Identifier
Values
[1] => [1] => [1] => ([],1) => 0
[1,2] => [1,2] => [1,2] => ([],2) => 0
[2,1] => [1,2] => [1,2] => ([],2) => 0
[1,2,3] => [1,2,3] => [1,2,3] => ([],3) => 0
[1,3,2] => [1,2,3] => [1,2,3] => ([],3) => 0
[2,1,3] => [1,2,3] => [1,2,3] => ([],3) => 0
[2,3,1] => [1,2,3] => [1,2,3] => ([],3) => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[1,2,4,3] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[1,3,2,4] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[1,3,4,2] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[2,1,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[2,1,4,3] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[2,3,1,4] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ([],4) => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,2,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,2,5,3,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,2,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[1,3,5,2,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,3,5,4,2] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,5,2,3,4] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[1,5,3,2,4] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,1,5,3,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,1,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5) => 0
[2,3,5,1,4] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,3,5,4,1] => [1,2,3,5,4] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[2,5,1,3,4] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[2,5,3,1,4] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,2,5,3,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,4,3,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,6,3,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,5,6,4,3] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,3,5,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,4,5,3] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,3,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,6,5,4,3] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,2,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[1,3,5,2,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,4,2,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,6,2,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,5,6,4,2] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,2,5,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,4,5,2] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,2,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,3,6,5,4,2] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,4,2,5,6,3] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
[1,4,3,5,6,2] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
[1,5,2,3,4,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,3,2,4,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,6,2,4,3] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,5,6,3,4,2] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,2,4,3,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,3,4,2,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,4,2,3,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,6,4,3,2,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,1,5,3,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,4,3,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,6,3,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,5,6,4,3] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,3,5,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,4,5,3] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,5,3,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,1,6,5,4,3] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
>>> Load all 375 entries. <<<
[2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([],6) => 0
[2,3,5,1,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,4,1,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,1,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,4,1] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,1,5,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,5,1] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,1,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,4,1] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,5,6,3] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
[2,4,3,5,6,1] => [1,2,4,5,6,3] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6
[2,5,1,3,4,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,3,1,4,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,6,1,4,3] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,5,6,3,4,1] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,1,4,3,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,3,4,1,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,4,1,3,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[2,6,4,3,1,5] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,2,5,3,4,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,3,4,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,3,7,6,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,4,7,6,3] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,2,5,6,3,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,6,3,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,6,4,3,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,6,4,7,3] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,5,6,7,3,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,2,5,6,7,4,3] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,2,6,3,5,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,3,7,4,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,4,7,3,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,5,3,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,5,7,3,4] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,6,5,7,4,3] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,3,5,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,3,6,5,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,4,5,6,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,4,6,5,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,5,3,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,5,4,6,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,5,6,3,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,2,7,5,6,4,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[1,3,5,2,4,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,2,4,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,2,7,6,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,4,7,6,2] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,3,5,6,2,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,6,2,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,6,4,2,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,6,4,7,2] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,5,6,7,2,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,3,5,6,7,4,2] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,3,6,2,5,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,2,7,4,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,4,5,2,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,4,7,2,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,5,2,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,5,4,2,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,5,7,2,4] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,6,5,7,4,2] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,2,5,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,2,6,5,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,4,5,6,2] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,4,6,5,2] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,5,2,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,5,4,6,2] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,5,6,2,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,3,7,5,6,4,2] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[1,4,2,5,6,3,7] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,4,3,5,6,2,7] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,4,7,5,6,2,3] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,4,7,5,6,3,2] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,5,2,3,4,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,2,3,4,7,6] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,2,4,6,7,3] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,5,2,7,4,6,3] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[1,5,3,2,4,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,3,2,4,7,6] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,3,4,6,7,2] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,5,3,7,4,6,2] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[1,5,4,2,6,7,3] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,5,4,3,6,7,2] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[1,5,6,2,4,3,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,6,2,4,7,3] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,6,3,4,2,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,6,3,4,7,2] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,5,6,7,4,2,3] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[1,5,6,7,4,3,2] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[1,6,2,4,3,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,2,7,3,5,4] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,3,4,2,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,3,7,2,5,4] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,4,2,3,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,4,3,2,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,4,7,2,5,3] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,6,4,7,3,5,2] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,2,4,5,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,2,5,4,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,3,4,5,2,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,3,5,4,2,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,4,2,5,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,4,3,5,2,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,4,5,2,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,7,4,5,3,2,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,1,5,3,4,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,3,4,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,3,7,6,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,4,7,6,3] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,1,5,6,3,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,6,3,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,6,4,3,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,6,4,7,3] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,5,6,7,3,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,1,5,6,7,4,3] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,1,6,3,5,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,3,7,4,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,4,5,3,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,4,7,3,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,5,3,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,5,4,3,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,5,7,3,4] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,6,5,7,4,3] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,3,5,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,3,6,5,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,4,5,6,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,4,6,5,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,5,3,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,5,4,6,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,5,6,3,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,1,7,5,6,4,3] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([],7) => 0
[2,3,5,1,4,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,1,4,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,1,7,6,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,6,4,1,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,6,4,7,1] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,5,6,7,1,4] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,3,5,6,7,4,1] => [1,2,3,5,7,4,6] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 6
[2,3,6,1,5,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,1,7,4,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,4,5,1,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,4,7,1,5] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,5,1,4,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,5,4,1,7] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,5,7,1,4] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,6,5,7,4,1] => [1,2,3,6,4,5,7] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,1,5,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,1,6,5,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,4,5,6,1] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,4,6,5,1] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,5,1,6,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,5,4,6,1] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,5,6,1,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,3,7,5,6,4,1] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[2,4,1,5,6,3,7] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,4,3,5,6,1,7] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,4,7,5,6,1,3] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,4,7,5,6,3,1] => [1,2,4,5,6,3,7] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,5,1,3,4,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,1,3,4,7,6] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,1,4,6,7,3] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,5,1,7,4,6,3] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[2,5,3,1,4,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,3,1,4,7,6] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,3,4,6,7,1] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,5,3,7,4,6,1] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[2,5,4,1,6,7,3] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,5,4,3,6,7,1] => [1,2,5,6,7,3,4] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[2,5,6,1,4,3,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,6,1,4,7,3] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,6,3,4,1,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,6,3,4,7,1] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,5,6,7,4,1,3] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[2,5,6,7,4,3,1] => [1,2,5,4,7,3,6] => [5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[2,6,1,4,3,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,1,7,3,5,4] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,3,4,1,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,3,7,1,5,4] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,4,1,3,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,4,3,1,5,7] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,4,7,1,5,3] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,6,4,7,3,5,1] => [1,2,6,5,3,4,7] => [1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,1,4,5,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,1,5,4,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,3,4,5,1,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,3,5,4,1,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,4,1,5,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,4,3,5,1,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,4,5,1,3,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[2,7,4,5,3,1,6] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).