Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
=>
Cc0010;cc-rep-0Cc0014;cc-rep-3
[.,.]=>[1]=>[1]=>([],1)
[.,[.,.]]=>[2,1]=>[2,1]=>([],2)
[[.,.],.]=>[1,2]=>[1,2]=>([(0,1)],2)
[.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>([(1,2)],3)
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>([],3)
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>([(1,2)],3)
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>([(0,2),(1,2)],3)
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3)
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>([(1,2),(2,3)],4)
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>([(1,2),(1,3)],4)
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>([(2,3)],4)
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>([],4)
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>([(2,3)],4)
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4)
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>([(1,2),(1,3)],4)
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4)
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>([(1,2),(2,3)],4)
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4)
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4)
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4)
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>([(1,4),(4,2),(4,3)],5)
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>([(1,3),(1,4),(4,2)],5)
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>([(1,2),(1,3),(1,4)],5)
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>([(1,3),(1,4),(4,2)],5)
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5)
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>([(1,4),(2,3),(2,4)],5)
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>([(2,4),(3,4)],5)
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>([(1,4),(2,3)],5)
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>([(3,4)],5)
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>([],5)
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>([(3,4)],5)
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>([(2,4),(3,4)],5)
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>([(2,3),(3,4)],5)
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5)
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(1,4)],5)
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(1,2),(1,3),(1,4)],5)
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>([(1,3),(1,4),(4,2)],5)
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5)
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(1,4),(4,2),(4,3)],5)
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5)
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>([(0,4),(1,4),(2,3),(2,4)],5)
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5)
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>([(1,4),(4,5),(5,2),(5,3)],6)
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>([(1,5),(4,3),(5,2),(5,4)],6)
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>([(1,5),(5,2),(5,3),(5,4)],6)
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>([(1,5),(4,3),(5,2),(5,4)],6)
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>([(1,4),(1,5),(4,3),(5,2)],6)
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>([(1,3),(1,4),(1,5),(5,2)],6)
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5)],6)
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>([(1,3),(1,4),(1,5),(5,2)],6)
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>([(1,3),(1,5),(4,2),(5,4)],6)
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>([(1,5),(2,3),(2,5),(5,4)],6)
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>([(1,4),(2,3),(3,5),(4,5)],6)
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>([(1,4),(2,3),(2,5),(4,5)],6)
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>([(2,5),(3,4),(4,5)],6)
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6)
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>([(1,5),(2,5),(3,4),(3,5)],6)
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>([(1,5),(2,4),(3,4),(3,5)],6)
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>([(1,3),(2,4),(4,5)],6)
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>([(3,4),(4,5)],6)
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>([(3,4),(3,5)],6)
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>([(4,5)],6)
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>([],6)
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>([(4,5)],6)
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>([(2,5),(3,4),(3,5)],6)
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>([(3,4),(3,5)],6)
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>([(2,5),(3,4),(3,5)],6)
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>([(3,4),(4,5)],6)
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>([(2,5),(3,4),(4,5)],6)
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>([(2,5),(3,5),(4,5)],6)
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>([(2,5),(3,4),(4,5)],6)
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>([(2,5),(3,5),(5,4)],6)
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>([(2,3),(3,5),(5,4)],6)
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>([(0,5),(1,3),(1,4),(1,5),(4,2)],6)
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>([(1,3),(1,4),(1,5),(5,2)],6)
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5)],6)
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>([(1,3),(1,4),(1,5),(5,2)],6)
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>([(1,3),(1,5),(4,2),(5,4)],6)
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,4),(4,2),(4,3),(4,5)],6)
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(1,5),(5,2),(5,3),(5,4)],6)
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(1,5),(4,3),(5,2),(5,4)],6)
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(1,4),(4,5),(5,2),(5,3)],6)
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>([(0,5),(1,4),(2,3),(2,5),(4,5)],6)
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>([(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7)
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>([(1,6),(4,3),(5,2),(6,4),(6,5)],7)
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>([(1,5),(1,6),(4,3),(5,4),(6,2)],7)
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>([(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>([(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(5,6)],7)
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>([(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>([(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>([(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>([(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>([(1,4),(2,3),(2,6),(4,6),(6,5)],7)
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>([(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>([(1,4),(2,3),(2,6),(4,5),(5,6)],7)
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>([(2,6),(3,4),(3,5),(5,6)],7)
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7)
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>([(2,6),(3,6),(4,5)],7)
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7)
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>([(1,6),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>([(1,6),(2,5),(3,4),(4,5),(4,6)],7)
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>([(1,6),(2,6),(3,5),(4,5),(4,6)],7)
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>([(1,6),(2,5),(3,5),(3,6),(6,4)],7)
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>([(1,6),(2,4),(5,3),(6,5)],7)
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>([(3,4),(4,6),(6,5)],7)
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>([(3,4),(4,5),(4,6)],7)
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>([(3,4),(3,5),(5,6)],7)
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>([(3,4),(3,5),(3,6)],7)
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>([(3,4),(3,5),(5,6)],7)
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>([(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>([(3,6),(4,5),(4,6)],7)
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>([(4,6),(5,6)],7)
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>([(3,6),(4,5)],7)
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>([(5,6)],7)
