Identifier
-
Mp00131:
Permutations
—descent bottoms⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤ
Values
[1] => => [1] => ([],1) => 0
[1,2] => 0 => [2] => ([],2) => 0
[2,1] => 1 => [1,1] => ([(0,1)],2) => 1
[1,2,3] => 00 => [3] => ([],3) => 0
[2,1,3] => 10 => [1,2] => ([(1,2)],3) => 1
[2,3,1] => 10 => [1,2] => ([(1,2)],3) => 1
[3,1,2] => 10 => [1,2] => ([(1,2)],3) => 1
[3,2,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[1,2,3,4] => 000 => [4] => ([],4) => 0
[2,1,3,4] => 100 => [1,3] => ([(2,3)],4) => 1
[2,3,1,4] => 100 => [1,3] => ([(2,3)],4) => 1
[2,3,4,1] => 100 => [1,3] => ([(2,3)],4) => 1
[2,4,1,3] => 100 => [1,3] => ([(2,3)],4) => 1
[3,1,2,4] => 100 => [1,3] => ([(2,3)],4) => 1
[3,1,4,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[3,2,1,4] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[3,2,4,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[3,4,1,2] => 100 => [1,3] => ([(2,3)],4) => 1
[3,4,2,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[4,1,2,3] => 100 => [1,3] => ([(2,3)],4) => 1
[4,1,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[4,2,1,3] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[4,2,3,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[4,3,2,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,2,3,4,5] => 0000 => [5] => ([],5) => 0
[1,2,3,5,4] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,5,4,3] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[2,1,3,4,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,3,1,4,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,3,4,1,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,3,4,5,1] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,3,5,1,4] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,4,1,3,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,4,5,1,3] => 1000 => [1,4] => ([(3,4)],5) => 1
[2,5,1,3,4] => 1000 => [1,4] => ([(3,4)],5) => 1
[3,1,2,4,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[3,1,4,2,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,1,4,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,1,5,2,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,2,1,4,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,2,4,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,2,4,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,2,5,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,4,1,2,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[3,4,1,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,4,2,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,4,2,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,4,5,1,2] => 1000 => [1,4] => ([(3,4)],5) => 1
[3,4,5,2,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,5,1,2,4] => 1000 => [1,4] => ([(3,4)],5) => 1
[3,5,1,4,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,5,2,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[3,5,2,4,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,1,2,3,5] => 1000 => [1,4] => ([(3,4)],5) => 1
[4,1,3,2,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,1,3,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,1,5,2,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,1,5,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,2,1,3,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,2,1,5,3] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,2,3,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,2,3,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,2,5,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,2,5,3,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,1,5,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,2,1,5] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,2,5,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,3,5,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[4,5,1,2,3] => 1000 => [1,4] => ([(3,4)],5) => 1
[4,5,1,3,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,5,2,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,5,2,3,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[4,5,3,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,1,2,3,4] => 1000 => [1,4] => ([(3,4)],5) => 1
[5,1,3,2,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,1,3,4,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,1,4,2,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,1,4,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,1,3,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,2,1,4,3] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,2,3,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,2,3,4,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,2,4,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[5,2,4,3,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,1,4,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,2,1,4] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,2,4,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,3,4,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,2,1] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[1,2,3,4,5,6] => 00000 => [6] => ([],6) => 0
[1,2,3,5,4,6] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,5,6,4] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,3,6,4,5] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,2,5,3,6,4] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,5,4,3,6] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,5,4,6,3] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,5,6,4,3] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,6,3,5,4] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,6,4,3,5] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,6,4,5,3] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,1,3,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
>>> Load all 2017 entries. <<<[2,3,1,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,4,1,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,4,5,1,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,4,5,6,1] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,4,6,1,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,5,1,4,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,5,6,1,4] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,3,6,1,4,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,4,1,3,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,4,5,1,3,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,4,5,6,1,3] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,4,6,1,3,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,5,1,3,4,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,5,6,1,3,4] => 10000 => [1,5] => ([(4,5)],6) => 1
[2,6,1,3,4,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,1,2,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,1,4,2,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,4,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,5,2,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,5,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,1,6,2,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,1,4,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,4,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,4,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,5,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,5,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,2,6,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,1,2,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,4,1,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,1,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,1,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,2,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,2,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,2,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,2,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,5,1,2,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,4,5,1,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,5,2,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,5,2,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,5,6,1,2] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,4,5,6,2,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,6,1,2,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,4,6,1,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,6,2,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,4,6,2,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,1,2,4,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,5,1,4,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,1,4,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,1,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,2,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,2,4,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,2,4,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,2,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,6,1,2,4] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,5,6,1,4,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,6,2,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,5,6,2,4,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,1,2,4,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[3,6,1,4,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,1,4,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,1,5,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,2,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,2,4,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,2,4,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[3,6,2,5,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,2,3,5,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[4,1,3,2,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,3,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,5,2,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,5,2,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,5,3,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,5,3,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,5,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,5,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,6,2,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,1,6,2,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,6,3,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,6,3,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,3,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,1,5,3,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,5,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,6,3,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,3,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,3,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,5,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,5,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,5,3,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,5,3,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,5,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,5,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,6,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,2,6,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,6,3,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,6,3,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,5,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,5,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,6,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,1,5,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,5,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,5,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,6,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,6,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,6,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,6,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,1,2,3,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[4,5,1,3,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,1,3,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,1,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,1,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,2,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,2,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,2,3,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,2,3,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,2,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,2,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,6,1,2,3] => 10000 => [1,5] => ([(4,5)],6) => 1
[4,5,6,1,3,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,6,2,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,6,2,3,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,5,6,3,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,1,2,3,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[4,6,1,3,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,1,3,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,1,5,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,1,5,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,2,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,2,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,2,3,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,2,3,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,2,5,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[4,6,2,5,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,3,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,3,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,3,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,6,3,5,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,2,3,4,6] => 10000 => [1,5] => ([(4,5)],6) => 1
