- FindStat

Identifier

Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 800 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [2,3,4,5,6,7,8,1,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [1,3,4,5,6,7,8,9,2] => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [1,3,4,5,6,7,8,9,10,2] => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)

[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [5,4,6,3,7,2,8,1,9] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5)

[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [1,3,5,7,9,8,6,4,2] => ([(0,5),(0,8),(6,2),(6,7),(7,3),(7,4),(8,1),(8,6)],9) => ([(0,4),(2,3),(3,1),(4,2)],5)

Map

to 132-avoiding permutation

Description

Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].

Map

complement

Description

Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$

Map

maximal antichains

Description

The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.