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>([],7)
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>([(5,6)],7)
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>([(4,6),(5,6)],7)
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>([(4,5),(5,6)],7)
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>([(2,6),(3,4),(3,6),(6,5)],7)
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>([(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>([(2,6),(3,4),(3,5),(3,6)],7)
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>([(3,4),(3,5),(3,6)],7)
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>([(3,4),(3,5),(5,6)],7)
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>([(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>([(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>([(3,4),(4,5),(4,6)],7)
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>([(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>([(2,6),(3,6),(4,5),(4,6)],7)
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>([(2,6),(3,4),(3,6),(6,5)],7)
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>([(3,4),(4,6),(6,5)],7)
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>([(2,6),(3,6),(4,6),(5,6)],7)
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>([(2,6),(3,6),(4,6),(6,5)],7)
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>([(2,6),(3,6),(4,5),(6,4)],7)
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>([(2,6),(4,5),(5,3),(6,4)],7)
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>([(0,6),(1,4),(1,6),(5,2),(5,3),(6,5)],7)
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7)
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7)
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7)
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7)
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(5,4),(6,2),(6,4)],7)
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7)
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(5,4),(6,3)],7)
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7)
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7)
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7)
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7)
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7)
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(4,6),(6,2)],7)
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7)
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(4,6)],7)
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7)
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>([(0,5),(0,6),(1,2),(1,4),(1,6),(3,5),(4,3)],7)
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7)
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>([(0,6),(1,2),(1,3),(1,4),(3,5),(4,5),(4,6)],7)
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>([(0,6),(1,3),(1,5),(1,6),(4,2),(5,4)],7)
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>([(0,5),(0,6),(1,4),(1,5),(4,6),(6,2),(6,3)],7)
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7)
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7)
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7)
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7)
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7)
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(6,3)],7)
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(6,2)],7)
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7)
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7)
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>([(0,6),(1,5),(5,2),(5,6),(6,3),(6,4)],7)
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7)
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>([(0,3),(1,4),(1,5),(1,6),(3,2),(3,4),(3,5),(3,6)],7)
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7)
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7)
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>([(0,5),(0,6),(1,4),(3,5),(4,2),(4,3),(4,6)],7)
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7)
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7)
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5)],7)
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7)
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>([(0,3),(1,4),(1,5),(1,6),(3,2),(3,4),(3,5),(3,6)],7)
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7)
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7)
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7)
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7)
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7)
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7)
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7)
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7)
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7)
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7)
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>([(0,5),(0,6),(1,3),(3,4),(4,2),(4,5),(4,6)],7)
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7)
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>([(0,5),(0,6),(1,3),(3,4),(4,2),(4,5),(4,6)],7)
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7)
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7)
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7)
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7)
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5)],7)
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>([(0,6),(1,5),(5,2),(5,6),(6,3),(6,4)],7)
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7)
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>([(0,5),(0,6),(1,4),(1,5),(4,6),(6,2),(6,3)],7)
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>([(0,6),(1,4),(1,6),(5,2),(5,3),(6,5)],7)
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>([(0,6),(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7)
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>([(0,6),(1,4),(2,3),(2,6),(4,5),(5,6)],7)
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7)
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2)],7)
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7)
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>([(0,6),(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>([(0,6),(1,4),(2,3),(2,6),(4,6),(6,5)],7)
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7)
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[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)
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7)
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(5,4),(6,5)],7)
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7)
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>([(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2),(5,6)],7)
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5),(5,6)],7)
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7)
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>([(0,6),(1,2),(1,4),(2,6),(3,5),(4,3),(4,6),(6,5)],7)
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>([(0,6),(1,3),(2,4),(2,6),(3,6),(4,5),(6,5)],7)
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7)
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7)
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7)
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[2,3,4,5,7,8,6,1]=>([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,1]=>([(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>([(1,4),(3,7),(4,6),(5,2),(5,7),(6,3),(6,5)],8)
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[2,3,4,7,6,8,5,1]=>([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>([(1,6),(4,3),(5,2),(6,7),(7,4),(7,5)],8)
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[2,3,5,6,4,8,7,1]=>([(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[2,3,5,7,4,8,6,1]=>([(1,5),(2,6),(3,6),(3,7),(4,2),(4,7),(5,3),(5,4)],8)
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>([(1,6),(3,7),(5,2),(5,7),(6,3),(6,5),(7,4)],8)
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[2,3,6,5,8,4,7,1]=>([(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[2,3,6,7,4,5,8,1]=>([(1,6),(2,7),(3,7),(4,3),(5,2),(6,4),(6,5)],8)
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>([(1,6),(3,7),(4,3),(5,2),(5,7),(6,4),(6,5)],8)
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>([(1,5),(2,7),(3,6),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>([(1,7),(6,5),(7,2),(7,3),(7,4),(7,6)],8)
