Processing math: 100%

Identifier
Values
[1] => => [1] => ([],1) => 1
[1,2] => 0 => [2] => ([],2) => 1
[2,1] => 1 => [1,1] => ([(0,1)],2) => 2
[1,2,3] => 00 => [3] => ([],3) => 1
[1,3,2] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[2,1,3] => 10 => [1,2] => ([(1,2)],3) => 2
[2,3,1] => 10 => [1,2] => ([(1,2)],3) => 2
[3,1,2] => 10 => [1,2] => ([(1,2)],3) => 2
[3,2,1] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,2,3,4] => 000 => [4] => ([],4) => 1
[1,2,4,3] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,3,2,4] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[1,3,4,2] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[1,4,2,3] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[2,1,3,4] => 100 => [1,3] => ([(2,3)],4) => 2
[2,3,1,4] => 100 => [1,3] => ([(2,3)],4) => 2
[2,3,4,1] => 100 => [1,3] => ([(2,3)],4) => 2
[2,4,1,3] => 100 => [1,3] => ([(2,3)],4) => 2
[3,1,2,4] => 100 => [1,3] => ([(2,3)],4) => 2
[3,1,4,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[3,2,1,4] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[3,2,4,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[3,4,1,2] => 100 => [1,3] => ([(2,3)],4) => 2
[3,4,2,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,1,2,3] => 100 => [1,3] => ([(2,3)],4) => 2
[4,1,3,2] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,2,1,3] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,2,3,1] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[4,3,2,1] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
[1,2,3,4,5] => 0000 => [5] => ([],5) => 1
[1,2,3,5,4] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,4,3,5] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,2,4,5,3] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,2,5,3,4] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2
[1,3,2,4,5] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,3,4,2,5] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,3,4,5,2] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,3,5,2,4] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,4,2,3,5] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,4,5,2,3] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[1,5,2,3,4] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[2,1,3,4,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,3,1,4,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,3,4,1,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,3,4,5,1] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,3,5,1,4] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,4,1,3,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,4,5,1,3] => 1000 => [1,4] => ([(3,4)],5) => 2
[2,5,1,3,4] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,1,2,4,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,1,4,2,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,1,4,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,1,5,2,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,2,1,4,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,2,4,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,2,4,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,2,5,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,4,1,2,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,4,1,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,4,2,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,4,2,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,4,5,1,2] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,4,5,2,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,5,1,2,4] => 1000 => [1,4] => ([(3,4)],5) => 2
[3,5,1,4,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,5,2,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[3,5,2,4,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,1,2,3,5] => 1000 => [1,4] => ([(3,4)],5) => 2
[4,1,3,2,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,1,3,5,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,1,5,2,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,1,5,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,2,1,3,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,2,1,5,3] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,2,3,1,5] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,2,3,5,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,2,5,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,2,5,3,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,1,5,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,2,1,5] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,2,5,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,3,5,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[4,5,1,2,3] => 1000 => [1,4] => ([(3,4)],5) => 2
[4,5,1,3,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,5,2,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,5,2,3,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[4,5,3,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,1,2,3,4] => 1000 => [1,4] => ([(3,4)],5) => 2
[5,1,3,2,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,1,3,4,2] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,1,4,2,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,1,4,3,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,2,1,3,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,2,1,4,3] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,2,3,1,4] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,2,3,4,1] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,2,4,1,3] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[5,2,4,3,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,1,4,2] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,2,1,4] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[5,3,2,4,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
>>> Load all 491 entries. <<<
[5,3,4,2,1] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[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) => 5
[1,2,3,4,5,6] => 00000 => [6] => ([],6) => 1
[1,2,3,4,6,5] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[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
[1,2,4,3,5,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,4,5,3,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,4,5,6,3] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,4,6,3,5] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,5,3,4,6] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,5,6,3,4] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,2,6,3,4,5] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2
[1,3,2,4,5,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,2,5,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,5,2,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,5,6,2] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,4,6,2,5] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,5,2,4,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,5,6,2,4] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,3,6,2,4,5] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,2,3,5,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,5,2,3,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,5,6,2,3] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,4,6,2,3,5] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,2,3,4,6] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,5,6,2,3,4] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[1,6,2,3,4,5] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[2,1,3,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,1,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,4,1,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,4,5,1,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,4,5,6,1] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,4,6,1,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,5,1,4,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,5,6,1,4] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,3,6,1,4,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,4,1,3,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,4,5,1,3,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,4,5,6,1,3] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,4,6,1,3,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,5,1,3,4,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,5,6,1,3,4] => 10000 => [1,5] => ([(4,5)],6) => 2
[2,6,1,3,4,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,1,2,4,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,1,4,2,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,4,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,4,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,4,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,5,2,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,5,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,1,6,2,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,1,4,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,4,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,4,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,4,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,4,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,5,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,5,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,2,6,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,1,2,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,4,1,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,1,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,1,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,2,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,2,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,2,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,2,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,5,1,2,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,4,5,1,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,5,2,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,5,2,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,5,6,1,2] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,4,5,6,2,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,6,1,2,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,4,6,1,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,6,2,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,4,6,2,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,1,2,4,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,5,1,4,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,1,4,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,1,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,2,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,2,4,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,2,4,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,2,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,6,1,2,4] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,5,6,1,4,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,6,2,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,5,6,2,4,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,1,2,4,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[3,6,1,4,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,1,4,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,1,5,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,2,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,2,4,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,2,4,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[3,6,2,5,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,2,3,5,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[4,1,3,2,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,3,5,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