[5,1,3,2,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,3,4,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,3,4,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,3,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,4,2,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,4,2,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,4,3,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,4,3,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,4,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,4,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,6,2,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,1,6,2,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,6,3,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,6,3,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,6,4,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,3,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,1,4,3,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,4,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,6,3,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,6,4,3] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,3,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,3,4,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,3,4,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,3,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,4,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,4,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,4,3,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,4,3,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,4,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,4,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,6,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,2,6,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,6,3,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,6,3,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,6,4,3,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,1,4,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,4,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,6,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,6,4,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,1,4,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,1,6,4] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,4,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,4,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,6,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,6,4,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,4,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,4,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,4,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,4,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,6,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,6,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,6,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,6,4,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,1,6,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,2,1,6,3] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,2,6,3,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,1,6,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,2,1,6] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,2,6,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,3,6,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,4,6,3,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,1,2,3,4] => 10000 => [1,5] => ([(4,5)],6) => 1
[5,6,1,3,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,1,3,4,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,1,4,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,1,4,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,2,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,2,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,2,3,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,2,3,4,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,2,4,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[5,6,2,4,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,3,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,3,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,3,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,3,4,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,6,4,3,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,2,3,4,5] => 10000 => [1,5] => ([(4,5)],6) => 1
[6,1,3,2,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,3,4,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,3,4,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,3,5,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,4,2,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,4,2,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,4,3,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,4,3,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,4,5,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,4,5,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,5,2,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,1,5,2,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,5,3,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,5,3,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,1,5,4,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,1,3,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,1,4,3,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,1,4,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,1,5,3,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,1,5,4,3] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,3,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,3,4,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,3,4,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,3,5,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,4,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,4,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,4,3,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,4,3,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,4,5,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,4,5,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,5,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[6,2,5,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,5,3,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,5,3,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,2,5,4,3,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,4,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,1,4,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,1,5,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,1,5,4,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,1,4,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,1,5,4] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,4,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,4,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,5,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,2,5,4,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,4,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,4,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,4,5,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,5,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,5,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,5,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,3,5,4,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,1,5,3,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,2,1,5,3] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,2,5,3,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,3,1,5,2] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,3,2,1,5] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,3,2,5,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,3,5,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,4,5,3,2,1] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,5,4,3,2,1] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,2,3,4,5,6,7] => 000000 => [7] => ([],7) => 0
[1,2,3,5,4,6,7] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,5,6,4,7] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,5,6,7,4] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,5,7,4,6] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,6,4,5,7] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,6,7,4,5] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,3,7,4,5,6] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[1,2,5,3,6,4,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,3,6,7,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,3,7,4,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,4,3,6,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,4,6,3,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,4,6,7,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,4,7,3,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,3,7,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,4,3,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,4,7,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,7,4,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,7,3,6,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,7,4,3,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,7,4,6,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,3,5,4,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,3,5,7,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,3,7,4,5] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,4,3,5,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,4,5,3,7] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,4,5,7,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,4,7,3,5] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,7,3,5,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,7,4,3,5] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,7,4,5,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,3,5,4,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,3,5,6,4] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,3,6,4,5] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,4,3,5,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,4,5,3,6] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,4,5,6,3] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,4,6,3,5] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,3,4,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,1,4,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,1,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,5,1,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,5,6,1,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,5,6,7,1] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,5,7,1,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,6,1,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,6,7,1,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,4,7,1,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,5,1,4,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,5,6,1,4,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,5,6,7,1,4] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,5,7,1,4,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,6,1,4,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,6,7,1,4,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,3,7,1,4,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,1,3,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,5,1,3,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,5,6,1,3,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,5,6,7,1,3] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,5,7,1,3,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,6,1,3,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,6,7,1,3,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,4,7,1,3,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,5,1,3,4,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,5,6,1,3,4,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,5,6,7,1,3,4] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,5,7,1,3,4,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,6,1,3,4,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,6,7,1,3,4,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[2,7,1,3,4,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,1,2,4,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,1,4,2,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,5,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,5,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,5,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,5,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,6,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,6,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,4,7,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,5,2,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,5,6,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,5,6,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,5,7,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,6,2,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,6,7,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,1,7,2,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,1,4,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,1,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,5,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,5,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,5,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,5,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,6,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,6,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,4,7,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,5,1,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,5,6,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,5,6,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,5,7,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,6,1,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,6,7,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,2,7,1,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,2,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,1,5,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,5,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,5,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,5,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,6,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,6,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,1,7,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,1,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,5,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,5,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,5,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,5,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,6,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