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>([(1,6),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>([(1,6),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>([(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,4,5,3,6,8,7,1]=>([(1,3),(1,6),(2,7),(3,7),(6,2),(7,4),(7,5)],8)
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[2,4,5,3,7,8,6,1]=>([(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,2)],8)
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>([(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,2)],8)
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8)
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>([(1,3),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(4,6),(6,7)],8)
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[2,4,7,3,6,8,5,1]=>([(1,3),(1,4),(2,7),(3,5),(3,6),(4,2),(4,5),(4,6),(6,7)],8)
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[2,4,7,3,8,5,6,1]=>([(1,4),(1,5),(3,6),(4,6),(4,7),(5,3),(5,7),(7,2)],8)
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>([(1,3),(1,4),(3,5),(3,6),(3,7),(4,2),(4,5),(4,6),(4,7)],8)
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>([(1,4),(1,5),(4,6),(4,7),(5,3),(5,6),(5,7),(7,2)],8)
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[2,4,8,3,6,5,7,1]=>([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>([(1,4),(1,5),(4,7),(5,3),(5,7),(6,2),(7,6)],8)
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[2,5,4,7,3,8,6,1]=>([(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6)],8)
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>([(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>([(1,2),(1,4),(1,5),(2,7),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>([(1,5),(1,6),(2,7),(3,7),(5,3),(6,2),(7,4)],8)
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[2,5,6,3,4,8,7,1]=>([(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2)],8)
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>([(1,4),(1,5),(2,6),(3,6),(3,7),(4,3),(5,2),(5,7)],8)
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>([(1,5),(1,6),(3,7),(5,3),(6,2),(6,7),(7,4)],8)
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[2,6,4,5,7,3,8,1]=>([(1,2),(1,4),(1,5),(2,7),(3,6),(4,6),(5,3),(6,7)],8)
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>([(1,2),(1,4),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[2,6,5,7,4,3,8,1]=>([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[2,6,5,3,7,4,8,1]=>([(1,2),(1,3),(1,5),(2,7),(3,7),(4,6),(5,4),(5,7),(7,6)],8)
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(3,7),(4,6),(4,7),(5,2),(5,7)],8)
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7)],8)
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,6,4,8,3,5,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(3,7),(4,5),(4,6),(6,7)],8)
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[2,7,4,6,8,5,3,1]=>([(1,3),(1,5),(1,6),(4,7),(5,7),(6,2),(6,4)],8)
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[2,7,6,3,8,5,4,1]=>([(1,4),(1,5),(1,6),(4,7),(5,7),(6,2),(6,3),(6,7)],8)
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[2,7,4,6,3,8,5,1]=>([(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(4,7),(5,2),(5,6)],8)
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[2,7,4,5,8,3,6,1]=>([(1,2),(1,3),(1,5),(2,7),(3,6),(4,6),(4,7),(5,4)],8)
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[2,7,4,8,3,5,6,1]=>([(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(5,7),(7,2)],8)
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[2,7,8,3,4,5,6,1]=>([(1,6),(1,7),(4,5),(5,3),(6,4),(7,2)],8)
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[2,8,5,7,4,6,3,1]=>([(1,3),(1,4),(1,5),(1,6),(5,7),(6,2),(6,7)],8)
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>([(1,3),(1,4),(1,5),(1,7),(6,2),(7,6)],8)
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[2,8,4,5,7,3,6,1]=>([(1,3),(1,4),(1,5),(4,7),(5,6),(6,2),(6,7)],8)
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[7,4,3,5,6,8,2,1]=>[2,8,4,7,3,5,6,1]=>([(1,3),(1,4),(1,6),(4,7),(6,2),(6,7),(7,5)],8)
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[2,8,7,3,4,5,6,1]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[2,8,4,6,5,3,7,1]=>([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[2,8,5,3,6,4,7,1]=>([(1,3),(1,4),(1,5),(2,7),(4,6),(5,2),(5,6),(6,7)],8)
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[2,8,6,3,4,5,7,1]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>([(1,2),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(7,6)],8)
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>([(1,3),(1,4),(1,5),(4,7),(5,7),(6,2),(7,6)],8)
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>([(1,3),(1,7),(4,6),(5,4),(6,2),(7,5)],8)
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[3,4,2,5,6,8,7,1]=>([(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[3,4,2,5,7,8,6,1]=>([(1,7),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[3,4,2,5,8,7,6,1]=>([(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[3,4,2,6,7,5,8,1]=>([(1,5),(1,7),(2,4),(3,6),(4,5),(4,7),(5,6),(7,3)],8)
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[3,4,2,6,8,5,7,1]=>([(1,6),(1,7),(2,4),(4,6),(4,7),(6,5),(7,3),(7,5)],8)
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>([(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>([(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>([(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>([(1,5),(1,7),(2,4),(2,5),(4,7),(5,6),(6,3),(7,6)],8)
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[3,5,2,6,4,8,7,1]=>([(1,3),(1,6),(2,6),(2,7),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>([(1,3),(1,7),(2,6),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>([(1,3),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5)],8)
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>([(1,5),(1,6),(2,4),(2,5),(4,6),(4,7),(5,7),(7,3)],8)
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[3,6,2,5,7,4,8,1]=>([(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(5,4),(6,5),(7,4)],8)
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>([(1,5),(1,6),(2,3),(2,5),(3,6),(3,7),(4,7),(5,4)],8)
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>([(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(7,4)],8)
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[3,7,2,8,4,5,6,1]=>([(1,6),(1,7),(2,3),(2,6),(3,7),(4,5),(6,4)],8)
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[3,8,2,5,7,4,6,1]=>([(1,5),(1,7),(2,4),(2,5),(2,7),(5,6),(7,3),(7,6)],8)
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(5,7),(6,7),(7,3)],8)
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>([(1,7),(2,4),(2,7),(5,3),(6,5),(7,6)],8)
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>([(1,6),(1,7),(2,5),(3,5),(5,6),(5,7),(7,4)],8)
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[4,3,6,2,7,5,8,1]=>([(1,4),(1,7),(2,4),(2,7),(3,6),(3,7),(4,6),(6,5),(7,5)],8)
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>([(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(7,5)],8)
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>([(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(5,6),(7,4)],8)
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]=>([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>([(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8)
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>([(1,5),(2,4),(4,7),(5,7),(6,3),(7,6)],8)
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>([(1,5),(2,4),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>([(1,4),(2,3),(2,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>([(1,4),(2,3),(2,6),(3,7),(4,6),(4,7),(6,5)],8)
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[4,8,2,3,6,5,7,1]=>([(1,4),(2,3),(2,6),(2,7),(4,6),(4,7),(6,5),(7,5)],8)
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>([(1,5),(2,4),(2,7),(5,7),(6,3),(7,6)],8)
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>([(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[5,4,6,3,2,7,8,1]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[5,4,6,3,2,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6)],8)
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[5,4,8,3,2,6,7,1]=>([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>([(1,7),(2,7),(3,4),(3,7),(4,6),(6,5),(7,6)],8)