,3,5,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,3,6,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,5,2,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,5,2,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,5,3,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,5,3,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,5,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,5,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,6,2,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,1,6,2,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,6,3,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,1,6,3,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,1,3,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,1,5,3,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,1,5,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,1,6,3,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,3,1,5,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,3,5,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,3,5,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,3,6,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,5,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,5,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,5,3,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,5,3,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,5,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,5,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,6,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,2,6,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,6,3,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,2,6,3,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,1,5,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,1,5,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,1,6,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,2,1,5,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,2,5,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,2,5,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,2,6,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,5,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,5,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,5,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,5,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,6,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,6,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,3,6,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,1,2,3,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[4,5,1,3,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,1,3,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,1,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,1,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,2,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,2,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,2,3,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,2,3,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,2,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,2,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,3,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,3,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,3,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,3,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,5,6,1,2,3] => 10000 => [1,5] => ([(4,5)],6) => 2
[4,5,6,1,3,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,6,2,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,6,2,3,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,5,6,3,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,1,2,3,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[4,6,1,3,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,1,3,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,1,5,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,1,5,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,2,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,2,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,2,3,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,2,3,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,2,5,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[4,6,2,5,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,3,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,3,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,3,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,3,5,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,2,3,4,6] => 10000 => [1,5] => ([(4,5)],6) => 2
[5,1,3,2,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,3,4,2,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,3,4,6,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,3,6,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,4,2,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,4,2,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,4,3,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,4,3,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,4,6,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,4,6,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,6,2,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,1,6,2,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,6,3,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,1,6,3,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,2,1,3,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,1,4,3,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,4,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,1,6,3,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,2,3,1,4,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,3,4,1,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,3,4,6,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,3,6,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,4,1,3,6] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,4,1,6,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,4,3,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,4,3,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,4,6,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,4,6,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,6,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,2,6,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,6,3,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,2,6,3,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,3,1,4,2,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,1,4,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,1,6,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,3,2,1,4,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,3,2,4,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,4,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,2,6,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[5,3,4,1,6,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,4,2,1,6] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,4,2,6,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,4,6,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,6,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,6,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,3,6,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[5,6,1,2,3,4] => 10000 => [1,5] => ([(4,5)],6) => 2
[5,6,1,3,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,1,3,4,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,1,4,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,1,4,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,2,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,2,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,2,3,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,2,3,4,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,2,4,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[5,6,2,4,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,3,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,3,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,3,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,6,3,4,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,1,2,3,4,5] => 10000 => [1,5] => ([(4,5)],6) => 2
[6,1,3,2,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,3,4,2,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,3,4,5,2] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,3,5,2,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,4,2,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,4,2,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,4,3,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,4,3,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,4,5,2,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,4,5,3,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,5,2,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,1,5,2,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,5,3,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,1,5,3,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,2,1,3,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,1,4,3,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,1,4,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,1,5,3,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,2,3,1,4,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,3,4,1,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,3,4,5,1] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,3,5,1,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,4,1,3,5] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,4,1,5,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,4,3,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,4,3,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,4,5,1,3] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,4,5,3,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,5,1,3,4] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[6,2,5,1,4,3] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,5,3,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,2,5,3,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,3,1,4,2,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,4,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,1,5,2,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,3,2,1,4,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,3,2,4,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,4,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,2,5,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[6,3,4,1,5,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,2,1,5] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,2,5,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,4,5,2,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,5,1,4,2] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,5,2,1,4] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,3,5,2,4,1] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 5
[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) => 6
[1,2,3,4,5,7,6] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 6
[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) => 7
[8,7,6,5,4,3,2,1] => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 8
[1,2,3,4,5,6,8,7] => 0000001 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[] => => [1] => ([],1) => 1
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Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) of a graph G is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
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.
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.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.