Identifier
-
Mp00059:
Permutations
—Robinson-Schensted insertion tableau⟶
Standard tableaux
Mp00294: Standard tableaux —peak composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤ
Values
[1] => [[1]] => [1] => ([],1) => 1
[1,2] => [[1,2]] => [2] => ([],2) => 1
[2,1] => [[1],[2]] => [2] => ([],2) => 1
[1,2,3] => [[1,2,3]] => [3] => ([],3) => 1
[1,3,2] => [[1,2],[3]] => [2,1] => ([(0,2),(1,2)],3) => 2
[2,1,3] => [[1,3],[2]] => [3] => ([],3) => 1
[2,3,1] => [[1,3],[2]] => [3] => ([],3) => 1
[3,1,2] => [[1,2],[3]] => [2,1] => ([(0,2),(1,2)],3) => 2
[3,2,1] => [[1],[2],[3]] => [3] => ([],3) => 1
[1,2,3,4] => [[1,2,3,4]] => [4] => ([],4) => 1
[1,2,4,3] => [[1,2,3],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,3,2,4] => [[1,2,4],[3]] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,3,4,2] => [[1,2,4],[3]] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,4,2,3] => [[1,2,3],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,4,3,2] => [[1,2],[3],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[2,1,3,4] => [[1,3,4],[2]] => [4] => ([],4) => 1
[2,1,4,3] => [[1,3],[2,4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,3,1,4] => [[1,3,4],[2]] => [4] => ([],4) => 1
[2,3,4,1] => [[1,3,4],[2]] => [4] => ([],4) => 1
[2,4,1,3] => [[1,3],[2,4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,4,3,1] => [[1,3],[2],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,1,2,4] => [[1,2,4],[3]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,1,4,2] => [[1,2],[3,4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,2,1,4] => [[1,4],[2],[3]] => [4] => ([],4) => 1
[3,2,4,1] => [[1,4],[2],[3]] => [4] => ([],4) => 1
[3,4,1,2] => [[1,2],[3,4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,4,2,1] => [[1,4],[2],[3]] => [4] => ([],4) => 1
[4,1,2,3] => [[1,2,3],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,1,3,2] => [[1,2],[3],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,2,1,3] => [[1,3],[2],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,2,3,1] => [[1,3],[2],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,3,1,2] => [[1,2],[3],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,3,2,1] => [[1],[2],[3],[4]] => [4] => ([],4) => 1
[1,2,3,4,5] => [[1,2,3,4,5]] => [5] => ([],5) => 1
[1,2,3,5,4] => [[1,2,3,4],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,4,3,5] => [[1,2,3,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,2,4,5,3] => [[1,2,3,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,2,5,3,4] => [[1,2,3,4],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,5,4,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,3,2,4,5] => [[1,2,4,5],[3]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,3,4,2,5] => [[1,2,4,5],[3]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,3,4,5,2] => [[1,2,4,5],[3]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,4,2,3,5] => [[1,2,3,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,4,2,5,3] => [[1,2,3],[4,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,4,3,2,5] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,4,3,5,2] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,4,5,2,3] => [[1,2,3],[4,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,4,5,3,2] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[1,5,2,3,4] => [[1,2,3,4],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,5,2,4,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,5,4,2,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,5,4,3,2] => [[1,2],[3],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 2
[2,1,3,4,5] => [[1,3,4,5],[2]] => [5] => ([],5) => 1
[2,1,3,5,4] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,1,4,3,5] => [[1,3,5],[2,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,1,4,5,3] => [[1,3,5],[2,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,1,5,3,4] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,1,5,4,3] => [[1,3],[2,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,3,1,4,5] => [[1,3,4,5],[2]] => [5] => ([],5) => 1
[2,3,1,5,4] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,3,4,1,5] => [[1,3,4,5],[2]] => [5] => ([],5) => 1
[2,3,4,5,1] => [[1,3,4,5],[2]] => [5] => ([],5) => 1
[2,3,5,1,4] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,3,5,4,1] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,4,1,3,5] => [[1,3,5],[2,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,4,1,5,3] => [[1,3,5],[2,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,4,3,1,5] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,4,3,5,1] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,4,5,1,3] => [[1,3,5],[2,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,4,5,3,1] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,5,1,3,4] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,5,1,4,3] => [[1,3],[2,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,5,3,1,4] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,5,3,4,1] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[2,5,4,1,3] => [[1,3],[2,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[2,5,4,3,1] => [[1,3],[2],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[3,1,2,4,5] => [[1,2,4,5],[3]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,1,4,2,5] => [[1,2,5],[3,4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,1,4,5,2] => [[1,2,5],[3,4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,2,1,4,5] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,2,1,5,4] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,2,4,1,5] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,2,4,5,1] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,2,5,1,4] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,2,5,4,1] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,4,1,2,5] => [[1,2,5],[3,4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,1,5,2] => [[1,2,5],[3,4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,2,1,5] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,4,2,5,1] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,4,5,1,2] => [[1,2,5],[3,4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[3,4,5,2,1] => [[1,4,5],[2],[3]] => [5] => ([],5) => 1
[3,5,2,1,4] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,5,2,4,1] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[3,5,4,2,1] => [[1,4],[2],[3],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,1,2,3,5] => [[1,2,3,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,1,2,5,3] => [[1,2,3],[4,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,1,3,2,5] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,1,3,5,2] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,1,5,2,3] => [[1,2,3],[4,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,1,5,3,2] => [[1,2],[3,5],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,2,1,3,5] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
>>> Load all 992 entries. <<<[4,2,1,5,3] => [[1,3],[2,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,2,3,1,5] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,2,3,5,1] => [[1,3,5],[2],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,2,5,1,3] => [[1,3],[2,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,2,5,3,1] => [[1,3],[2,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,3,1,2,5] => [[1,2,5],[3],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,1,5,2] => [[1,2],[3,5],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,2,1,5] => [[1,5],[2],[3],[4]] => [5] => ([],5) => 1
[4,3,2,5,1] => [[1,5],[2],[3],[4]] => [5] => ([],5) => 1
[4,3,5,1,2] => [[1,2],[3,5],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,3,5,2,1] => [[1,5],[2],[3],[4]] => [5] => ([],5) => 1
[4,5,1,2,3] => [[1,2,3],[4,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,5,1,3,2] => [[1,2],[3,5],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,5,2,1,3] => [[1,3],[2,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,5,2,3,1] => [[1,3],[2,5],[4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[4,5,3,1,2] => [[1,2],[3,5],[4]] => [2,3] => ([(2,4),(3,4)],5) => 2
[4,5,3,2,1] => [[1,5],[2],[3],[4]] => [5] => ([],5) => 1
[5,1,2,3,4] => [[1,2,3,4],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,1,2,4,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,1,4,2,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,1,4,3,2] => [[1,2],[3],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,2,1,3,4] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,2,1,4,3] => [[1,3],[2,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,2,3,1,4] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,2,3,4,1] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,2,4,1,3] => [[1,3],[2,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,2,4,3,1] => [[1,3],[2],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,3,2,1,4] => [[1,4],[2],[3],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,3,2,4,1] => [[1,4],[2],[3],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,3,4,2,1] => [[1,4],[2],[3],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[5,4,1,2,3] => [[1,2,3],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,4,1,3,2] => [[1,2],[3],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,4,2,1,3] => [[1,3],[2],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,4,2,3,1] => [[1,3],[2],[4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[5,4,3,1,2] => [[1,2],[3],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 2