,6,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,2,7,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,1,2,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,5,1,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,1,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,1,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,2,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,2,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,2,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,2,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,6,1,2,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,5,6,1,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,6,2,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,6,2,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,6,7,1,2] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,5,6,7,2,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,7,1,2,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,5,7,1,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,7,2,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,5,7,2,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,1,2,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,6,1,5,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,1,5,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,1,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,2,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,2,5,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,2,5,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,2,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,7,1,2,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,6,7,1,5,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,7,2,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,6,7,2,5,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,1,2,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,4,7,1,5,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,1,5,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,1,6,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,2,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,2,5,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,2,5,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,4,7,2,6,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,2,4,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,5,1,4,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,4,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,4,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,4,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,6,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,6,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,1,7,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,1,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,4,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,4,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,4,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,4,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,6,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,6,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,2,7,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,1,2,4,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,5,6,1,4,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,1,4,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,1,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,2,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,2,4,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,2,4,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,2,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,7,1,2,4] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,5,6,7,1,4,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,7,2,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,6,7,2,4,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,1,2,4,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,5,7,1,4,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,1,4,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,1,6,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,2,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,2,4,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,2,4,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,5,7,2,6,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,2,4,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,6,1,4,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,4,5,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,4,5,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,4,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,5,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,5,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,1,7,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,1,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,4,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,4,5,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,4,5,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,4,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,5,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,5,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,2,7,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,1,2,4,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,6,7,1,4,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,1,4,5,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,1,5,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,2,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,2,4,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,2,4,5,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,6,7,2,5,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,2,4,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[3,7,1,4,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,4,5,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,4,5,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,4,6,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,5,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,5,6,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,1,6,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,1,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,4,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,4,5,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,4,5,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,4,6,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,5,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,5,6,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[3,7,2,6,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,2,3,5,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,1,3,2,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,5,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,5,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,5,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,5,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,6,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,6,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,3,7,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,5,2,3,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,5,2,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,2,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,2,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,3,2,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,3,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,3,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,3,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,6,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,5,6,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,6,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,6,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,6,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,5,6,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,7,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,5,7,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,7,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,7,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,2,3,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,6,2,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,2,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,2,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,3,2,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,3,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,3,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,3,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,7,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,6,7,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,7,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,6,7,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,2,3,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,1,7,2,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,2,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,2,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,3,2,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,3,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,3,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,7,3,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,3,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,1,5,3,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,5,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,5,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,5,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,6,3,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,6,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,7,3,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,3,1,5,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,5,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,5,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,5,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,5,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,6,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,6,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,3,7,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,5,1,3,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,5,1,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,1,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,1,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,3,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,3,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,3,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,3,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,6,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,5,6,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,6,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,6,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,6,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,5,6,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,7,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,5,7,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,7,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,5,7,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,1,3,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,6,1,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,1,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,1,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,3,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,3,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,3,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,3,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,7,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,6,7,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,7,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,6,7,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,1,3,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,2,7,1,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,1,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,1,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,3,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,3,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,3,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,7,3,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,5,2,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,5,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,5,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,5,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,6,2,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,6,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,7,2,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,1,5,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,5,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,5,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,5,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,5,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,6,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,6,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,2,7,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,1,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,1,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,1,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,2,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,2,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,2,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,2,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,6,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,6,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,6,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,6,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,7,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,7,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,5,7,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,1,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,1,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,1,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,2,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,2,