- FindStat

Identifier

Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000422: Graphs ⟶ ℤ

Values

[1] => ([],1) => ([],1) => 0

[1,2] => ([],2) => ([],1) => 0

[2,1] => ([(0,1)],2) => ([(0,1)],2) => 2

[1,2,3] => ([],3) => ([],1) => 0

[1,3,2] => ([(1,2)],3) => ([(1,2)],3) => 2

[2,1,3] => ([(1,2)],3) => ([(1,2)],3) => 2

[2,3,1] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

[3,1,2] => ([(0,2),(1,2)],3) => ([(0,1)],2) => 2

[3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => 4

[1,2,3,4] => ([],4) => ([],1) => 0

[1,2,4,3] => ([(2,3)],4) => ([(1,2)],3) => 2

[1,3,2,4] => ([(2,3)],4) => ([(1,2)],3) => 2

[1,3,4,2] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2

[1,4,2,3] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2

[1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 4

[2,1,3,4] => ([(2,3)],4) => ([(1,2)],3) => 2

[2,1,4,3] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 4

[2,3,1,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2

[2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2

[3,1,2,4] => ([(1,3),(2,3)],4) => ([(1,2)],3) => 2

[3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => 2

[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 4

[4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => 2

[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 4

[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => 4

[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[1,2,3,4,5] => ([],5) => ([],1) => 0

[1,2,3,5,4] => ([(3,4)],5) => ([(1,2)],3) => 2

[1,2,4,3,5] => ([(3,4)],5) => ([(1,2)],3) => 2

[1,2,4,5,3] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,2,5,3,4] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[1,3,2,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2

[1,3,2,5,4] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 4

[1,3,4,2,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,4,2,3,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2

[1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2

[1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,4,2,3] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[2,1,3,4,5] => ([(3,4)],5) => ([(1,2)],3) => 2

[2,1,3,5,4] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 4

[2,1,4,3,5] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 4

[2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 4

[2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 4

[2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,1,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 4

[2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2

[2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2

[3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(1,2)],3) => 2

[3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,3),(1,2)],4) => 4

[3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => ([(1,2)],3) => 2

[3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

[3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(1,2)],3) => 2

[4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(2,3)],4) => 4

[4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => 2

[4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => 2

[5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => 4

[5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[1,2,3,4,5,6] => ([],6) => ([],1) => 0

[1,2,3,4,6,5] => ([(4,5)],6) => ([(1,2)],3) => 2

[1,2,3,5,4,6] => ([(4,5)],6) => ([(1,2)],3) => 2

[1,2,3,5,6,4] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,3,6,4,5] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,4,3,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2

[1,2,4,3,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[1,2,4,5,3,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,5,3,4,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[1,2,5,6,4,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,2,6,4,5,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,5,3,4] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,3,2,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2

[1,3,2,4,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[1,3,2,5,4,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

>>> Load all 763 entries. <<<

[1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,4,2,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,4,2,3,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[1,4,5,3,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,5,3,4,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,4,2,3,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,4,3,2,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[1,5,6,3,4,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[1,6,3,4,5,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,4,5,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,4,5,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,5,3,4,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,3,4,5,6] => ([(4,5)],6) => ([(1,2)],3) => 2

[2,1,3,4,6,5] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[2,1,3,5,4,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,4,3,5,6] => ([(2,5),(3,4)],6) => ([(1,4),(2,3)],5) => 4

[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 4

[2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => 4

[2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 4

[2,1,6,4,5,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,5,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,3,1,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 4

[2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 4

[2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 4

[2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

[3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(1,2)],3) => 2

[3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(1,4),(2,3)],5) => 4

[3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 4

[3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,3),(1,2)],4) => 4

[3,1,2,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,5,4,6] => ([(1,2),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,6,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2)],4) => 4

[3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,2,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

[3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,3),(1,2)],4) => 4

[4,2,3,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[4,2,3,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[4,3,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2)],3) => 2

[4,5,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => 2

[4,5,6,2,3,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => ([(1,2)],3) => 2

[5,2,3,4,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[5,3,4,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,3)],4) => 4