[5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [5] => ([],5) => 1
[1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [6] => ([],6) => 1
[1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,5,6,4] => [[1,2,3,4,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,6,4,5] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,4,5,3,6] => [[1,2,3,5,6],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,4,5,6,3] => [[1,2,3,5,6],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,5,3,4,6] => [[1,2,3,4,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,5,3,6,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,5,4,6,3] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,5,6,4,3] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,6,3,4,5] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,6,3,5,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,6,5,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,2,5,6] => [[1,2,4,5,6],[3]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,5,2,6] => [[1,2,4,5,6],[3]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,5,6,2] => [[1,2,4,5,6],[3]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,2,3,5,6] => [[1,2,3,5,6],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,2,5,3,6] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,2,5,6,3] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,3,5,2,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,3,5,6,2] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,5,2,6,3] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,5,3,2,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,5,3,6,2] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,5,6,2,3] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,4,5,6,3,2] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,2,3,4,6] => [[1,2,3,4,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,5,2,3,6,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,5,2,4,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,2,4,6,3] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,2,6,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,5,2,6,4,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,4,2,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,4,2,6,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,4,3,6,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,4,6,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,4,6,3,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,6,2,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,5,6,2,4,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,5,6,4,3,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[1,6,2,3,4,5] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,6,2,3,5,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,6,2,5,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,6,2,5,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,6,5,2,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,6,5,2,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,6,5,4,2,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 2
[2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [6] => ([],6) => 1
[2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,5,6,4] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,6,4,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,4,5,3,6] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,4,5,6,3] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,5,3,4,6] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,5,3,6,4] => [[1,3,4],[2,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,5,4,6,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,5,6,4,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,1,6,3,4,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,6,3,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,6,5,3,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,3,1,4,5,6] => [[1,3,4,5,6],[2]] => [6] => ([],6) => 1
[2,3,1,4,6,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,5,4,6] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,5,6,4] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,6,4,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,1,6,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,4,1,5,6] => [[1,3,4,5,6],[2]] => [6] => ([],6) => 1
[2,3,4,1,6,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,4,5,1,6] => [[1,3,4,5,6],[2]] => [6] => ([],6) => 1
[2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => [6] => ([],6) => 1
[2,3,4,6,1,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,4,6,5,1] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,1,4,6] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,1,6,4] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,4,1,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,4,6,1] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,6,1,4] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,5,6,4,1] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,1,4,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,1,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,4,1,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,4,5,1] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,5,1,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,3,6,5,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,4,1,3,5,6] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,1,5,3,6] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,1,5,6,3] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,3,1,5,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,3,5,1,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,3,5,6,1] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,1,3,6] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,1,6,3] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,3,1,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,3,6,1] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,6,1,3] => [[1,3,5,6],[2,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,4,5,6,3,1] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,1,3,4,6] => [[1,3,4,6],[2,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,1,3,6,4] => [[1,3,4],[2,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,1,4,3,6] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,1,4,6,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,1,6,3,4] => [[1,3,4],[2,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,1,6,4,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,3,1,4,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,3,1,6,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,3,4,1,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,3,4,6,1] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,3,6,1,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,3,6,4,1] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,4,1,3,6] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,4,1,6,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,4,3,6,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,4,6,1,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,4,6,3,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,6,1,3,4] => [[1,3,4],[2,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,6,1,4,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,6,3,1,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,6,3,4,1] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,5,6,4,1,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,5,6,4,3,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,6,1,3,4,5] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,1,3,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,1,5,3,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,1,5,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,6,3,1,4,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,3,1,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,3,4,1,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,3,4,5,1] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,3,5,1,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,3,5,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,5,1,3,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,5,1,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,6,5,3,1,4] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,5,3,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[2,6,5,4,1,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[3,1,2,4,5,6] => [[1,2,4,5,6],[3]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,4,2,5,6] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,4,5,2,6] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,1,4,5,6,2] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,1,5,6,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,1,6,4,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,4,1,5,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,2,4,1,6,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,4,5,1,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,2,4,5,6,1] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,2,4,6,1,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,4,6,5,1] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,1,4,6] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,1,6,