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,2,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,2,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,7,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,7,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,6,7,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,1,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,1,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,1,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,2,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,2,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,2,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,2,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,2,3,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,5,1,3,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,3,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,3,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,3,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,6,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,6,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,6,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,6,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,6,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,6,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,7,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,1,7,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,7,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,7,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,1,3,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,1,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,1,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,1,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,3,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,3,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,3,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,3,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,6,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,6,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,6,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,6,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,6,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,6,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,7,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,2,7,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,7,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,2,7,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,1,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,1,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,1,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,2,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,2,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,2,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,2,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,6,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,6,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,6,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,6,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,7,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,7,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,3,7,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,1,2,3,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,5,6,1,3,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,1,3,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,1,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,1,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,2,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,2,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,2,3,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,2,3,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,2,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,2,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,3,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,3,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,3,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,3,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,6,7,1,2,3] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,5,6,7,1,3,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,7,2,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,7,2,3,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,6,7,3,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,1,2,3,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,5,7,1,3,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,1,3,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,1,6,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,1,6,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,2,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,2,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,2,3,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,2,3,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,2,6,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,5,7,2,6,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,3,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,3,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,3,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,3,6,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,2,3,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,6,1,3,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,3,5,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,3,5,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,3,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,5,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,5,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,5,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,5,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,5,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,5,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,7,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,1,7,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,7,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,1,7,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,1,3,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,1,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,1,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,1,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,3,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,3,5,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,3,5,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,3,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,5,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,5,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,5,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,5,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,5,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,5,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,7,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,2,7,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,7,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,7,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,1,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,1,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,1,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,2,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,2,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,2,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,2,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,5,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,5,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,5,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,5,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,7,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,7,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,3,7,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,1,2,3,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,6,7,1,3,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,1,3,5,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,1,5,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,1,5,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,2,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,2,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,2,3,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,2,3,5,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,2,5,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,6,7,2,5,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,3,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,3,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,3,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,7,3,5,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,2,3,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[4,7,1,3,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,3,5,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,3,5,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,3,6,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,5,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,5,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,5,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,5,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,5,6,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,5,6,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,6,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,1,6,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,6,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,1,6,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,1,3,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,1,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,1,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,1,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,3,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,3,5,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,3,5,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,3,6,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,5,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,5,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,5,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,5,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,5,6,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,5,6,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,6,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[4,7,2,6,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,6,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,2,6,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,1,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,1,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,1,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,5,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,5,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,5,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,5,6,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,6,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,6,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,6,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,2,3,4,6,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[5,1,3,2,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,4,2,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,4,6,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,4,6,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,4,7,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,6,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,6,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,3,7,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,4,2,3,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,4,2,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,2,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,2,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,3,2,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,3,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,3,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,3,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,6,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,4,6,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,6,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,6,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,6,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,4,6,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,7,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,4,7,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,7,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,7,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,2,3,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,6,2,4,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,2,4,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,2,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,2,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,3,2,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,3,2,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,3,4,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,3,4,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,3,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,3,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,4,2,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,4,3,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,4,3,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,4,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,7,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,6,7,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,7,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,7,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,6,7,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,2,3,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,1,7,2,4,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,2,4,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,2,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,2,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