[5,4,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => 2

[5,6,2,3,4,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,4,3,2,1] => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => 2

[6,2,3,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,4,5,3,2,1] => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => 4

[6,5,2,3,4,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,5,3,4,2,1] => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,5,4,2,3,1] => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,5,4,3,1,2] => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,5,4,3,2,1] => ([(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) => ([(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) => 10

[1,2,3,4,5,6,7] => ([],7) => ([],1) => 0

[1,2,3,4,5,7,6] => ([(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,4,6,5,7] => ([(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,4,7,5,6] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,3,5,4,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,2,3,5,6,4,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,6,4,5,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,6,5,4,7] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,2,3,6,7,5,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,3,7,4,5,6] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,3,7,5,6,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,3,7,6,4,5] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,4,3,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2

[1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,2,4,3,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,2,4,3,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,2,4,5,3,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,5,3,4,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,5,3,4,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,2,5,4,3,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,5,4,3,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,2,5,6,4,3,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,2,5,6,7,4,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,3,4,5,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,6,4,5,3,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,5,3,4,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,2,6,7,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,7,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,2,7,4,5,6,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,7,5,6,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,7,6,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,2,7,6,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,7,6,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,2,7,6,5,4,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,3,2,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2

[1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 6

[1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,6,5,4,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,6,7,5,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,2,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,2,7,5,6,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,2,7,6,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,2,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[1,3,4,2,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,3,4,2,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,3,4,2,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,4,2,3,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,4,2,3,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,4,2,3,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,4,2,3,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,4,2,3,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[1,4,2,3,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,3,2,5,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,3,2,5,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,3,2,6,5,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,3,2,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,3,2,7,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,3,2,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 8

[1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[1,4,5,3,2,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,5,3,2,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,4,5,6,3,2,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,4,5,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,2,3,4,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,5,2,3,4,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[1,5,3,4,2,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,3,4,2,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,5,4,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,4,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,5,4,3,2,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,5,6,3,4,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,4,2,3,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2

[1,5,6,7,3,4,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,7,4,2,3] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,6,3,4,5,2,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,4,5,2,3,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,4,5,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,5,3,4,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,4,2,3,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,5,4,3,2,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[1,6,7,3,4,5,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,7,4,5,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,7,4,5,3,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,7,5,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,6,7,5,3,4,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,7,5,4,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,6,7,5,4,3,2] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,7,2,3,4,5,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[1,7,3,4,5,6,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,7,4,5,6,2,3] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,7,4,5,6,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,5,6,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,7,5,6,3,4,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,5,6,4,3,2] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,7,6,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[1,7,6,3,4,5,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,6,4,5,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,6,4,5,3,2] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,7,6,5,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[1,7,6,5,3,4,2] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,7,6,5,4,2,3] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[1,7,6,5,4,3,2] => ([(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) => ([(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) => 10

[2,1,3,4,5,6,7] => ([(5,6)],7) => ([(1,2)],3) => 2

[2,1,3,4,5,7,6] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,4,6,5,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,3,5,4,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 6

[2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,6,5,4,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,6,7,5,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,3,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,3,7,5,6,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,3,7,6,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,3,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[2,1,4,3,5,6,7] => ([(3,6),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 6

[2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 6

[2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,4,3,7,5,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,4,3,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,4,5,3,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 4

[2,1,5,3,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,5,3,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,5,4,3,6,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,5,4,3,7,6] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[2,1,5,6,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,5,6,4,3,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,5,6,7,3,4] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 4

[2,1,5,6,7,4,3] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,3,4,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,1,6,4,5,3,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,6,5,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,1,6,5,4,3,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[2,1,6,7,3,4,5] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 4

[2,1,6,7,4,5,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,7,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,7,5,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,3,4,5,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 4

[2,1,7,4,5,6,3] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,7,5,6,3,4] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,7,5,6,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,6,3,4,5] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,7,6,4,5,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,6,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10

[2,3,1,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,4,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[2,3,1,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[2,3,1,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[2,3,1,6,5,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 4

[2,3,1,6,7,5,4] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[2,3,1,7,5,6,4] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,1,7,6,4,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,1,7,6,5,4] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[2,3,4,1,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 4