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,4,1,6] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,4,6,1] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,6,1,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,5,6,4,1] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,1,4,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,1,5,4] => [[1,4],[2,5],[3,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,4,1,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,4,5,1] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,5,1,4] => [[1,4],[2,5],[3,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,2,6,5,4,1] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,5,2,6] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,1,5,6,2] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,2,1,5,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,2,1,6,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,2,5,1,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,2,5,6,1] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,2,6,1,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,2,6,5,1] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,5,1,2,6] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,5,1,6,2] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,5,2,1,6] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,5,2,6,1] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,5,6,1,2] => [[1,2,5,6],[3,4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[3,4,5,6,2,1] => [[1,4,5,6],[2],[3]] => [6] => ([],6) => 1
[3,4,6,2,1,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,6,2,5,1] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,4,6,5,2,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,1,4,6] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,1,6,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,4,1,6] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,4,6,1] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,6,1,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,2,6,4,1] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,4,2,1,6] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,4,2,6,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,4,6,2,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,6,2,1,4] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,6,2,4,1] => [[1,4,6],[2,5],[3]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,5,6,4,2,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,1,4,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,1,5,4] => [[1,4],[2,5],[3,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,4,1,5] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,4,5,1] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,5,1,4] => [[1,4],[2,5],[3,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,2,5,4,1] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,4,2,1,5] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,4,2,5,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,4,5,2,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,5,2,1,4] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,5,2,4,1] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,1,2,3,5,6] => [[1,2,3,5,6],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,2,5,3,6] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,2,5,6,3] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,3,2,5,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,3,5,2,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,3,5,6,2] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,5,2,3,6] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,5,2,6,3] => [[1,2,3],[4,5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,5,3,2,6] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,5,3,6,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,1,5,6,2,3] => [[1,2,3],[4,5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,1,5,6,3,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,2,1,3,5,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,1,5,3,6] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,1,5,6,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,3,5,1,6] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,3,5,6,1] => [[1,3,5,6],[2],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,1,6,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,3,1,6] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,3,6,1] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,6,1,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,2,5,6,3,1] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,3,1,2,5,6] => [[1,2,5,6],[3],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,1,5,2,6] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,1,5,6,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,2,5,1,6] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,2,5,6,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,2,6,1,5] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,2,6,5,1] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,5,1,2,6] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,1,6,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,2,1,6] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,5,2,6,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,5,6,1,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,3,5,6,2,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,3,6,2,1,5] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,6,2,5,1] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,3,6,5,2,1] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,5,1,2,3,6] => [[1,2,3,6],[4,5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,1,2,6,3] => [[1,2,3],[4,5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,1,3,2,6] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,1,3,6,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,1,6,2,3] => [[1,2,3],[4,5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,1,6,3,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,2,1,3,6] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,2,1,6,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,2,3,1,6] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,2,3,6,1] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,2,6,1,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,2,6,3,1] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,3,1,6,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,3,2,1,6] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,5,3,2,6,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,5,3,6,1,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,3,6,2,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,6,1,3,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,6,2,1,3] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,6,2,3,1] => [[1,3,6],[2,5],[4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[4,5,6,3,1,2] => [[1,2,6],[3,5],[4]] => [2,4] => ([(3,5),(4,5)],6) => 2
[4,5,6,3,2,1] => [[1,5,6],[2],[3],[4]] => [6] => ([],6) => 1
[4,6,3,2,1,5] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,6,3,2,5,1] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,6,3,5,2,1] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[4,6,5,3,2,1] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,1,2,3,4,6] => [[1,2,3,4,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,1,2,3,6,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,1,2,4,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,2,4,6,3] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,2,6,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,1,2,6,4,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,4,2,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,4,2,6,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,4,3,6,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,4,6,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,4,6,3,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,1,6,2,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,1,6,2,4,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,6,4,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,1,6,4,3,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,2,1,3,4,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,1,3,6,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,1,4,3,6] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,1,4,6,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,1,6,3,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,1,6,4,3] => [[1,3],[2,4],[5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,3,1,4,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,3,1,6,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,3,4,6,1] => [[1,3,4,6],[2],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,3,6,4,1] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,4,1,3,6] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,4,1,6,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,4,3,6,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,4,6,1,3] => [[1,3,6],[2,4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,4,6,3,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,6,1,3,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,6,1,4,3] => [[1,3],[2,4],[5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,6,3,1,