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[5,4,2,6,3,8,7,1]=>([(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,7),(7,5)],8)
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>([(1,6),(2,5),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[5,3,6,2,4,8,7,1]=>([(1,5),(2,4),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]=>([(1,5),(2,4),(2,6),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>([(1,6),(2,5),(2,7),(3,5),(3,6),(6,7),(7,4)],8)
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[5,7,2,3,4,8,6,1]=>([(1,4),(2,3),(2,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>([(1,4),(2,3),(2,6),(2,7),(4,5),(5,6),(5,7)],8)
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>([(1,6),(2,5),(2,7),(3,7),(6,3),(7,4)],8)
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[6,3,4,5,7,2,8,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[6,5,4,8,3,2,7,1]=>([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1]=>[6,5,8,3,4,2,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,7)],8)
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[6,4,2,5,8,3,7,1]=>([(1,6),(1,7),(2,5),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8)
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>([(1,7),(2,5),(2,6),(3,4),(4,6),(4,7),(7,5)],8)
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[6,4,7,3,2,5,8,1]=>([(1,7),(2,7),(3,5),(4,5),(4,7),(5,6),(7,6)],8)
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]=>([(1,6),(2,5),(2,6),(3,5),(3,7),(4,7),(6,4)],8)
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[6,7,2,3,4,5,8,1]=>([(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>([(2,7),(3,6),(3,7),(4,5),(4,6),(5,7)],8)
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>([(4,7),(5,7),(6,7)],8)
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[7,6,4,8,3,5,2,1]=>([(2,7),(3,7),(4,6),(5,6),(5,7)],8)
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[7,6,8,3,4,5,2,1]=>([(2,7),(3,7),(4,5),(5,6)],8)
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]=>([(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(6,7)],8)
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[7,6,2,5,8,4,3,1]=>([(1,7),(2,7),(3,4),(3,5),(3,6),(6,7)],8)
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[7,6,2,3,4,8,5,1]=>([(1,4),(2,7),(3,7),(4,6),(6,5),(6,7)],8)
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(5,7)],8)
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[7,3,5,8,4,2,6,1]=>([(1,7),(2,6),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>([(1,7),(2,6),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[8,4,3,5,2,6,7,1]=>[7,5,4,8,3,2,6,1]=>([(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>([(1,7),(2,6),(3,6),(3,7),(4,5),(5,7)],8)
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>([(1,6),(2,5),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8)
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>([(1,7),(2,7),(3,6),(4,6),(4,7),(7,5)],8)
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[7,3,8,2,4,5,6,1]=>([(1,7),(2,6),(3,6),(3,7),(4,5),(7,4)],8)
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[7,8,2,3,4,5,6,1]=>([(1,7),(2,4),(5,6),(6,3),(7,5)],8)
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>([(3,4),(4,7),(7,5),(7,6)],8)
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>([(3,4),(4,5),(4,6),(4,7)],8)
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,3,5,6,4,7,2,1]=>([(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[8,3,6,5,7,4,2,1]=>([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>([(3,4),(3,5),(3,6),(6,7)],8)
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>([(3,4),(3,5),(3,6),(3,7)],8)
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[8,3,7,5,4,6,2,1]=>([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>([(3,4),(3,5),(5,6),(6,7)],8)
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>([(3,6),(3,7),(4,5),(4,6),(5,7)],8)
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>([(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,4,7,3,5,6,2,1]=>([(3,7),(4,5),(4,7),(7,6)],8)
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[8,5,4,7,3,6,2,1]=>([(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>([(5,7),(6,7)],8)
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[8,6,7,3,4,5,2,1]=>([(3,5),(4,6),(6,7)],8)
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>([(5,6),(6,7)],8)
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>([(5,6),(5,7)],8)
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>([(6,7)],8)
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>([],8)
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>([(6,7)],8)
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>([(4,7),(5,6),(5,7)],8)
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>([(5,6),(5,7)],8)
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>([(4,7),(5,6),(5,7)],8)
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>([(5,6),(6,7)],8)
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]=>([(4,7),(5,6),(6,7)],8)
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>([(4,7),(5,7),(6,7)],8)
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>([(4,7),(5,6),(6,7)],8)
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>([(4,7),(5,7),(7,6)],8)
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>([(4,5),(5,7),(7,6)],8)
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,4,2,5,6,7,3,1]=>([(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>([(2,7),(3,4),(3,7),(7,5),(7,6)],8)
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]=>([(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>([(2,6),(2,7),(3,4),(3,5),(3,6),(5,7)],8)
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>([(2,7),(3,4),(3,5),(3,6),(6,7)],8)
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>([(2,7),(3,4),(3,5),(3,7),(5,6)],8)
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>([(3,4),(3,5),(3,6),(6,7)],8)
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>([(3,4),(3,5),(3,6),(6,7)],8)
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>([(3,4),(3,5),(5,6),(6,7)],8)
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[8,3,6,2,7,5,4,1]=>([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,7)],8)
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>([(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[8,6,2,3,7,5,4,1]=>([(2,4),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>([(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6),(4,7),(5,7)],8)
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,3,6,2,4,7,5,1]=>([(2,6),(3,4),(3,6),(4,7),(6,5),(6,7)],8)
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[7,4,5,3,2,6,8,1]=>[8,3,5,7,4,2,6,1]=>([(2,7),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[8,4,5,3,7,2,6,1]=>([(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>([(2,7),(3,6),(4,5),(4,7),(6,7)],8)
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[8,4,2,5,7,3,6,1]=>([(2,6),(3,4),(3,6),(4,7),(6,5),(6,7)],8)
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6),(4,7),(5,7)],8)
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>([(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8)
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[8,3,4,7,2,5,6,1]=>([(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[8,4,7,3,2,5,6,1]=>([(2,7),(3,7),(4,5),(4,7),(7,6)],8)
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,4,2,7,3,5,6,1]=>([(2,6),(2,7),(3,4),(3,6),(4,7),(7,5)],8)
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,7,2,4,5,6,1]=>([(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,7,2,3,4,5,6,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]=>([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>([(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[8,4,5,3,6,2,7,1]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,4,6,3,5,2,7,1]=>([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[8,5,4,6,3,2,7,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[8,6,5,3,4,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,4,2,5,6,3,7,1]=>([(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[8,4,2,6,5,3,7,1]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,6,2,5,4,3,7,1]=>([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>([(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[6,3,2,4,5,7,8,1]=>[8,3,6,2,4,5,7,1]=>([(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,6,2,3,4,5,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>([(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,4,5,3,2,6,7,1]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,4,2,5,3,6,7,1]=>([(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>([(0,7),(1,4),(1,7),(5,6),(6,2),(6,3),(7,5)],8)