[2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2

[3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(1,2)],3) => 2

[3,1,2,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,4,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,1,2,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3)],6) => 6

[3,1,2,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[3,1,2,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,4),(2,3)],5) => 4

[3,1,2,6,5,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,1,2,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 4

[3,1,2,6,7,5,4] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,1,2,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[3,1,2,7,5,6,4] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,1,2,7,6,4,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,1,2,7,6,5,4] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[3,2,1,4,5,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,4,6,5,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,4,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,4,7,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 8

[3,2,1,5,4,6,7] => ([(2,3),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,5,4,7,6] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[3,2,1,5,6,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,6,4,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,2,1,6,5,4,7] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 8

[3,2,1,6,7,4,5] => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,6,7,5,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,2,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,2,1,7,5,6,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,2,1,7,6,4,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10

[3,2,5,4,7,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 10

[3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[3,4,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[3,4,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,4),(2,3)],5) => 4

[3,4,1,2,6,7,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 4

[3,4,1,2,7,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => ([(0,3),(1,2)],4) => 4

[3,4,1,2,7,6,5] => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,2,1,5,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,2,1,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,4,2,1,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[3,4,2,1,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,2,1,7,5,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,4,5,1,2,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[3,4,5,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 4

[3,4,5,2,1,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,5,2,1,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[3,4,5,6,2,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2

[3,4,5,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[3,6,2,1,7,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 10

[4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[4,1,2,3,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[4,1,2,3,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => ([(1,4),(2,3)],5) => 4

[4,1,2,3,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[4,1,2,3,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => ([(0,3),(1,2)],4) => 4

[4,1,2,3,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,2,3,1,5,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,2,3,1,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[4,2,3,1,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[4,2,3,1,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,2,3,1,7,5,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,2,3,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[4,3,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,3,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[4,3,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(4,5)],6) => 6

[4,3,1,2,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,7,5,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[4,3,1,7,6,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 10

[4,3,2,1,5,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,3,2,1,5,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[4,3,2,1,6,5,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8

[4,3,2,1,6,7,5] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,3,2,1,7,5,6] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10

[4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[4,5,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2)],4) => 4

[4,5,2,3,1,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,2,3,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,5,3,1,2,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,3,1,2,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,5,3,2,1,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,5,3,2,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(1,2)],3) => 2

[4,5,6,2,3,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,6,3,1,2,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[4,5,6,3,2,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2

[4,5,6,7,2,3,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,6,7,3,1,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[4,5,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,3),(1,2)],4) => 4

[5,2,3,4,1,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,2,3,4,1,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[5,3,4,1,2,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,3,4,1,2,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[5,3,4,2,1,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,3,4,2,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,4,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,4,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[5,4,2,3,1,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,4,2,3,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,4,3,1,2,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,4,3,1,2,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,4,3,2,1,7,6] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10

[5,4,7,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12

[5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2)],3) => 2

[5,6,2,3,4,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,6,3,4,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,6,3,4,2,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,6,4,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[5,6,4,2,3,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,6,4,3,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[5,6,4,3,2,1,7] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,1)],2) => 2

[5,6,7,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,7,3,4,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,7,3,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,7,4,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,4,3,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(1,2)],3) => 2

[6,2,3,4,5,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[6,3,4,5,1,2,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[6,3,4,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,4,5,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[6,4,5,2,3,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,4,5,3,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,4,5,3,2,1,7] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[6,5,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(2,3)],4) => 4

[6,5,2,3,4,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,5,3,4,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,5,3,4,2,1,7] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[6,5,4,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

[6,5,4,2,3,1,7] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[6,5,4,3,1,2,7] => ([(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) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[6,5,4,3,2,1,7] => ([(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) => ([(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) => 10

[6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1)],2) => 2

[6,7,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[6,7,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[6,7,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[6,7,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,7,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[6,7,5,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,7,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,7,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[6,7,5,4,3,2,1] => ([(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) => ([(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) => 10

[7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1)],2) => 2

[7,2,1,4,3,6,5] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 10

[7,2,3,4,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[7,3,4,5,6,1,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[7,3,4,5,6,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12

