Identifier
-
Mp00070:
Permutations
—Robinson-Schensted recording tableau⟶
Standard tableaux
Mp00295: Standard tableaux —valley composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001570: Graphs ⟶ ℤ
Values
[1,2,3] => [[1,2,3]] => [3] => ([],3) => 3
[1,3,2] => [[1,2],[3]] => [3] => ([],3) => 3
[2,1,3] => [[1,3],[2]] => [2,1] => ([(0,2),(1,2)],3) => 1
[2,3,1] => [[1,2],[3]] => [3] => ([],3) => 3
[3,1,2] => [[1,3],[2]] => [2,1] => ([(0,2),(1,2)],3) => 1
[3,2,1] => [[1],[2],[3]] => [3] => ([],3) => 3
[1,2,3,4] => [[1,2,3,4]] => [4] => ([],4) => 4
[1,2,4,3] => [[1,2,3],[4]] => [4] => ([],4) => 4
[1,3,2,4] => [[1,2,4],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,3,4,2] => [[1,2,3],[4]] => [4] => ([],4) => 4
[1,4,2,3] => [[1,2,4],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,4,3,2] => [[1,2],[3],[4]] => [4] => ([],4) => 4
[2,1,3,4] => [[1,3,4],[2]] => [2,2] => ([(1,3),(2,3)],4) => 2
[2,1,4,3] => [[1,3],[2,4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[2,3,1,4] => [[1,2,4],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,3,4,1] => [[1,2,3],[4]] => [4] => ([],4) => 4
[2,4,1,3] => [[1,2],[3,4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,4,3,1] => [[1,2],[3],[4]] => [4] => ([],4) => 4
[3,1,2,4] => [[1,3,4],[2]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,1,4,2] => [[1,3],[2,4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,2,1,4] => [[1,4],[2],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,2,4,1] => [[1,3],[2],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[3,4,1,2] => [[1,2],[3,4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,4,2,1] => [[1,2],[3],[4]] => [4] => ([],4) => 4
[4,1,2,3] => [[1,3,4],[2]] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,1,3,2] => [[1,3],[2],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,2,1,3] => [[1,4],[2],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,2,3,1] => [[1,3],[2],[4]] => [2,2] => ([(1,3),(2,3)],4) => 2
[4,3,1,2] => [[1,4],[2],[3]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,3,2,1] => [[1],[2],[3],[4]] => [4] => ([],4) => 4
[1,2,3,4,5] => [[1,2,3,4,5]] => [5] => ([],5) => 5
[1,2,3,5,4] => [[1,2,3,4],[5]] => [5] => ([],5) => 5
[1,2,4,3,5] => [[1,2,3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,2,4,5,3] => [[1,2,3,4],[5]] => [5] => ([],5) => 5
[1,2,5,3,4] => [[1,2,3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,2,5,4,3] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[1,3,2,4,5] => [[1,2,4,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,3,2,5,4] => [[1,2,4],[3,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,3,4,2,5] => [[1,2,3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,3,4,5,2] => [[1,2,3,4],[5]] => [5] => ([],5) => 5
[1,3,5,2,4] => [[1,2,3],[4,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,3,5,4,2] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[1,4,2,3,5] => [[1,2,4,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,2,5,3] => [[1,2,4],[3,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,3,2,5] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,4,3,5,2] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,4,5,2,3] => [[1,2,3],[4,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,4,5,3,2] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[1,5,2,3,4] => [[1,2,4,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,2,4,3] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,3,2,4] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,5,3,4,2] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,5,4,2,3] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,5,4,3,2] => [[1,2],[3],[4],[5]] => [5] => ([],5) => 5
[2,1,3,4,5] => [[1,3,4,5],[2]] => [2,3] => ([(2,4),(3,4)],5) => 3
[2,1,3,5,4] => [[1,3,4],[2,5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[2,1,4,3,5] => [[1,3,5],[2,4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,1,4,5,3] => [[1,3,4],[2,5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[2,1,5,3,4] => [[1,3,5],[2,4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,1,5,4,3] => [[1,3],[2,4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[2,3,1,4,5] => [[1,2,4,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,3,1,5,4] => [[1,2,4],[3,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,3,4,1,5] => [[1,2,3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,3,4,5,1] => [[1,2,3,4],[5]] => [5] => ([],5) => 5
[2,3,5,1,4] => [[1,2,3],[4,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,3,5,4,1] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[2,4,1,3,5] => [[1,2,5],[3,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,1,5,3] => [[1,2,4],[3,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,3,1,5] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,3,5,1] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,4,5,1,3] => [[1,2,3],[4,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,5,3,1] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[2,5,1,3,4] => [[1,2,5],[3,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,1,4,3] => [[1,2],[3,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,3,1,4] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,3,4,1] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[2,5,4,1,3] => [[1,2],[3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,4,3,1] => [[1,2],[3],[4],[5]] => [5] => ([],5) => 5
[3,1,2,4,5] => [[1,3,4,5],[2]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,1,2,5,4] => [[1,3,4],[2,5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,1,4,2,5] => [[1,3,5],[2,4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,1,4,5,2] => [[1,3,4],[2,5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,1,5,2,4] => [[1,3,5],[2,4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,1,5,4,2] => [[1,3],[2,4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,2,1,4,5] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,2,1,5,4] => [[1,4],[2,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,2,4,1,5] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,2,4,5,1] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,2,5,1,4] => [[1,3],[2,5],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,2,5,4,1] => [[1,3],[2,4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[3,4,1,2,5] => [[1,2,5],[3,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,4,1,5,2] => [[1,2,4],[3,5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,4,2,1,5] => [[1,2,5],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,2,5,1] => [[1,2,4],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,4,5,1,2] => [[1,2,3],[4,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,5,2,1] => [[1,2,3],[4],[5]] => [5] => ([],5) => 5
[3,5,1,2,4] => [[1,2,5],[3,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,5,1,4,2] => [[1,2],[3,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,5,2,1,4] => [[1,2],[3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,2,4,1] => [[1,2],[3,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[3,5,4,1,2] => [[1,2],[3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
>>> Load all 870 entries. <<<[3,5,4,2,1] => [[1,2],[3],[4],[5]] => [5] => ([],5) => 5
[4,1,2,3,5] => [[1,3,4,5],[2]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,1,2,5,3] => [[1,3,4],[2,5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,1,3,2,5] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[4,1,3,5,2] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,1,5,2,3] => [[1,3,5],[2,4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[4,1,5,3,2] => [[1,3],[2,4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,2,1,3,5] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,2,1,5,3] => [[1,4],[2,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,2,3,1,5] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[4,2,3,5,1] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,2,5,1,3] => [[1,3],[2,5],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[4,2,5,3,1] => [[1,3],[2,4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,3,1,2,5] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,3,1,5,2] => [[1,4],[2,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,3,2,1,5] => [[1,5],[2],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,3,2,5,1] => [[1,4],[2],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,3,5,1,2] => [[1,3],[2,5],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[4,3,5,2,1] => [[1,3],[2],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[4,5,1,2,3] => [[1,2,5],[3,4]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,5,1,3,2] => [[1,2],[3,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,5,2,1,3] => [[1,2],[3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,2,3,1] => [[1,2],[3,4],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[4,5,3,1,2] => [[1,2],[3,5],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,3,2,1] => [[1,2],[3],[4],[5]] => [5] => ([],5) => 5