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[3,1,4,5,7,8,6,2]=>([(0,7),(1,4),(1,7),(5,3),(6,2),(6,5),(7,6)],8)
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>([(0,7),(1,4),(1,7),(5,3),(6,2),(6,5),(7,6)],8)
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[3,1,4,6,7,5,8,2]=>([(0,7),(1,2),(1,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>([(0,7),(1,3),(1,7),(4,6),(5,2),(5,6),(7,4),(7,5)],8)
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[3,1,4,7,6,8,5,2]=>([(0,7),(1,3),(1,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>([(0,7),(1,2),(1,7),(7,3),(7,4),(7,5),(7,6)],8)
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>([(0,7),(1,3),(1,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>([(0,7),(1,3),(1,7),(5,2),(6,5),(7,4),(7,6)],8)
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[3,1,5,6,4,7,8,2]=>([(0,5),(0,7),(1,2),(1,5),(1,7),(3,6),(5,6),(6,4),(7,3)],8)
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>([(0,6),(0,7),(1,2),(1,6),(1,7),(3,4),(3,5),(6,3),(7,4),(7,5)],8)
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[3,1,5,7,4,8,6,2]=>([(0,6),(0,7),(1,2),(1,6),(1,7),(3,5),(6,3),(6,4),(7,4),(7,5)],8)
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(4,3),(5,4),(6,4),(7,3)],8)
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>([(0,6),(0,7),(1,2),(1,6),(1,7),(4,5),(6,4),(7,3),(7,5)],8)
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,2),(6,7)],8)
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[3,1,8,6,7,5,4,2]=>([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>([(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(6,4),(7,2),(7,4)],8)
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>([(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(6,4),(7,2),(7,4)],8)
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>([(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(4,2),(6,4),(7,4)],8)
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>([(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(5,4),(7,5)],8)
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>([(0,7),(1,3),(1,4),(1,7),(4,6),(5,2),(6,5),(7,6)],8)
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]=>([(0,6),(1,4),(1,5),(1,6),(5,7),(6,7),(7,2),(7,3)],8)
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[4,1,5,3,8,7,6,2]=>([(0,7),(1,2),(1,3),(1,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[4,1,5,3,8,6,7,2]=>([(0,6),(1,3),(1,4),(1,6),(4,5),(4,7),(6,5),(6,7),(7,2)],8)
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>([(0,2),(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>([(0,2),(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[4,1,7,3,6,8,5,2]=>([(0,2),(0,3),(0,7),(1,5),(1,6),(1,7),(3,5),(3,6),(6,4),(7,4)],8)
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>([(0,6),(0,7),(1,3),(1,4),(1,6),(4,5),(4,7),(6,5),(7,2)],8)
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(4,5),(4,7),(7,2)],8)
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(4,5),(4,7),(7,2)],8)
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>([(0,2),(0,3),(0,5),(1,5),(1,6),(1,7),(3,6),(3,7),(6,4),(7,4)],8)
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>([(0,6),(0,7),(1,3),(1,4),(1,7),(4,6),(5,2),(6,5)],8)
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[5,1,6,3,4,7,8,2]=>([(0,6),(1,4),(1,5),(1,6),(3,7),(5,3),(6,7),(7,2)],8)
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>([(0,6),(0,7),(1,2),(1,4),(1,7),(3,5),(3,6),(4,3),(7,5)],8)
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[5,1,8,3,4,6,7,2]=>([(0,6),(0,7),(1,4),(1,5),(1,6),(3,7),(5,3),(7,2)],8)
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>([(0,6),(0,7),(1,2),(1,3),(1,5),(3,7),(4,6),(4,7),(5,4)],8)
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]=>([(0,6),(0,7),(1,2),(1,4),(1,5),(3,6),(4,6),(4,7),(5,3),(5,7)],8)
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(3,5),(4,5),(4,6),(5,7)],8)
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>([(0,6),(0,7),(1,2),(1,5),(1,7),(3,6),(4,3),(5,4)],8)
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[7,1,4,5,6,8,3,2]=>([(0,7),(1,2),(1,3),(1,6),(4,7),(5,4),(6,5)],8)
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]=>([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,1,4,6,3,8,5,2]=>([(0,7),(1,2),(1,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6)],8)
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>([(0,7),(1,2),(1,4),(1,5),(3,6),(4,6),(4,7),(5,3),(5,7)],8)
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>([(0,6),(1,3),(1,4),(1,5),(4,7),(5,6),(5,7),(7,2)],8)
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>([(0,7),(1,3),(1,6),(1,7),(4,5),(5,2),(6,4)],8)
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[8,1,4,5,7,6,3,2]=>([(1,4),(1,5),(1,6),(6,7),(7,2),(7,3)],8)
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[8,1,4,7,6,5,3,2]=>([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,3,8,1,2]=>[8,1,5,6,4,7,3,2]=>([(1,2),(1,3),(1,5),(1,6),(4,7),(5,7),(6,4)],8)
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>([(1,3),(1,4),(1,5),(1,6),(5,7),(6,2),(6,7)],8)
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>([(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8)
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>([(1,4),(1,5),(1,6),(5,7),(6,2),(6,3),(6,7)],8)
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[8,1,7,3,6,5,4,2]=>([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[8,1,7,3,5,6,4,2]=>([(1,4),(1,5),(1,7),(6,3),(7,2),(7,6)],8)
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[8,1,4,6,3,7,5,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(4,7),(5,3),(5,7)],8)
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>([(1,3),(1,4),(1,5),(4,6),(4,7),(5,2),(5,6),(5,7)],8)
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>([(1,3),(1,4),(1,5),(4,7),(5,6),(6,2),(6,7)],8)
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(4,7),(5,3),(5,7)],8)
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[8,1,4,6,5,3,7,2]=>([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[8,1,5,3,6,4,7,2]=>([(1,3),(1,4),(1,5),(2,7),(4,6),(5,2),(5,6),(6,7)],8)
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>([(1,3),(1,4),(1,5),(2,7),(4,6),(5,2),(5,6),(6,7)],8)
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>([(1,2),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(7,6)],8)
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]=>([(1,3),(1,4),(1,5),(4,7),(5,7),(6,2),(7,6)],8)
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>([(1,3),(1,7),(4,6),(5,4),(6,2),(7,5)],8)
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5)],8)
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]=>([(0,6),(0,7),(1,5),(1,6),(5,7),(7,2),(7,3),(7,4)],8)
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>([(0,3),(0,6),(1,4),(1,6),(1,7),(2,5),(3,4),(3,7),(4,2),(7,5)],8)
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>([(0,3),(0,5),(1,5),(1,6),(1,7),(3,6),(3,7),(6,4),(7,2),(7,4)],8)
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[2,4,1,7,6,8,5,3]=>([(0,2),(0,5),(1,4),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(6,3),(7,3)],8)
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(6,2)],8)
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>([(0,2),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6)],8)
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>([(0,5),(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(6,4)],8)
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>([(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(7,3),(7,4)],8)
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[2,5,1,8,4,6,7,3]=>([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(3,4),(3,5),(5,2),(7,5)],8)
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>([(0,4),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,5),(5,3),(6,5),(7,3)],8)
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[2,6,1,5,8,4,7,3]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,7),(5,7),(6,3),(6,7)],8)
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(2,5),(3,4),(3,5),(7,2)],8)