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,6,3,4,1] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,2,6,4,3,1] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,3,2,1,4,6] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,2,1,6,4] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,2,4,6,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,2,6,4,1] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,4,2,1,6] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,4,2,6,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,4,6,2,1] => [[1,4,6],[2],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,6,2,1,4] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,6,2,4,1] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,3,6,4,2,1] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,4,1,2,3,6] => [[1,2,3,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,1,2,6,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,1,3,2,6] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,1,3,6,2] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,1,6,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,1,6,3,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,2,1,3,6] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,2,1,6,3] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,2,3,1,6] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,2,3,6,1] => [[1,3,6],[2],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,2,6,1,3] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,2,6,3,1] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,3,1,2,6] => [[1,2,6],[3],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,3,1,6,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [6] => ([],6) => 1
[5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5]] => [6] => ([],6) => 1
[5,4,3,6,1,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5]] => [6] => ([],6) => 1
[5,4,6,1,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,6,1,3,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,6,2,3,1] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,4,6,3,1,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,4,6,3,2,1] => [[1,6],[2],[3],[4],[5]] => [6] => ([],6) => 1
[5,6,1,2,3,4] => [[1,2,3,4],[5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,1,2,4,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,1,4,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,1,4,3,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,6,2,1,3,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,2,1,4,3] => [[1,3],[2,4],[5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,2,3,1,4] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,2,3,4,1] => [[1,3,4],[2,6],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,2,4,1,3] => [[1,3],[2,4],[5,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,2,4,3,1] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,3,2,1,4] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,3,2,4,1] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,3,4,2,1] => [[1,4],[2,6],[3],[5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[5,6,4,1,2,3] => [[1,2,3],[4,6],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,4,1,3,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,6,4,2,1,3] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,4,2,3,1] => [[1,3],[2,6],[4],[5]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => [2,4] => ([(3,5),(4,5)],6) => 2
[5,6,4,3,2,1] => [[1,6],[2],[3],[4],[5]] => [6] => ([],6) => 1
[6,1,2,3,4,5] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,1,2,3,5,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,1,2,5,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,1,2,5,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,1,5,2,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,1,5,2,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,1,5,4,2,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,1,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,2,1,3,4,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,1,3,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,1,5,3,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,1,5,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,2,3,1,4,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,3,1,5,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,3,4,1,5] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,3,5,1,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,5,1,3,4] => [[1,3,4],[2,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,5,1,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,2,5,3,1,4] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,5,3,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,2,5,4,1,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,3,2,1,4,5] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,2,1,5,4] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,2,4,1,5] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,2,5,1,4] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,4,2,1,5] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,4,2,5,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,4,5,2,1] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,5,2,1,4] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,5,2,4,1] => [[1,4],[2,5],[3],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,3,5,4,2,1] => [[1,4],[2],[3],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,3,2,1,5] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,1,2,3,4] => [[1,2,3,4],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,1,2,4,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,1,4,2,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,1,4,3,2] => [[1,2],[3],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,5,2,1,3,4] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,2,1,4,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,2,3,1,4] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,2,3,4,1] => [[1,3,4],[2],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,2,4,1,3] => [[1,3],[2,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,2,4,3,1] => [[1,3],[2],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,3,2,1,4] => [[1,4],[2],[3],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,3,2,4,1] => [[1,4],[2],[3],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[6,5,4,1,2,3] => [[1,2,3],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,4,1,3,2] => [[1,2],[3],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,5,4,2,1,3] => [[1,3],[2],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,4,2,3,1] => [[1,3],[2],[4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[6,5,4,3,1,2] => [[1,2],[3],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 2
[6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [6] => ([],6) => 1
[1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,4,7,5,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,7,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,7,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,4,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,3,7,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,1,7,3,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,4,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,1,7,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,1,7,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,7,1,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,7,5,1,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,7,5,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,7,1,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,7,4,1,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,7,4,5,1,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,3,7,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,7,3,1,4,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,7,3,4,1,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,7,3,4,5,1,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[2,7,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,1,4,7,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,1,7,4,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,1,7,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,5,7,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,7,1,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,7,5,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,4,7,5,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,7,1,4,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,7,4,1,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,7,4,5,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,2,7,4,5,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,1,7,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,5,7,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,7,1,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,7,5,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,2,7,5,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,2,1,7,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,2,7,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,2,7,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,7,2,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,7,2,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,5,7,6,2,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,2,1,