[5,1,2,3,4] => [[1,3,4,5],[2]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,1,2,4,3] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,1,3,2,4] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[5,1,3,4,2] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,1,4,2,3] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[5,1,4,3,2] => [[1,3],[2],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,2,1,3,4] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,2,1,4,3] => [[1,4],[2,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,2,3,1,4] => [[1,3,5],[2],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[5,2,3,4,1] => [[1,3,4],[2],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,2,4,1,3] => [[1,3],[2,5],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[5,2,4,3,1] => [[1,3],[2],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,3,1,2,4] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,3,1,4,2] => [[1,4],[2,5],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,3,2,1,4] => [[1,5],[2],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,2,4,1] => [[1,4],[2],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,3,4,1,2] => [[1,3],[2,5],[4]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[5,3,4,2,1] => [[1,3],[2],[4],[5]] => [2,3] => ([(2,4),(3,4)],5) => 3
[5,4,1,2,3] => [[1,4,5],[2],[3]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,4,1,3,2] => [[1,4],[2],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,4,2,1,3] => [[1,5],[2],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,2,3,1] => [[1,4],[2],[3],[5]] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[5,4,3,1,2] => [[1,5],[2],[3],[4]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [5] => ([],5) => 5
[1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [6] => ([],6) => 6
[1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [6] => ([],6) => 6
[1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => [6] => ([],6) => 6
[1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => [6] => ([],6) => 6
[1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,3,6,4] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,3,5,4] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,4,3,5] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,3,4] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,3,2,6,4,5] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => [6] => ([],6) => 6
[1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,2,6,4] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,2,5,4] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,4,2,5] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,4,5,2] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,2,4] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,2,3,6,5] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,2,5,3,6] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,5,6,3] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,2,6,3,5] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,6,5,3] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,3,6,2,5] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,2,6,3] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,3,2,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,2,5,3] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,3,2,5] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,3,5,2] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,5,2,3] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,2,3,6,4] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,2,4,3,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,4,6,3] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,2,6,3,4] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,6,4,3] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,3,2,4,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,3,2,6,4] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,4,6,2] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,6,4,2] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,4,2,3,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,2,6,3] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,4,6,2,3] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,6,3,2] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,6,2,4,3] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,6,3,2,4] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,6,3,4,2] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,2,3,5,4] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,2,4,3,5] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,4,5,3] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,2,5,3,4] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,2,5,4,3] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,3,2,4,5] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,3,2,5,4] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,3,4,2,5] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,3,5,2,4] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,4,2,3,5] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,4,2,5,3] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,4,3,2,5] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,4,5,2,3] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,6,4,5,3,2] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[1,6,5,2,3,4] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,5,2,4,3] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,5,3,2,4] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,5,3,4,2] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,5,4,2,3] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [6] => ([],6) => 6
[2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,3,6,4,5] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,4,6,3,5] => [[1,3,4],[2,5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,5,3,4,6] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,3,6,4] => [[1,3,5],[2,4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,1,6,3,4,5] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,3,5,4] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,3,5] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,3,4] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,3,1,6,4,5] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => [6] => ([],6) => 6
[2,3,4,6,1,5] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[2,3,5,1,4,6] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,1,6,4] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,1,4] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[2,3,6,1,4,5] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,1,5,4] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,1,5] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,5,1] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,1,4] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[2,4,1,3,5,6] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,1,3,6,5] => [[1,2,5],[3,4,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,1,5,3,6] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,1,5,6,3] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,1,6,3,5] => [[1,2,4],[3,5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,1,6,5,3] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,3,6,1,5] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,4,5,1,3,6] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,1,6,3] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,3,1,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,6,1,3] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[2,4,6,1,3,5] => [[1,2,3],[4,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,1,5,3] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,3,1,5] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,