Identifier
Values
[[1,3,5],[2,4]] => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,2,4],[3,5]] => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 0
[[1,3,5],[2],[4]] => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,2,4],[3],[5]] => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[4]] => [1,2,2] => [[3,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,2],[3,4],[5]] => [2,2,1] => [[3,3,2],[2,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,5,6],[4]] => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,3,5,6],[2,4]] => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,6],[2,5]] => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,6],[3,5]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,6],[4,5]] => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,2,4,5],[3,6]] => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4,6]] => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 0
[[1,3,5,6],[2],[4]] => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,6],[2],[5]] => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,6],[3],[5]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,5],[3],[6]] => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4],[6]] => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 0
[[1,3,5],[2,4,6]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,5],[3,4,6]] => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,4],[2,5,6]] => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3,5,6]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3],[4,5,6]] => [3,3] => [[5,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,4,6],[2,5],[3]] => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6],[2,5],[4]] => [1,2,3] => [[4,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6],[2,4],[5]] => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,6],[3,4],[5]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,3,5],[2,6],[4]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,5],[3,6],[4]] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,4],[2,6],[5]] => [1,3,2] => [[4,3,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3,6],[5]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,3,5],[2,4],[6]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,5],[3,4],[6]] => [2,3,1] => [[4,4,2],[3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3,5],[6]] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3],[4,5],[6]] => [3,2,1] => [[4,4,3],[3,2]] => ([(0,2),(2,1)],3) => 0
[[1,4,6],[2],[3],[5]] => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6],[2],[4],[5]] => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,5],[2],[4],[6]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,5],[3],[4],[6]] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3],[5],[6]] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2,5],[3,6]] => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[4,6]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2],[3,5],[4,6]] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3],[2,4],[5,6]] => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2],[3,4],[5,6]] => [2,2,2] => [[4,3,2],[2,1]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,4],[2,6],[3],[5]] => [1,1,2,2] => [[3,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,6],[4],[5]] => [1,2,1,2] => [[3,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4],[2,5],[3],[6]] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[4],[6]] => [1,2,2,1] => [[3,3,2,1],[2,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2],[3,5],[4],[6]] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,5,6,7],[4]] => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,4,6,7],[5]] => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 0
[[1,3,5,6,7],[2,4]] => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,6,7],[2,5]] => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,6,7],[3,5]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,6,7],[4,5]] => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,5,7],[2,6]] => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5,7],[3,6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5,7],[4,6]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,4,7],[5,6]] => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 0
[[1,2,4,5,6],[3,7]] => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5,6],[4,7]] => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,4,6],[5,7]] => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 0
[[1,3,5,6,7],[2],[4]] => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,6,7],[2],[5]] => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,6,7],[3],[5]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,6,7],[4],[5]] => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 0
[[1,3,4,5,7],[2],[6]] => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5,7],[3],[6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5,7],[4],[6]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,4,5,6],[3],[7]] => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5,6],[4],[7]] => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,4,6],[5],[7]] => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 0
[[1,2,5,7],[3,4,6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,3,4,7],[2,5,6]] => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,7],[3,5,6]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,7],[4,5,6]] => [3,4] => [[6,3],[2]] => ([(0,2),(2,1)],3) => 0
[[1,2,5,6],[3,4,7]] => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4,5,7]] => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,3,4,5],[2,6,7]] => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5],[3,6,7]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5],[4,6,7]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,4],[5,6,7]] => [4,3] => [[6,4],[3]] => ([(0,2),(2,1)],3) => 0
[[1,4,6,7],[2,5],[3]] => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6,7],[2,5],[4]] => [1,2,4] => [[5,2,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6,7],[2,4],[5]] => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,6,7],[3,4],[5]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,4,5,7],[2,6],[3]] => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,4,7],[2,6],[5]] => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,7],[3,6],[5]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,7],[4,6],[5]] => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,5,7],[3,4],[6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,7],[4,5],[6]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,6],[4,7],[5]] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,4,5],[2,7],[6]] => [1,4,2] => [[5,4,1],[3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5],[3,7],[6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5],[4,7],[6]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,5,6],[3,4],[7]] => [2,4,1] => [[5,5,2],[4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4,5],[7]] => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
>>> Load all 386 entries. <<<
[[1,2,4,5],[3,6],[7]] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4,6],[7]] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,4],[5,6],[7]] => [4,2,1] => [[5,5,4],[4,3]] => ([(0,2),(2,1)],3) => 0