,3,2,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,3,2,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,3,4,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,3,4,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,3,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,3,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,4,2,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,4,3,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,4,3,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,7,4,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,3,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,1,4,3,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,4,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,4,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,4,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,6,3,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,6,3,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,6,4,3,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,6,4,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,6,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,6,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,7,3,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,1,7,3,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,7,4,3,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,1,7,4,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,3,1,4,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,4,1,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,4,6,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,4,6,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,4,7,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,6,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,6,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,3,7,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,4,1,3,6,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,4,1,6,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,1,6,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,1,7,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,3,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,3,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,3,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,3,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,6,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,4,6,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,6,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,6,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,6,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,4,6,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,7,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,4,7,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,7,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,7,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,1,3,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,6,1,4,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,1,4,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,1,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,1,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,3,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,3,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,3,4,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,3,4,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,3,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,3,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,3,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,3,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,7,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,6,7,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,7,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,7,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,6,7,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,1,3,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,2,7,1,4,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,1,4,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,1,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,1,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,3,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,3,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,3,4,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,3,4,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,3,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,3,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,4,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,4,3,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,4,3,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,4,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,4,2,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,4,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,4,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,4,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,6,2,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,6,2,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,6,4,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,6,4,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,6,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,6,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,7,2,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,7,2,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,7,4,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,7,4,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,1,4,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,1,6,4,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,1,6,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,1,7,4,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,4,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,4,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,4,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,4,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,6,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,6,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,6,4,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,6,4,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,6,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,6,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,7,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,7,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,7,4,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,7,4,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,4,1,6,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,1,6,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,1,7,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,2,1,6,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,2,6,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,2,6,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,2,7,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,6,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,6,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,6,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,6,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,7,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,7,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,4,7,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,1,4,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,1,4,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,1,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,1,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,2,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,2,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,2,4,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,2,4,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,2,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,2,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,4,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,4,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,4,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,4,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,7,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,7,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,7,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,7,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,1,4,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,1,4,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,1,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,1,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,2,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,2,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,2,4,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,2,4,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,2,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,7,2,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,4,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,4,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,4,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,4,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,6,2,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,6,3,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,6,3,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,6,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,7,2,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,7,3,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,7,3,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,1,6,3,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,1,6,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,1,7,3,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,6,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,6,3,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,6,3,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,6,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,7,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,7,3,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,7,3,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,1,6,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,1,6,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,1,7,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,2,1,6,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,2,6,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,2,6,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,2,7,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,6,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,6,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,6,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,6,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,7,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,7,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,7,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,1,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,2,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,2,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,7,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,1,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,2,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,2,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,3,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,3,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,3,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,3,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,1,2,3,4,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[5,6,1,3,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,3,4,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,3,4,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,3,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,4,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,4,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,4,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,4,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,4,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,4,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,7,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,1,7,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,7,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,7,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,1,7,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,2,1,3,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,1,4,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,1,4,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,1,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,1,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,2,3,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,3,4,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,3,4,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,3,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,4,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,4,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,4,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,4,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,4,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,4,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,7,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,2,7,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,7,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,7,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,2,7,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,3,1,4,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,1,4,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,1,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,1,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,3,2,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,2,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,3,2,4,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,2,4,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,2,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,2,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,3,4,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,4,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,4,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,4,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,7,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,7,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,7,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,3,7,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,1,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,2,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,2,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,7,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,7,1,2,3,4] => 100000 => [1,6] => ([(5,6)],7) => 1