3,5,1] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,5,1,3] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[2,5,1,3,4,6] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,1,3,6,4] => [[1,2,5],[3,4,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,1,4,3,6] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,1,4,6,3] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,1,6,3,4] => [[1,2,4],[3,5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,1,6,4,3] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,3,1,4,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,1,6,4] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,4,1,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,3,4,6,1] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,3,6,1,4] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,3,6,4,1] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,4,1,3,6] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,1,6,3] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,6,1,3] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,5,4,6,3,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,5,6,1,3,4] => [[1,2,3],[4,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,1,4,3] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,3,1,4] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,3,4,1] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,4,1,3] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[2,6,1,3,4,5] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,1,3,5,4] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,1,4,3,5] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,1,4,5,3] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,1,5,3,4] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,3,1,4,5] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,1,5,4] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,4,1,5] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,3,4,5,1] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,3,5,1,4] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,3,5,4,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,4,1,3,5] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,1,5,3] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,3,1,5] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,3,5,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,5,1,3] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,6,4,5,3,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[2,6,5,1,3,4] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,3,1,4] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,3,4,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => [6] => ([],6) => 6
[3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,2,4,6,5] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,2,5,4,6] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,2,5,6,4] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,2,6,4,5] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,2,6,5,4] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,4,2,5,6] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,2,6,5] => [[1,3,5],[2,4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,2,6] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,6,2] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,4,6,2,5] => [[1,3,4],[2,5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,6,5,2] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,5,2,4,6] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,2,6,4] => [[1,3,5],[2,4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,4,2,6] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,4,6,2] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,6,2,4] => [[1,3,4],[2,5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,5,6,4,2] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,1,6,2,4,5] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,2,5,4] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,4,2,5] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,4,5,2] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,5,2,4] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,6,5,4,2] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,2,1,6,4,5] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,2,4,6,1,5] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,2,5,1,4,6] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,1,6,4] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,6,1,4] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,5,6,4,1] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,2,6,1,4,5] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,1,5,4] => [[1,3],[2,5],[4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,4,1,5] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,4,5,1] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,5,1,4] => [[1,3],[2,4],[5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,1,5,2,6] => [[1,2,4,6],[3,5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,1,5,6,2] => [[1,2,4,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,1,6,2,5] => [[1,2,4],[3,5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,1,6,5,2] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,2,6,1,5] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,2,6,5,1] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,1,6,2] => [[1,2,3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => [6] => ([],6) => 6
[3,4,6,1,2,5] => [[1,2,3],[4,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,1,5,2] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,2,1,5] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,2,5,1] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,5,1,2] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[3,5,1,2,4,6] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,1,2,6,4] => [[1,2,5],[3,4,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,1,4,2,6] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,1,4,6,2] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,1,6,4,2] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,2,1,4,6] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,1,6,4] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,4,1,6] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,2,4,6,1] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,2,6,1,4] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,2,6,4,1] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,4,1,2,6] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,1,6,2] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,2,1,6] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,2,6,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,6,1,2] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,5,4,6,2,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,5,6,1,2,4] => [[1,2,3],[4,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,1,4,2] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,2,1,4] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,2,4,1] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,4,1,2] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[3,6,1,2,4,5] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,1,2,5,4] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,1,4,2,5] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,1,5,2,4] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,1,5,4,2] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,2,1,4,5] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,1,5,4] => [[1,2],[3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,4,1,5] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,2,4,5,1] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,2,5,1,4] => [[1,2],[3,4],[5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,2,5,4,1] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,4,1,2,5] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,1,5,2] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,2,1,5] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,2,5,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,5,1,2] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,6,4,5,2,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[3,6,5,1,2,4] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,1,4,2] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,2,1,4] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,2,4,1] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,4,1,2] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => [6] => ([],6) => 6