[[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4],[5],[7]] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5],[3],[6],[7]] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4],[6],[7]] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,4,6],[2,5,7],[3]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3,6],[2,4,7],[5]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,5],[2,6,7],[3]] => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,4],[2,6,7],[5]] => [1,3,3] => [[5,3,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4],[3,6,7],[5]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3],[4,6,7],[5]] => [3,1,3] => [[5,3,3],[2,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,5],[3,4,7],[6]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3],[4,5,7],[6]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,3,5],[2,4,6],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,4,6],[7]] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3],[4,5,6],[7]] => [3,3,1] => [[5,5,3],[4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,4,7],[2,5],[3,6]] => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,7],[2,4],[5,6]] => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,7],[3,4],[5,6]] => [2,2,3] => [[5,3,2],[2,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,4,6],[2,5],[3,7]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3,6],[2,4],[5,7]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,5],[2,6],[3,7]] => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3],[4,6],[5,7]] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,5],[3,4],[6,7]] => [2,3,2] => [[5,4,2],[3,1]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3],[4,5],[6,7]] => [3,2,2] => [[5,4,3],[3,2]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,5,7],[2,6],[3],[4]] => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => [[4,2,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => [[4,2,2,1],[1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,7],[2,5],[3],[6]] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3,7],[2,4],[5],[6]] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2,7],[3],[5]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3,6],[2,7],[4],[5]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,6],[3,7],[4],[5]] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => [[4,3,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2,5],[3],[7]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3,6],[2,4],[5],[7]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,5],[2,6],[3],[7]] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 0
[[1,3,5],[2,6],[4],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,6],[4],[7]] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,3],[4,6],[5],[7]] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,3,5],[2,4],[6],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,4],[6],[7]] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3,5],[6],[7]] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,6],[3],[4],[5],[7]] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => ([(0,2),(2,1)],3) => 0
[[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3],[4],[6],[7]] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,4],[3],[5],[6],[7]] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2,6],[3,7],[4]] => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2,6],[3,7],[5]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3],[2,6],[4,7],[5]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,6],[4,7],[5]] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4],[2,5],[3,7],[6]] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3],[2,4],[5,7],[6]] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4],[2,5],[3,6],[7]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3],[2,5],[4,6],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,5],[4,6],[7]] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3],[2,4],[5,6],[7]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5],[2,6],[3],[4],[7]] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4],[2,5],[3],[6],[7]] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,4,6,7,8],[5]] => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,3,4,5,7,8],[2,6]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5,7,8],[3,6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5,7,8],[4,6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,7,8],[5,6]] => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,4,5,6,8],[3,7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,5,6,8],[4,7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,6,8],[5,7]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5,6,7],[4,8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,4,6,7],[5,8]] => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,3,4,5,7,8],[2],[6]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5,7,8],[3],[6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5,7,8],[4],[6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,7,8],[5],[6]] => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 0
[[1,2,4,5,6,8],[3],[7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,5,6,8],[4],[7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,6,8],[5],[7]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,5,6,7],[4],[8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,4,6,7],[5],[8]] => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,5,7,8],[3,4,6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,5,6,8],[3,4,7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6,8],[4,5,7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,3,4,5,8],[2,6,7]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5,8],[3,6,7]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5,8],[4,6,7]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,8],[5,6,7]] => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,2,3,6,7],[4,5,8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,4,7],[5,6,8]] => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,5,6],[3,7,8]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,5,6],[4,7,8]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,6],[5,7,8]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,4,5,7,8],[2,6],[3]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,5,7,8],[3,4],[6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,7,8],[4,5],[6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,3,4,5,8],[2,7],[6]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5,8],[3,7],[6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5,8],[4,7],[6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,8],[5,7],[6]] => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 0
[[1,2,5,6,8],[3,4],[7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6,8],[4,5],[7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,8],[5,6],[7]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,4,7],[5,8],[6]] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5,6],[3,8],[7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,5,6],[4,8],[7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4,6],[5,8],[7]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,6,7],[4,5],[8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,4,7],[5,6],[8]] => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,5,6],[3,7],[8]] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5,6],[4,7],[8]] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,4,6],[5,7],[8]] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 0
[[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,7,8],[4],[5],[6]] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,4,7],[5],[6],[8]] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4,5,6],[3],[7],[8]] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5,6],[4],[7],[8]] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,4,6],[5],[7],[8]] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,7],[4,5,6,8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,5,6],[3,4,7,8]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6],[4,5,7,8]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,3,4,5],[2,6,7,8]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5],[3,6,7,8]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5],[4,6,7,8]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4],[5,6,7,8]] => [4,4] => [[7,4],[3]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4,5,8],[2,6,7],[3]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,5,8],[3,4,7],[6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,8],[4,5,7],[6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,8],[4,5,6],[7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,3,4,5],[2,7,8],[6]] => [1,4,3] => [[6,4,1],[3]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,4,5],[3,7,8],[6]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,5],[4,7,8],[6]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4],[5,7,8],[6]] => [4,1,3] => [[6,4,4],[3,3]] => ([(0,2),(2,1)],3) => 0