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,2,5,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,2,5,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,5,2,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,5,2,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,4,7,5,6,2,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,2,1,4,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,2,4,1,5,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,2,4,5,1,6] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,2,4,5,6,1] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,2,1,5,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,2,5,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,2,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,5,2,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,5,2,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[3,7,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,1,7,5,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,5,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,5,7,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,5,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,7,1,5,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,7,5,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,2,7,5,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,2,7,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,7,2,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,7,2,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,5,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,2,1,5,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,2,5,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,2,5,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,5,2,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,5,2,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,3,7,5,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,2,7,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,7,2,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,7,2,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,3,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,7,3,2,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,7,3,2,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,7,3,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,5,7,6,3,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,2,1,5,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,2,5,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,2,5,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,5,2,1,6] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,5,2,6,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,3,5,6,2,1] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,5,3,2,1,6] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,5,3,2,6,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,5,3,6,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[4,7,5,6,3,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,2,7,1,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,7,2,1,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,7,2,6,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,3,7,6,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,7,3,2,1,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,7,3,2,6,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,7,3,6,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,4,7,6,3,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,7,4,3,2,1,6] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,7,4,3,2,6,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,7,4,3,6,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,7,4,6,3,2,1] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[5,7,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,2,1,3,4,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,2,3,1,4,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,2,3,4,1,5,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,2,3,4,5,1,6] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,2,1,4,5,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,2,4,1,5,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,2,4,5,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,2,1,5,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,2,5,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,2,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,5,2,1,6] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,5,2,6,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,2,1,5,6] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,2,5,1,6] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,5,2,1,6] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,5,2,6,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,5,3,2,1,6] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,5,3,2,6,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,5,3,6,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,4,5,6,3,2,1] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,5,4,6,3,2,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[7,5,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[8,6,7,5,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,6,5,7,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,6,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,6,4,7,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,6,7,3,2,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,6,5,4,3,7,2,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,5,6,7,2,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,5,6,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,3,6,2,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,5,6,2,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,3,2,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,5,2,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,2,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,6,4,3,2,1,7] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,6,3,2,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,3,6,2,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,5,6,2,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,5,6,2,1,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,4,3,2,6,1,7] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,5,2,6,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,2,4,5,6,1,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,5,3,2,1,6,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,5,2,1,6,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,5,2,1,6,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,4,2,1,5,6,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,7,5,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,8,7,4,3,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,8,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,8,7,3,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,8,7,3,2,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,8,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,3,8,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,3,8,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,6,8,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,6,8,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,6,8,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,2,8,7,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,6,3,2,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,6,2,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,6,2,8,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,6,2,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,6,8,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,5,6,8,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,5,6,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,5,6,8,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,6,8,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,3,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,6,3,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,3,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,6,2,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,6,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,6,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,6,2,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,6,1,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,6,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,2,6,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,5,6,1,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,5,6,1,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,2,1,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,1,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,2,1,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,1,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,8,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,8,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,8,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,8,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,5,8,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,8,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,8,4,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,8,5,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,8,6,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,8,