[4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,2,3,6,5] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,2,5,3,6] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,2,5,6,3] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,2,6,3,5] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,2,6,5,3] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,3,2,5,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,2,6,5] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,2,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,6,2] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,3,6,2,5] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,6,5,2] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,5,2,3,6] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,2,6,3] => [[1,3,5],[2,4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,3,2,6] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,3,6,2] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,6,2,3] => [[1,3,4],[2,5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,5,6,3,2] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,1,6,2,3,5] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,2,5,3] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,3,2,5] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,3,5,2] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,5,2,3] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,6,5,3,2] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,2,1,3,6,5] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,2,1,5,3,6] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,5,6,3] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,2,1,6,3,5] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,6,5,3] => [[1,4],[2,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,2,3,6,1,5] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,6,5,1] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,1,6,3] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,3,1,6] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,3,6,1] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,6,1,3] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,5,6,3,1] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,2,6,1,3,5] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,3,1,5] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,3,5,1] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,5,1,3] => [[1,3],[2,4],[5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,6,5,3,1] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,1,2,6,5] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,1,5,2,6] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,5,6,2] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,1,6,2,5] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,6,5,2] => [[1,4],[2,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,2,6,1,5] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,1,6,2] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,3,6,1,2,5] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,1,5,2] => [[1,3],[2,5],[4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,2,1,5] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,2,5,1] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,5,1,2] => [[1,3],[2,4],[5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,1,2,6,3] => [[1,2,5],[3,4,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,1,3,2,6] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,1,3,6,2] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,1,6,2,3] => [[1,2,4],[3,5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,1,6,3,2] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,1,6,3] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,2,6,1,3] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,2,6,3,1] => [[1,2,4],[3,5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,1,6,2] => [[1,2,5],[3,6],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,1,3,2] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => [6] => ([],6) => 6
[4,6,1,2,3,5] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,1,2,5,3] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,1,3,2,5] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,1,3,5,2] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,1,5,2,3] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,1,5,3,2] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,2,1,3,5] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,1,5,3] => [[1,2],[3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,3,1,5] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,2,3,5,1] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,2,5,1,3] => [[1,2],[3,4],[5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,2,5,3,1] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,3,1,2,5] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,2,1,5] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,2,5,1] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,5,1,2] => [[1,2],[3,4],[5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,6,3,5,2,1] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[4,6,5,1,2,3] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,1,3,2] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,2,1,3] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,2,3,1] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,3,1,2] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => [6] => ([],6) => 6
[5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,2,3,6,4] => [[1,3,4,5],[2,6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,2,4,3,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,2,4,6,3] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,2,6,3,4] => [[1,3,4,6],[2,5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,2,6,4,3] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,3,2,4,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,2,6,4] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,4,2,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,4,6,2] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,3,6,2,4] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,3,6,4,2] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,4,2,3,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,2,6,3] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,3,2,6] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,3,6,2] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,6,2,3] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,4,6,3,2] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,1,6,2,3,4] => [[1,3,5,6],[2,4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,2,4,3] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,3,2,4] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,3,4,2] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,4,2,3] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,1,6,4,3,2] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,2,1,3,6,4] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,2,1,4,3,6] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,4,6,3] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,2,1,6,3,4] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,1,6,4,3] => [[1,4],[2,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,3,1,6,4] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,3,6,4,1] => [[1,3,4],[2,5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,2,4,1,3,6] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,1,6,3] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,3,6,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,6,1,3] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,4,6,3,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,2,6,1,3,4] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,1,4,3] => [[1,3],[2,5],[4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,3,1,4] => [[1,3,6],[2,4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,3,4,1] => [[1,3,5],[2,4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,2,6,4,3,1] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,1,2,6,4] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