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[2,7,1,5,8,4,6,3]=>([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(6,3),(7,3),(7,4)],8)
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[2,8,1,7,5,6,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[2,8,1,7,4,6,5,3]=>([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[2,8,1,5,6,4,7,3]=>([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(3,4),(6,3),(7,4)],8)
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>([(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(4,2),(6,4),(7,4)],8)
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>([(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(5,4),(7,5)],8)
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>([(0,7),(1,5),(4,2),(5,3),(5,7),(6,4),(7,6)],8)
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>([(0,7),(1,5),(5,4),(5,7),(6,2),(6,3),(7,6)],8)
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[4,1,2,5,8,7,6,3]=>([(0,7),(1,6),(6,2),(6,7),(7,3),(7,4),(7,5)],8)
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>([(0,7),(1,5),(5,3),(5,7),(6,2),(7,4),(7,6)],8)
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>([(0,6),(0,7),(1,4),(4,3),(4,6),(4,7),(6,5),(7,2),(7,5)],8)
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>([(0,6),(0,7),(1,5),(5,2),(5,6),(5,7),(6,4),(7,3)],8)
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>([(0,3),(1,4),(1,5),(1,6),(1,7),(3,2),(3,4),(3,5),(3,6),(3,7)],8)
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>([(0,5),(0,6),(0,7),(1,4),(4,3),(4,5),(4,6),(4,7),(7,2)],8)
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>([(0,6),(0,7),(1,4),(4,3),(4,6),(4,7),(5,2),(7,5)],8)
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>([(0,7),(1,4),(3,5),(3,6),(4,2),(4,3),(4,7),(7,5),(7,6)],8)
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>([(0,6),(0,7),(1,5),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>([(0,7),(1,5),(3,6),(4,3),(5,2),(5,4),(5,7),(7,6)],8)
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>([(0,6),(0,7),(1,5),(3,6),(4,3),(5,2),(5,4),(5,7)],8)
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>([(0,7),(1,6),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>([(0,7),(1,5),(3,6),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>([(0,7),(1,6),(4,5),(5,3),(6,2),(6,4),(6,7)],8)
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>([(1,7),(6,5),(7,2),(7,3),(7,4),(7,6)],8)
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>([(1,6),(4,7),(5,3),(5,7),(6,2),(6,4),(6,5)],8)
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>([(1,6),(4,7),(5,3),(5,7),(6,2),(6,4),(6,5)],8)
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>([(0,6),(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5)],8)
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]=>([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6)],8)
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>([(0,3),(1,5),(1,6),(1,7),(2,7),(3,2),(3,5),(3,6),(6,4),(7,4)],8)
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>([(0,3),(1,4),(1,6),(1,7),(2,5),(2,6),(3,2),(3,4),(3,7),(7,5)],8)
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>([(0,3),(1,4),(1,5),(1,7),(2,6),(3,2),(3,4),(3,5),(3,7),(7,6)],8)
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]=>([(0,5),(0,6),(0,7),(1,4),(3,5),(4,3),(4,6),(4,7),(7,2)],8)
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>([(0,5),(0,6),(0,7),(1,4),(4,3),(4,5),(4,6),(4,7),(7,2)],8)
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>([(0,3),(1,4),(1,5),(1,6),(1,7),(3,2),(3,4),(3,5),(3,6),(3,7)],8)
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>([(0,3),(1,5),(1,6),(1,7),(3,2),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>([(0,6),(0,7),(1,4),(4,3),(4,6),(4,7),(5,2),(7,5)],8)
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(4,5),(7,4)],8)
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(7,4),(7,5)],8)
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(4,6),(4,7),(7,3)],8)
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>([(0,3),(0,4),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(6,4),(7,4)],8)
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(4,5),(7,4)],8)
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>([(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(5,4),(7,5)],8)
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[3,1,5,2,8,7,6,4]=>([(0,2),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(7,3),(7,4),(7,5)],8)
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[3,1,5,2,8,6,7,4]=>([(0,3),(0,7),(1,5),(1,7),(3,4),(3,5),(3,6),(6,2),(7,4),(7,6)],8)
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>([(0,2),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,5)],8)
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>([(0,2),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(6,3),(7,3),(7,4)],8)
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>([(0,3),(0,7),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(6,2),(7,4)],8)
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(6,2)],8)
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>([(0,2),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6)],8)
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(6,2)],8)
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>([(0,2),(0,5),(1,4),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(6,3),(7,3)],8)
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>([(0,5),(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(6,4)],8)
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>([(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2),(7,6)],8)
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>([(0,6),(1,4),(1,6),(4,7),(6,5),(6,7),(7,2),(7,3)],8)
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[2,5,1,3,7,8,6,4]=>([(0,7),(1,3),(1,7),(3,5),(3,6),(6,4),(7,2),(7,5),(7,6)],8)
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>([(0,7),(1,3),(1,7),(3,5),(3,6),(6,4),(7,2),(7,5),(7,6)],8)
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>([(0,7),(1,4),(1,7),(3,5),(4,5),(4,6),(7,2),(7,3),(7,6)],8)
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>([(0,7),(1,5),(1,7),(4,6),(5,6),(7,2),(7,3),(7,4)],8)
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>([(0,7),(1,3),(1,7),(6,2),(7,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>([(0,7),(1,2),(1,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>([(0,7),(1,3),(1,7),(6,2),(7,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>([(0,7),(1,3),(1,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>([(0,7),(1,3),(1,7),(5,2),(6,5),(7,4),(7,6)],8)
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>([(0,7),(1,4),(4,5),(5,2),(5,7),(6,3),(7,6)],8)
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>([(0,7),(1,5),(5,6),(6,2),(6,7),(7,3),(7,4)],8)
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>([(0,6),(0,7),(1,4),(4,5),(5,2),(5,6),(5,7),(7,3)],8)
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>([(0,5),(0,6),(0,7),(1,3),(3,4),(4,2),(4,5),(4,6),(4,7)],8)
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>([(0,6),(0,7),(1,4),(4,5),(5,2),(5,6),(5,7),(7,3)],8)
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>([(0,7),(1,4),(3,6),(4,5),(5,2),(5,3),(5,7),(7,6)],8)
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>([(0,6),(0,7),(1,4),(3,6),(4,5),(5,2),(5,3),(5,7)],8)
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>([(0,7),(1,5),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>([(0,7),(1,5),(4,3),(5,6),(6,2),(6,4),(6,7)],8)
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>([(0,6),(0,7),(1,4),(2,7),(4,5),(5,2),(5,6),(7,3)],8)
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>([(0,5),(0,6),(0,7),(1,3),(2,6),(2,7),(3,4),(4,2),(4,5)],8)
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>([(0,5),(0,6),(0,7),(1,3),(3,4),(4,2),(4,5),(4,6),(4,7)],8)
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>([(0,6),(0,7),(1,4),(4,5),(5,2),(5,6),(5,7),(7,3)],8)
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[3,4,2,8,1,7,6,5]=>([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(3,4),(3,5),(3,6),(3,7)],8)
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5)],8)
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(6,4),(7,2),(7,5)],8)
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>([(0,7),(1,3),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,4)],8)