[5,6,7,1,3,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,1,3,4,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,1,4,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,1,4,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,2,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,2,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,2,3,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,2,3,4,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,2,4,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,6,7,2,4,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,3,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,3,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,3,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,3,4,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,6,7,4,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,1,2,3,4,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[5,7,1,3,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,3,4,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,3,4,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,3,6,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,4,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,4,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,4,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,4,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,4,6,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,4,6,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,6,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,1,6,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,6,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,6,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,1,6,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,2,1,3,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,1,4,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,1,4,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,1,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,1,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,2,3,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,3,4,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,3,4,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,3,6,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,4,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,4,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,4,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,4,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,4,6,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,4,6,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,6,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[5,7,2,6,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,6,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,6,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,2,6,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,1,4,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,1,4,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,1,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,1,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,2,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,2,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,2,4,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,2,4,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,2,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,2,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,4,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,4,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,4,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,4,6,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,6,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,6,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,6,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,7,3,6,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,1,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,2,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,2,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,3,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,3,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,3,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,3,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,6,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,2,3,4,5,7] => 100000 => [1,6] => ([(5,6)],7) => 1
[6,1,3,2,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,4,2,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,4,5,2,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,4,5,7,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,4,7,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,5,2,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,5,7,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,3,7,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,4,2,3,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,4,2,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,2,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,2,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,3,2,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,3,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,3,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,3,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,5,2,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,4,5,2,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,5,3,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,5,3,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,5,7,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,4,5,7,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,7,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,4,7,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,7,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,4,7,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,2,3,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,5,2,4,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,2,4,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,2,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,2,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,3,2,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,3,2,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,3,4,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,3,4,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,3,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,3,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,4,2,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,4,3,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,4,3,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,4,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,7,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,5,7,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,7,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,7,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,5,7,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,2,3,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,1,7,2,4,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,2,4,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,2,5,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,2,5,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,3,2,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,3,2,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,3,4,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,3,4,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,3,5,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,7,3,5,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,4,2,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,4,3,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,4,3,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,4,5,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,7,5,4,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,2,1,3,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,1,4,3,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,4,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,4,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,4,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,5,3,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,5,3,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,5,4,3,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,5,4,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,5,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,5,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,7,3,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,1,7,3,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,7,4,3,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,7,4,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,7,5,4,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,2,3,1,4,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,4,1,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,4,5,1,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,4,5,7,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,4,7,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,5,1,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,5,7,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,3,7,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,4,1,3,5,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,4,1,5,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,1,5,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,1,7,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,3,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,3,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,3,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,3,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,5,1,3,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,4,5,1,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,5,3,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,5,3,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,5,7,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,4,5,7,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,7,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,4,7,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,7,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,7,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,1,3,4,7] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,5,1,4,3,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,1,4,7,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,1,7,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,1,7,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,3,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,3,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,3,4,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,3,4,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,3,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,3,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,4,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,4,3,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,4,3,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,4,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,7,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,5,7,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,7,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,7,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,5,7,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,1,3,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,2,7,1,4,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,1,4,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,1,5,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,1,5,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,3,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,3,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,3,4,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,3,4,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,3,5,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,7,3,5,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,4,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,4,3,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,4,3,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,4,5,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,5,4,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,1,4,2,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,4,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,4,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,4,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,5,2,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,5,2,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,5,4,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,5,4,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,5,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,5,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,7,2,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,1,7,2,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,7,4,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,7,4,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,7,5,4,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,2,1,4,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,1,5,4,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,1,5,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,1,7,4,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,1,