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,8,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,8,1,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,8,1,5,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,1,3,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,1,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,1,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,1,8,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,8,1,6,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,6,8,1,7] => [[1,3,4,5,6,7],[2,8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,8,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,8,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,8,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,8,5,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,7],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,8,1,4,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,8,1,5,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,8,1,6,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,2,8,1,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,1,8,5,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,1,5,8,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,3,2,8,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,4,2,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,2,5,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,8,6,2,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,8,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,8,6,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,1,8,6,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,2,6,8,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,2,8,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,5,6,8,1,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,5,6,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,8,4,3,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,3,5,2,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,8,2,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,6,2,8,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,5,2,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,1,8,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,1,5,8,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,3,2,1,5,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,2,1,5,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,8,6,3,2,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,1,8,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,8,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,1,4,8,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,2,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,1,8,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,8,5,6,1,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,8,5,1,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,5,6,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,8,6,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,6,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,8,3,2,1,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,5,7,4,3,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,3,2,1,6,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,5,4,3,2,1,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,3,2,5,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,5,2,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,5,1,8,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,5,2,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,8,3,2,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,5,6,3,2,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,8,2,1,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,2,1,6,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,5,6,8,1,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,5,4,3,2,7,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,5,4,3,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,3,8,2,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,5,8,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,5,3,6,2,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,2,1,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,2,1,4,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,8,3,2,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,8,3,6,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,3,6,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,3,8,2,7,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,5,6,8,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,4,5,8,6,1,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,1,8,4,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,6,3,8,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,5,2,1,6,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,8,4,3,2,1,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,8,3,2,7,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,2,4,5,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,8,4,7,3,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,6,8,2,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,3,2,6,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,3,2,5,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,6,3,8,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,8,1,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,2,5,1,8,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,8,4,3,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,6,8,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,8,3,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,6,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,2,5,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,2,6,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,8,4,3,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,2,8,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,8,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,4,2,1,5,6,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,3,8,4,1,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,8,1,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,8,4,1,5,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,3,2,8,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,6,4,3,2,1,7] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,8,6,7,2,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,4,5,6,2,1,7] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,8,5,4,7,3,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,4,5,2,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,6,3,8,2,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,8,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,8,2,1,6,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[6,5,4,8,3,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,8,6,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,8,4,5,6,7,2,1] => [[1,4,5,6,7],[2],[3],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,8,3,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,2,8,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,8,2,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,6,3,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,3,8,6,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,3,8,2,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,6,2,8,1,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,8,6,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,5,3,2,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,8,2,6,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,3,2,6,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,2,1,8,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,6,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,3,6,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,5,3,2,6,1,7] => [[1,5,6,7],[2],[3],[4],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,2,8,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[2,8,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,5,8,3,2,6,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,8,2,5,6,1,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,2,8,5,1,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,8,5,6,2,7,1] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,6,4,3,8,2,7,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,2,4,5,8,1,6,7] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,4,8,6,3,2,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,6,7,2,1] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[3,4,5,6,8,2,7,1] => [[1,4,5,6,7],[2,8],[3]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,6,4,7,3,2,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[5,8,4,3,2,6,1,7] => [[1,6,7],[2,8],[3],[4],[5]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,8,3,5,2,1,6,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[4,3,5,6,2,8,1,7] => [[1,5,6,7],[2,8],[3],[4]] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
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Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,16
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + 2\ q^{2}$
$F_{4} = 8\ q + 16\ q^{2}$
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
peak composition
Description
The composition corresponding to the peak set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
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