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>([(0,7),(1,3),(1,7),(3,5),(3,6),(6,4),(7,2),(7,5),(7,6)],8)
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,7),(7,2)],8)
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7)],8)
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(7,2)],8)
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>([(0,2),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(6,3),(7,3),(7,4),(7,5)],8)
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>([(0,5),(0,6),(1,4),(3,5),(3,7),(4,3),(4,6),(6,7),(7,2)],8)
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5)],8)
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>([(0,2),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(7,4)],8)
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>([(0,5),(0,6),(0,7),(1,4),(3,5),(3,7),(4,3),(4,6),(7,2)],8)
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>([(0,7),(1,5),(3,6),(5,3),(5,7),(6,4),(7,2),(7,6)],8)
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>([(0,7),(1,4),(3,5),(3,6),(4,3),(4,7),(7,2),(7,5),(7,6)],8)
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>([(0,7),(1,5),(4,6),(5,4),(5,7),(7,2),(7,3),(7,6)],8)
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>([(0,7),(1,5),(5,3),(5,7),(6,2),(7,4),(7,6)],8)
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>([(0,7),(1,7),(2,4),(2,7),(4,6),(6,5),(7,3),(7,6)],8)
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>([(0,7),(1,7),(2,4),(2,7),(4,5),(4,6),(7,3),(7,5),(7,6)],8)
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>([(0,7),(1,7),(2,5),(2,7),(5,6),(7,3),(7,4),(7,6)],8)
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]=>([(0,7),(1,7),(2,4),(2,7),(6,3),(7,5),(7,6)],8)
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>([(0,5),(0,7),(1,3),(1,5),(3,7),(5,6),(6,4),(7,2),(7,6)],8)
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>([(0,3),(0,7),(1,6),(1,7),(3,6),(6,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>([(0,6),(0,7),(1,5),(1,6),(5,7),(7,2),(7,3),(7,4)],8)
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>([(0,6),(1,4),(1,6),(4,7),(5,3),(5,7),(6,5),(7,2)],8)
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>([(0,7),(1,4),(1,7),(4,6),(5,2),(5,3),(5,6),(7,5)],8)
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>([(0,7),(1,4),(1,7),(5,3),(6,2),(6,5),(7,6)],8)
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>([(0,7),(1,5),(4,6),(5,4),(6,2),(6,7),(7,3)],8)
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>([(0,6),(0,7),(1,4),(3,5),(4,3),(5,2),(5,6),(5,7)],8)
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>([(0,7),(1,5),(4,6),(5,4),(6,2),(6,3),(6,7)],8)
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>([(0,6),(0,7),(1,4),(2,7),(3,5),(4,3),(5,2),(5,6)],8)
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>([(0,6),(0,7),(1,4),(3,5),(4,3),(5,2),(5,6),(5,7)],8)
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6)],8)
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6)],8)
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>([(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(3,5),(3,7),(4,6),(4,7),(5,6)],8)
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>([(0,4),(1,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5)],8)
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[4,3,5,2,8,1,7,6]=>([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(4,5),(4,6),(4,7)],8)
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[4,5,2,3,7,1,8,6]=>([(0,5),(0,7),(1,4),(2,3),(3,6),(3,7),(4,6),(4,7),(6,5)],8)
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>([(0,6),(0,7),(1,4),(2,3),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[5,4,2,7,3,1,8,6]=>([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6)],8)
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[5,4,2,8,3,1,7,6]=>([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7)],8)
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[5,3,8,2,4,1,7,6]=>([(0,6),(0,7),(1,5),(2,4),(2,6),(2,7),(3,4),(3,5),(5,6),(5,7)],8)
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>([(0,7),(1,3),(1,7),(2,5),(3,5),(3,6),(4,2),(4,6),(7,4)],8)
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>([(0,6),(1,2),(1,3),(1,6),(2,5),(2,7),(3,4),(3,7),(5,4),(6,5),(6,7)],8)
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>([(0,4),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>([(0,5),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[5,1,4,8,3,2,7,6]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>([(0,5),(0,7),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,6)],8)
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,2)],8)
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>([(0,3),(0,7),(1,6),(1,7),(2,5),(3,6),(6,2),(6,4),(7,4),(7,5)],8)
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>([(0,3),(0,7),(1,6),(1,7),(3,6),(6,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(2,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>([(0,7),(1,4),(2,5),(3,5),(3,6),(4,3),(4,7),(7,2),(7,6)],8)
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>([(0,7),(1,4),(3,5),(3,6),(4,3),(4,7),(7,2),(7,5),(7,6)],8)
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>([(0,5),(0,6),(0,7),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(4,5)],8)
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5)],8)
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(6,4),(6,5),(7,4)],8)
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(6,3),(6,4),(7,3),(7,4),(7,5)],8)
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>([(0,7),(1,3),(1,7),(2,4),(2,5),(3,4),(3,6),(6,5),(7,2),(7,6)],8)
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>([(0,7),(1,3),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,4)],8)
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>([(0,6),(0,7),(1,3),(2,5),(2,7),(3,4),(4,2),(4,6),(6,5)],8)
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>([(0,5),(0,6),(0,7),(1,3),(2,6),(2,7),(3,4),(4,2),(4,5)],8)
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>([(0,7),(1,5),(3,6),(4,3),(4,7),(5,4),(7,2),(7,6)],8)
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>([(0,7),(1,5),(5,6),(6,2),(6,7),(7,3),(7,4)],8)
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>([(0,7),(1,2),(1,5),(2,7),(4,6),(5,4),(5,7),(7,3),(7,6)],8)
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>([(0,7),(1,3),(1,6),(3,7),(6,2),(6,7),(7,4),(7,5)],8)
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[4,3,7,2,1,5,8,6]=>([(0,7),(1,7),(2,5),(2,7),(3,5),(3,7),(5,6),(7,4),(7,6)],8)
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>([(0,7),(1,6),(2,5),(2,7),(6,7),(7,3),(7,4)],8)
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>([(0,7),(1,3),(1,7),(2,5),(3,6),(6,4),(6,5),(7,2),(7,6)],8)
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]=>([(0,6),(1,4),(1,6),(4,7),(6,5),(6,7),(7,2),(7,3)],8)
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>([(0,6),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(6,5),(7,4),(7,5)],8)
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>([(0,3),(0,7),(1,5),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,6)],8)
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>([(0,5),(0,6),(1,4),(1,6),(4,5),(4,7),(6,7),(7,2),(7,3)],8)
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>([(0,6),(0,7),(1,4),(3,7),(4,3),(4,6),(6,5),(7,2),(7,5)],8)
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(5,6),(7,5)],8)
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>([(0,7),(1,5),(5,4),(5,7),(6,2),(6,3),(7,6)],8)
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[3,7,2,1,4,5,8,6]=>([(0,7),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(7,4)],8)
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>([(0,7),(1,7),(2,5),(2,7),(6,3),(6,4),(7,6)],8)
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]=>([(0,6),(0,7),(1,4),(1,7),(4,6),(5,2),(5,3),(6,5)],8)
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>([(0,7),(1,3),(1,7),(3,6),(4,5),(5,2),(5,6),(7,4)],8)
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>([(0,7),(1,4),(1,7),(5,6),(6,2),(6,3),(7,5)],8)
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8)
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8)
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[2,3,4,6,8,5,1,7]=>([(0,7),(1,4),(3,7),(4,6),(5,2),(5,7),(6,3),(6,5)],8)