7,5,4] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,2,4,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,4,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,4,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,4,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,5,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,5,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,5,4,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,5,4,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,5,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,5,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,7,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,7,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,7,4,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,7,4,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,7,5,4,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,3,4,1,5,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,1,5,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,1,7,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,2,1,5,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,2,5,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,2,5,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,2,7,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,5,1,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,5,2,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,5,2,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,5,7,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,7,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,7,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,4,7,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,1,4,2,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,1,4,7,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,1,7,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,1,7,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,2,1,4,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,2,1,7,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,2,4,1,7] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,2,4,7,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,2,7,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,2,7,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,7,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,7,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,7,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,5,7,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,1,4,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,1,4,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,1,5,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,1,5,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,2,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,2,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,2,4,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,2,4,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,2,5,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,7,2,5,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,4,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,4,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,4,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,4,5,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,5,4,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,1,5,2,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,5,3,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,5,3,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,5,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,7,2,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,7,3,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,7,3,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,7,5,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,2,1,5,3,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,1,5,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,1,7,3,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,1,7,5,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,2,5,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,5,3,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,5,3,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,5,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,7,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,7,3,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,7,3,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,2,7,5,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,3,1,5,2,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,1,5,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,1,7,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,1,7,5,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,3,2,1,5,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,2,1,7,5] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,3,2,5,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,2,5,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,2,7,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,2,7,5,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,3,5,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,5,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,5,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,5,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,5,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,4,5,1,7,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,2,1,7,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,2,7,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,3,1,7,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,3,2,1,7] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,3,2,7,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,3,7,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,7,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,1,5,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,2,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,2,5,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,3,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,3,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,3,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,3,5,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,7,5,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,1,7,4,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,2,1,7,4,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,2,7,4,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,3,1,7,4,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,3,2,1,7,4] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,3,2,7,4,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,3,7,4,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,1,7,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,2,1,7,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,2,7,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,3,1,7,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,3,2,1,7] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,3,2,7,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,3,7,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,4,7,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,5,7,4,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[6,7,1,2,3,4,5] => 100000 => [1,6] => ([(5,6)],7) => 1
[6,7,1,3,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,3,4,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,3,4,5,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,3,5,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,4,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,4,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,4,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,4,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,4,5,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,4,5,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,5,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,1,5,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,5,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,5,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,1,5,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,2,1,3,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,1,4,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,1,4,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,1,5,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,1,5,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,2,3,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,3,4,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,3,4,5,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,3,5,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,4,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,4,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,4,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,4,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,4,5,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,4,5,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,5,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[6,7,2,5,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,5,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,5,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,2,5,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,3,1,4,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,1,4,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,1,5,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,1,5,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,3,2,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,2,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,3,2,4,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,2,4,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,2,5,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,2,5,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,3,4,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,4,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,4,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,4,5,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,5,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,5,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,5,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,3,5,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,1,5,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,2,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,2,5,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,3,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,3,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,3,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,3,5,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,5,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,5,4,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,1,2,3,4,5,6] => 100000 => [1,6] => ([(5,6)],7) => 1
[7,1,3,2,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,4,2,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,4,5,2,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,4,5,6,2] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,4,6,2,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,5,2,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,5,6,2,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,3,6,2,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,4,2,3,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,4,2,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,2,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,2,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,3,2,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,3,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,3,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,3,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,5,2,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,4,5,2,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,5,3,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,5,3,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,5,6,2,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,4,5,6,3,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,6,2,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,4,6,2,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,6,3,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,6,3,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,2,3,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,5,2,4,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,2,4,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,2,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,2,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,3,2,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,3,2,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,3,4,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,3,4,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,3,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,3,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,4,2,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,4,3,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,4,3,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,4,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,5,6,2,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,5,6,2,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,6,3,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,6,3,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,5,6,4,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,2,3,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,1,6,2,4,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,2,4,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,2,5,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,2,5,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,3,2,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,3,2,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,3,4,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,3,4,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,3,5,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,6,3,5,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,4,2,