,1,4,2,6] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,1,4,6,2] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,1,6,2,4] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,1,6,4,2] => [[1,4],[2,5],[3,6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,1,6,4] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,2,6,4,1] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,1,6,2] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,3,6,1,2,4] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,1,4,2] => [[1,3],[2,5],[4,6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,2,1,4] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,2,4,1] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,4,1,2] => [[1,3],[2,4],[5,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,3,6,4,2,1] => [[1,3],[2,4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,1,2,6,3] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,1,3,2,6] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,3,6,2] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,1,6,2,3] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,1,6,3,2] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,1,6,3] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,2,6,1,3] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,2,6,3,1] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,1,6,2] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,1,3,2] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,1,2,4,3] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,1,3,2,4] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,1,3,4,2] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,1,4,2,3] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,1,4,3,2] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,1,4,3] => [[1,2],[3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,2,4,1,3] => [[1,2],[3,4],[5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,2,4,3,1] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,1,4,2] => [[1,2],[3,5],[4,6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,1,3,2] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => [6] => ([],6) => 6
[6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,2,3,5,4] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,2,4,3,5] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,2,4,5,3] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,2,5,3,4] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,2,5,4,3] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,3,2,4,5] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,2,5,4] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,4,2,5] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,4,5,2] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,3,5,2,4] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,3,5,4,2] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,4,2,3,5] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,2,5,3] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,3,2,5] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,3,5,2] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,5,2,3] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,4,5,3,2] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,1,5,2,3,4] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,2,4,3] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,3,2,4] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,3,4,2] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,4,2,3] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,1,5,4,3,2] => [[1,3],[2],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,2,1,3,5,4] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,2,1,4,3,5] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,4,5,3] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,2,1,5,3,4] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,1,5,4,3] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,3,1,5,4] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,2,3,5,1,4] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,2,4,1,3,5] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,1,5,3] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,3,1,5] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,5,1,3] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,4,5,3,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,2,5,1,3,4] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,1,4,3] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,3,1,4] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,3,4,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,4,1,3] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,1,2,5,4] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,1,4,2,5] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,1,4,5,2] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,1,5,2,4] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,1,5,4,2] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,1,5,4] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,2,5,1,4] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,1,5,2] => [[1,3,5],[2,6],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,3,5,1,2,4] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,1,4,2] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,2,1,4] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,2,4,1] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,4,1,2] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,3,5,4,2,1] => [[1,3],[2],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,1,2,5,3] => [[1,4,5],[2,6],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,1,3,2,5] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,3,5,2] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,1,5,2,3] => [[1,4,6],[2,5],[3]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,1,5,3,2] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,1,5,3] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,2,5,1,3] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,2,5,3,1] => [[1,4],[2,5],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,1,5,2] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,1,3,2] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => [2,4] => ([(3,5),(4,5)],6) => 4
[6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,1,2,4,3] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,1,3,2,4] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,3,4,2] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,1,4,2,3] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,1,4,3,2] => [[1,4],[2],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,1,4,3] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,2,4,1,3] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,2,4,3,1] => [[1,4],[2],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,1,4,2] => [[1,5],[2,6],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 4
[6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,1,3,2] => [[1,5],[2],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [6] => ([],6) => 6
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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:
2,0,4 16,0,8 16,0,88,0,16 272,0,416,0,32
F3=2 q+4 q3
F4=16 q2+8 q4
F5=16 q+88 q3+16 q5
F6=272 q2+416 q4+32 q6
Description
The minimal number of edges to add to make a graph Hamiltonian.
A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
A graph is Hamiltonian if it contains a cycle as a subgraph, which contains all vertices.
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
valley composition
Description
The composition corresponding to the valley 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≤i≤n−1 is a valley if i−1 is a descent and i is an ascent.
This map returns the composition c1,…,ck of n such that {c1,c1+c2,…,c1+⋯+ck} is the valley 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≤i≤n−1 is a valley if i−1 is a descent and i is an ascent.
This map returns the composition c1,…,ck of n such that {c1,c1+c2,…,c1+⋯+ck} is the valley set of T.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording 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 recording 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 recording tableau.
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