[7,4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[7,4,5,6,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,5,6,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[7,5,6,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,5,6,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,5,6,4,3,2,1] => ([(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) => ([(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) => 10

[7,6,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,2)],3) => 4

[7,6,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12

[7,6,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,4,5,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,4,5,3,2,1] => ([(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) => ([(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) => 10

[7,6,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,6,5,2,1,4,3] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12

[7,6,5,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,5,3,4,2,1] => ([(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) => ([(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) => 10

[7,6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,6,5,4,2,3,1] => ([(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) => ([(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) => 10

[7,6,5,4,3,1,2] => ([(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) => ([(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) => 10

[7,6,5,4,3,2,1] => ([(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) => ([(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) => 12

[7,8,5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[5,6,7,8,4,3,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,8,6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,6,7,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,4,5,6,7,3,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,8,6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,6,7,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,7,5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[5,6,7,8,3,4,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,8,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,7,3,4,5,6,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,8,3,4,5,6,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,8,6,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,6,7,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,7,5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[5,6,7,8,4,2,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,7,6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,4,5,6,7,2,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,8,5,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,5,6,7,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,8,2,3,4,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,7,6,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,8,6,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,6,7,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,8,2,3,4,5,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[7,8,6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,6,7,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,7,5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[5,6,7,8,4,3,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,7,6,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[8,7,6,5,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(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) => ([(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) => 10

[7,8,5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,8,3,4,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,7,3,4,5,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,8,3,4,5,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[6,7,8,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,5,6,7,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[5,6,7,8,4,1,2,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,7,4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,7,6,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8

[7,8,6,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[8,6,7,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[6,7,8,5,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,7,5,6,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

[7,8,5,6,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[8,5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,2)],3) => 4

[5,6,7,8,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,1)],2) => 2

[2,1,6,7,8,5,4,3] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[3,4,2,1,7,8,6,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[2,1,4,3,7,8,6,5] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[4,5,6,3,2,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,5,6,4,3,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[3,4,2,1,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[2,1,4,3,8,6,7,5] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[2,1,6,4,5,3,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[2,1,8,5,6,7,4,3] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,2,3,1,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[4,2,3,1,8,6,7,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[6,3,4,5,2,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,4,3,7,8,5,6] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,5,6,3,4,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 6

[2,1,6,7,8,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,3),(1,2)],4) => 4

[3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8) => ([(0,5),(1,4),(2,3)],6) => 6

[3,4,1,2,7,8,5,6] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8) => ([(0,3),(1,2)],4) => 4

[4,5,6,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,3),(1,2)],4) => 4

[6,4,5,2,3,1,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,6,4,3,1,2,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,8,6,7,4,5,3] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,3,2,1,7,8,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[3,4,1,2,8,7,6,5] => ([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,8,6,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,5,6,2,3,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,5,6,3,1,2,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,7,8,4,5,3] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,2,1,7,8,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,1,2,7,8,6,5] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,7,8,5,3,4] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,8,7,5,6] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[4,3,1,2,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[6,4,5,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,6,5,3,4,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[5,6,4,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[6,5,4,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,8,6,7,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,7,8,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,4,3,8,7,5,6] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => 8

[3,4,1,2,8,7,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,7,8,6,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[2,1,8,7,6,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,8,5,6,4,3] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,8,7,5,6,3,4] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[5,6,4,2,3,1,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[6,4,5,3,1,2,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,8,6,4,5,3] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,8,6,7,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,8,5,6,7,3,4] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[3,4,1,2,8,6,7,5] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,2,3,1,7,8,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 6

[4,3,1,2,8,6,7,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[4,3,1,2,7,8,6,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,4,2,1,8,7,5,6] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[4,2,3,1,7,8,6,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[3,4,2,1,8,6,7,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[5,6,3,4,2,1,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[4,2,3,1,8,7,5,6] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 8

[6,5,3,4,1,2,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8

[2,1,7,8,4,5,6,3] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8) => ([(0,1),(2,3),(2,4),(3,4)],5) => 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

click to show known generating functions

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

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

de-duplicate

Description

The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.