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,4,3,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,4,3,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,4,5,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,6,5,4,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,2,1,3,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,1,4,3,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,4,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,4,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,4,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,5,3,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,5,3,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,5,4,3,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,5,4,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,5,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,5,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,6,3,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,6,3,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,6,4,3,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,6,4,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,6,5,4,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,2,3,1,4,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,4,1,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,4,5,1,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,4,5,6,1] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,4,6,1,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,5,1,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,5,6,1,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,3,6,1,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,4,1,3,5,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,4,1,5,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,1,5,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,1,6,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,3,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,3,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,3,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,3,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,5,1,3,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,4,5,1,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,5,3,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,5,3,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,5,6,1,3] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,4,5,6,3,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,6,1,3,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,4,6,1,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,6,3,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,4,6,3,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,1,3,4,6] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,5,1,4,3,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,1,4,6,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,1,6,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,1,6,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,3,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,3,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,3,4,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,3,4,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,3,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,3,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,4,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,4,3,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,4,3,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,4,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,6,1,3,4] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,5,6,1,4,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,6,3,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,6,3,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,5,6,4,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,1,3,4,5] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[7,2,6,1,4,3,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,1,4,5,3] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,1,5,3,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,1,5,4,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,3,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,3,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,3,4,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,3,4,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,3,5,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,6,3,5,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,4,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,4,3,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,4,3,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,4,5,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,6,5,4,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,3,1,4,2,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,4,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,4,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,4,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,5,2,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,5,2,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,5,4,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,5,4,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,5,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,5,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,6,2,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,6,2,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,6,4,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,6,4,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,6,5,4,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,3,2,1,4,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,1,5,4,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,1,5,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,1,6,4,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,1,6,5,4] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,3,2,4,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,4,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,4,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,4,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,5,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,5,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,5,4,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,5,4,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,5,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,5,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,6,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,6,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,6,4,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,6,4,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,2,6,5,4,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,3,4,1,5,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,1,5,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,1,6,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,2,1,5,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,2,5,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,2,5,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,2,6,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,5,1,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,5,2,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,5,2,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,5,6,2,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,6,1,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,6,2,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,4,6,2,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,1,4,2,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,1,4,6,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,1,6,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,1,6,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,2,1,4,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,2,1,6,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,2,4,1,6] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,2,4,6,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,2,6,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,2,6,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,4,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,4,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,4,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,4,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,6,1,4,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,6,2,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,6,2,4,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,6,4,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,1,4,2,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,1,4,5,2] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,1,5,2,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,1,5,4,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,2,1,4,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,2,1,5,4] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,2,4,1,5] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,2,4,5,1] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,2,5,1,4] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,6,2,5,4,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,4,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,4,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,4,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,4,5,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,5,4,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,1,5,2,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,5,3,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,5,3,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,5,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,6,2,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,6,3,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,6,3,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,6,5,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,2,1,5,3,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,1,5,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,1,6,3,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,1,6,5,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,2,5,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,5,3,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,5,3,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,5,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,6,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,6,3,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,6,3,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,2,6,5,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,3,1,5,2,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,1,5,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,1,6,2,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,1,6,5,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,3,2,1,5,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,2,1,6,5] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,3,2,5,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,2,5,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,2,6,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,2,6,5,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,3,5,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,5,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,5,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,5,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,6,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,6,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,6,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,6,5,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,4,5,1,6,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,2,1,6,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,2,6,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,3,1,6,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,3,2,1,6] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,3,2,6,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,3,6,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,5,6,3,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,1,5,3,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,2,1,5,3] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,2,5,3,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,3,1,5,2] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,3,2,1,5] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,3,2,5,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,3,5,2,1] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,6,5,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,1,6,4,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,2,1,6,4,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,2,6,4,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,3,1,6,4,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,3,2,1,6,4] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,3,2,6,4,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,3,6,4,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,1,6,3,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,2,1,6,3] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,2,6,3,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,3,1,6,2] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,3,2,1,6] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,3,2,6,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,3,6,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,4,6,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,5,6,4,3,2,1] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[7,6,5,4,3,2,1] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[] => => [1] => ([],1) => 0
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Generating function
F1=1
F2=1+q
Description
The largest eigenvalue of a graph if it is integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
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
to composition
Description
The composition corresponding to a binary word.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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