]] => [2,2,1,1,1] => 2
[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]] => [5,1,1,1,1] => 1
[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]] => [4,1,1,1,1] => 1
[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]] => [3,1,1,1,1] => 1
[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]] => [2,1,1,1,1] => 1
[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] => 5
[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]] => [3,2,2,2] => 1
[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]] => [2,2,2,2] => 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]] => [3,3,2,1] => 2
[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]] => [4,2,2,1] => 1
[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]] => [3,2,2,1] => 1
[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]] => [2,2,2,1] => 3
[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]] => [4,3,1,1] => 1
[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]] => [3,3,1,1] => 2
[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]] => [5,2,1,1] => 1
[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]] => [4,2,1,1] => 1
[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]] => [3,2,1,1] => 1
[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]] => [2,2,1,1] => 2
[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
[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
[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
[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
[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
[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] => 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]] => [3,3,3] => 3
[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]] => [4,3,2] => 1
[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]] => [3,3,2] => 2
[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]] => [5,2,2] => 1
[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]] => [4,2,2] => 1
[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]] => [3,2,2] => 1
[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]] => [2,2,2] => 3
[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]] => [4,4,1] => 2
[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]] => [5,3,1] => 1
[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]] => [4,3,1] => 1
[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]] => [3,3,1] => 2
[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]] => [6,2,1] => 1
[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]] => [5,2,1] => 1
[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]] => [4,2,1] => 1
[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]] => [3,2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [[1,2],[3,4],[5]] => [2,2,1] => 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
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 3
[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]] => [5,4] => 1
[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]] => [4,4] => 2
[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]] => [6,3] => 1
[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]] => [5,3] => 1
[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]] => [4,3] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => [3,3] => 2
[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]] => [7,2] => 1
[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]] => [6,2] => 1
[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]] => [5,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [[1,2,3],[4,5]] => [3,2] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [2,2] => 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
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[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
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [[1,2,3,4,5,6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [[1,2,3,4]] => [4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [[1,2,3]] => [3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [[1,2]] => [2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [[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
[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] => 8
[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
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[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]] => [2,1,1,1,1,1,1,1] => 1
[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] => 9
[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]] => [2,2,1,1,1,1,1] => 2
[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]] => [3,1,1,1,1,1,1] => 1
[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]] => [2,1,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1,1] => 7
[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]] => [2,2,2,1,1,1] => 3
[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]] => [3,2,1,1,1,1] => 1
[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]] => [2,2,1,1,1,1] => 2
[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]] => [4,1,1,1,1,1] => 1
[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]] => [3,1,1,1,1,1] => 1
[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]] => [2,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1] => 6
[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]] => [2,2,2,2,1] => 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]] => [3,2,2,1,1] => 1
[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]] => [2,2,2,1,1] => 3
[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]] => [3,3,1,1,1] => 2
[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]] => [3,2,1,1,1] => 1
[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]] => [2,2,1,1,1] => 2
[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] => 1
[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] => 1
[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] => 5
[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]] => [3,3,2,1] => 2
[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]] => [4,2,2,1] => 1
[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]] => [3,2,2,1] => 1
[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]] => [2,2,2,1] => 3
[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]] => [4,3,1,1] => 1
[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]] => [3,3,1,1] => 2
[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]] => [4,2,1,1] => 1
[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]] => [3,2,1,1] => 1
[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]] => [2,2,1,1] => 2
[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
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => [1,1,1,1] => 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]] => [3,3,3] => 3
[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]] => [4,3,2] => 1
[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]] => [3,3,2] => 2
[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]] => [4,2,2] => 1
[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]] => [3,2,2] => 1
[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]] => [2,2,2] => 3
[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]] => [4,4,1] => 2
[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]] => [5,3,1] => 1
[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]] => [4,3,1] => 1
[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]] => [3,3,1] => 2
[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]] => [6,2,1] => 1
[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]] => [5,2,1] => 1
[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]] => [4,2,1] => 1
[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]] => [3,2,1] => 1
[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]] => [2,2,1] => 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
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [[1,2,3],[4],[5]] => [3,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => [1,1,1] => 3
[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]] => [4,4] => 2
[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]] => [4,3] => 1
[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]] => [3,3] => 2
[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]] => [7,2] => 1
[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]] => [4,2] => 1
[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]] => [3,2] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [2,2] => 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
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[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
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [[1,2,3,4,5,6]] => [6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [[1,2,3,4]] => [4] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [[1,2,3]] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [[1,2]] => [2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [[1]] => [1] => 1
[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] => 2
[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
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[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]] => [2,2,1] => 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]] => [3,2] => 1
[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
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 8
[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
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => [9] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [[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] => 3
[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] => 4
[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] => 5
[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]] => [1,1,1,1,1,1] => 6
[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] => 7
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [[1,2,3,4,5,6,7]] => [7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [[1,2,3,4,5,6]] => [6] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [[1,2,3,4,5]] => [5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [[1,2,3,4]] => [4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => [2,2] => 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]] => [3,3] => 2
[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]] => [3,3,3] => 3
[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] => 1
[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]] => [2,1,1,1,1,1,1,1] => 1
[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]] => [1,1,1,1,1,1,1,1,1] => 9
[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]] => [4,3,2] => 1
[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
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1
[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]] => [3,1,1,1,1,1] => 1
[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]] => [4,1,1,1,1,1] => 1
[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
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [[1,2],[3]] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 1
[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
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [[1,2,3],[4]] => [3,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [[1,2,3,4],[5,6]] => [4,2] => 1
[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]] => [4,3,1] => 1
[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]] => [2,2,2] => 3
[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
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 1
[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
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,2],[3],[4]] => [2,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 1
[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] => 3
[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
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 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]] => [3,2,1,1] => 1
[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]] => [2,2] => 2
[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]] => [3,3] => 2
[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
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => [1,1] => 2
[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
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [[1,2,3,4,5],[6]] => [5,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [[1,2,3,4],[5]] => [4,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => [4,4] => 2
[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]] => [5,3,1] => 1
[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]] => [2,2,2,1] => 3
[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]] => [3,3,2] => 2