[[1,2,5,6],[3,4,8],[7]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6],[4,5,8],[7]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4],[5,6,8],[7]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,2,3,7],[4,5,6],[8]] => [3,4,1] => [[6,6,3],[5,2]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,5,6],[3,4,7],[8]] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4,5,7],[8]] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => [[6,6,4],[5,3]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,4,5,8],[2,6],[3,7]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,5,8],[3,4],[6,7]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,8],[4,5],[6,7]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4],[5,7],[6,8]] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,5,6],[3,4],[7,8]] => [2,4,2] => [[6,5,2],[4,1]] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6],[4,5],[7,8]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [[6,5,4],[4,3]] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[[1,5,6,8],[2,7],[3],[4]] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3,8],[4,7],[5],[6]] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,7],[4,8],[5],[6]] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4,7],[5],[8]] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4,5],[7],[8]] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,4,5],[3,6],[7],[8]] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4,6],[7],[8]] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => ([(0,2),(2,1)],3) => 0
[[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,7],[4],[5],[6],[8]] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,6],[4],[5],[7],[8]] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3,5],[4],[6],[7],[8]] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,4,5],[2,6,8],[3,7]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,5],[3,4,8],[6,7]] => [2,3,3] => [[6,4,2],[3,1]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3],[4,5,8],[6,7]] => [3,2,3] => [[6,4,3],[3,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => [[6,5,3],[4,2]] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => 2
[[1,5,7],[2,6,8],[3],[4]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,7],[2,5,8],[3],[6]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,7],[2,4,8],[5],[6]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,5,6],[2,7,8],[3],[4]] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => [[5,3,1,1],[2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => ([(0,2),(2,1)],3) => 0
[[1,4,6],[2,5,7],[3],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,6],[2,4,7],[5],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,5],[2,4,6],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,4,6],[7],[8]] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[[1,5,7],[2,6],[3,8],[4]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,7],[2,5],[3,8],[6]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,7],[2,4],[5,8],[6]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,5,6],[2,7],[3,8],[4]] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,3],[4,7],[5,8],[6]] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2,5],[3,7],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,6],[2,4],[5,7],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,2,3],[4,6],[5,7],[8]] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,6,8],[2,7],[3],[4],[5]] => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,5,8],[2,6],[3],[4],[7]] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,4,8],[2,5],[3],[6],[7]] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,8],[2,4],[5],[6],[7]] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5,7],[2,8],[3],[4],[6]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,7],[2,8],[3],[5],[6]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,7],[2,8],[4],[5],[6]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,2,7],[3,8],[4],[5],[6]] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5,7],[2,6],[3],[4],[8]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,7],[2,5],[3],[6],[8]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,7],[2,4],[5],[6],[8]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,4,6],[2,7],[3],[5],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,6],[2,7],[4],[5],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,2,6],[3,7],[4],[5],[8]] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2,5],[3],[7],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,6],[2,4],[5],[7],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,5],[2,6],[4],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,6],[4],[7],[8]] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,3],[4,6],[5],[7],[8]] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3,5],[2,4],[6],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,2,4],[3,5],[6],[7],[8]] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => ([(0,2),(2,1)],3) => 0
[[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2,6],[3,7],[4,8]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4],[2,5],[3,7],[6,8]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,4],[5,7],[6,8]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,6],[2,7],[3,8],[4],[5]] => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2,7],[3,8],[4],[6]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4],[2,7],[3,8],[5],[6]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,7],[4,8],[5],[6]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,2],[3,7],[4,8],[5],[6]] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5],[2,6],[3,8],[4],[7]] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,4],[2,5],[3,8],[6],[7]] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,4],[5,8],[6],[7]] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5],[2,6],[3,7],[4],[8]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4],[2,6],[3,7],[5],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,6],[4,7],[5],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,2],[3,6],[4,7],[5],[8]] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4],[2,5],[3,7],[6],[8]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,4],[5,7],[6],[8]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,4],[2,5],[3,6],[7],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,5],[4,6],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,5],[4,6],[7],[8]] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,3],[2,4],[5,6],[7],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,6],[2,7],[3],[4],[5],[8]] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[[1,5],[2,6],[3],[4],[7],[8]] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => 2
[[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4],[2,5],[3],[6],[7],[8]] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 0
[[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,2),(2,1)],3) => 0
[[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => ([(0,2),(2,1)],3) => 0
[[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => ([(0,3),(2,1),(3,2)],4) => 0
[[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,2),(2,1)],3) => 0
search for individual values
searching the database for the individual values of this statistic
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
dominating sublattice
Description
Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.