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[2,3,6,5,8,4,1,7]=>([(0,7),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>([(0,7),(1,6),(3,7),(4,3),(5,2),(5,7),(6,4),(6,5)],8)
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[2,4,5,3,6,8,1,7]=>([(0,6),(1,4),(1,5),(3,7),(4,7),(5,3),(7,2),(7,6)],8)
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>([(0,7),(1,3),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(4,6),(6,7)],8)
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[2,6,4,5,8,3,1,7]=>([(0,7),(1,2),(1,4),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[3,4,2,5,6,8,1,7]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>([(0,7),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(4,7),(6,5),(6,7)],8)
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>([(0,7),(1,5),(1,6),(2,3),(2,5),(3,6),(3,7),(4,7),(5,4)],8)
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[4,3,5,2,6,8,1,7]=>([(0,7),(1,5),(2,5),(3,6),(5,7),(7,4),(7,6)],8)
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[5,3,4,6,2,8,1,7]=>([(0,6),(1,7),(2,5),(2,7),(3,4),(4,6),(6,5),(6,7)],8)
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>([(0,7),(1,5),(2,4),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(4,7),(5,6),(5,7)],8)
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[8,5,3,4,2,6,1,7]=>[6,4,5,3,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[6,5,4,8,3,2,1,7]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,7)],8)
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[6,5,2,8,4,3,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7)],8)
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[6,4,2,8,3,5,1,7]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(3,4),(3,6),(4,5),(5,7)],8)
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[6,3,8,2,4,5,1,7]=>([(0,6),(1,7),(2,5),(2,6),(3,5),(3,7),(4,7),(6,4)],8)
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>([(0,7),(1,3),(1,7),(3,6),(4,5),(5,2),(5,6),(7,4)],8)
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[4,1,5,3,6,8,2,7]=>([(0,6),(1,3),(1,4),(1,6),(3,7),(4,5),(6,7),(7,2),(7,5)],8)
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(2,7),(3,4),(3,5),(5,7),(6,4),(6,7)],8)
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[5,1,6,3,4,8,2,7]=>([(0,6),(1,2),(1,4),(1,6),(2,7),(3,5),(3,7),(4,3),(6,5),(6,7)],8)
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[6,1,4,5,8,3,2,7]=>([(0,6),(0,7),(1,2),(1,3),(1,5),(2,7),(3,7),(4,6),(4,7),(5,4)],8)
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[6,1,8,3,4,5,2,7]=>([(0,6),(0,7),(1,3),(1,5),(1,6),(2,7),(3,7),(4,2),(5,4)],8)
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]=>([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(4,5),(6,4),(7,5)],8)
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,2),(5,7),(6,7)],8)
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[2,5,1,6,4,8,3,7]=>([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(4,7),(5,3),(5,7),(6,3),(6,7)],8)
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[2,6,1,8,4,5,3,7]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,7),(5,7),(6,2)],8)
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(5,6),(7,5)],8)
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>([(0,5),(0,6),(1,4),(3,7),(4,3),(4,5),(4,6),(5,7),(6,2),(6,7)],8)
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[5,1,2,6,4,8,3,7]=>([(0,6),(1,4),(2,7),(3,5),(3,7),(4,2),(4,3),(4,6),(6,5),(6,7)],8)
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>([(0,6),(0,7),(1,4),(3,7),(4,3),(4,6),(6,5),(7,2),(7,5)],8)
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>([(0,3),(1,4),(1,5),(1,6),(2,6),(2,7),(3,2),(3,4),(3,5),(4,7),(5,7)],8)
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(6,5),(7,4),(7,5)],8)
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>([(0,3),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(6,4),(7,4)],8)
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[3,1,5,2,6,8,4,7]=>([(0,3),(0,7),(1,5),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,6)],8)
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>([(0,7),(1,3),(1,7),(2,5),(3,6),(6,4),(6,5),(7,2),(7,6)],8)
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[2,6,1,3,8,5,4,7]=>([(0,6),(1,4),(1,6),(2,7),(3,7),(4,5),(4,7),(6,2),(6,3),(6,5)],8)
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>([(0,7),(1,5),(3,6),(4,3),(4,7),(5,4),(7,2),(7,6)],8)
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>([(0,6),(0,7),(1,4),(2,7),(3,7),(4,5),(5,2),(5,3),(5,6)],8)
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>([(0,6),(0,7),(1,3),(2,5),(2,7),(3,4),(4,2),(4,6),(6,5)],8)
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>([(0,6),(0,7),(1,2),(1,4),(2,6),(2,7),(3,5),(3,6),(4,3),(4,7),(7,5)],8)
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,7),(3,4),(3,7),(4,5),(4,6),(7,5)],8)
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>([(0,7),(1,3),(1,7),(2,4),(2,5),(3,4),(3,6),(6,5),(7,2),(7,6)],8)
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]=>([(0,7),(1,4),(2,5),(3,5),(3,6),(4,3),(4,7),(7,2),(7,6)],8)
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[3,6,2,1,4,8,5,7]=>([(0,7),(1,7),(2,4),(2,7),(3,6),(4,5),(4,6),(7,3),(7,5)],8)
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>([(0,6),(0,7),(1,4),(2,7),(3,5),(4,3),(5,2),(5,6)],8)
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>([(0,7),(1,5),(4,6),(5,4),(6,2),(6,7),(7,3)],8)
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>([(0,7),(1,2),(1,4),(1,5),(2,7),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>([(0,7),(1,5),(1,6),(3,7),(5,3),(6,2),(6,7),(7,4)],8)
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[4,3,5,2,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,5),(3,5),(5,6),(5,7),(7,4)],8)
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>([(0,7),(1,5),(2,4),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,7),(7,5)],8)
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[8,3,2,4,5,1,6,7]=>[5,3,8,2,4,1,6,7]=>([(0,7),(1,6),(2,5),(2,7),(3,5),(3,6),(6,7),(7,4)],8)
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>([(0,7),(1,6),(2,5),(2,7),(3,7),(6,3),(7,4)],8)
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[8,5,4,3,1,2,6,7]=>[3,1,4,5,8,2,6,7]=>([(0,6),(1,4),(1,6),(4,7),(5,3),(5,7),(6,5),(7,2)],8)
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>([(0,6),(1,2),(1,4),(1,6),(2,7),(4,5),(4,7),(6,5),(6,7),(7,3)],8)
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[8,4,3,5,1,2,6,7]=>[5,1,4,8,3,2,6,7]=>([(0,6),(0,7),(1,2),(1,3),(1,5),(2,7),(3,7),(5,6),(5,7),(7,4)],8)
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>([(0,5),(0,7),(1,3),(1,5),(3,7),(5,6),(6,4),(7,2),(7,6)],8)
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[4,1,2,5,8,3,6,7]=>([(0,7),(1,5),(3,6),(5,3),(5,7),(6,4),(7,2),(7,6)],8)
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]=>([(0,5),(0,6),(1,4),(3,5),(3,7),(4,3),(4,6),(6,7),(7,2)],8)
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(6,4),(7,2),(7,5)],8)
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>([(0,6),(0,7),(1,4),(2,7),(4,5),(5,2),(5,6),(7,3)],8)
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>([(0,7),(1,4),(4,5),(5,2),(5,7),(6,3),(7,6)],8)
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>([(0,7),(1,4),(1,5),(4,7),(5,3),(5,7),(6,2),(7,6)],8)
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>([(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>([(0,7),(1,5),(2,4),(2,7),(5,7),(6,3),(7,6)],8)
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>([(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2),(7,6)],8)
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>([(0,6),(0,7),(1,3),(1,4),(1,6),(3,7),(4,7),(5,2),(7,5)],8)
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>([(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(5,4),(7,5)],8)
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>([(0,6),(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5)],8)
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>([(0,7),(1,5),(4,2),(5,3),(5,7),(6,4),(7,6)],8)
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>([(0,7),(1,7),(2,4),(2,7),(5,3),(6,5),(7,6)],8)
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5)],8)
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>([(0,7),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[2,3,4,6,7,5,1,8]=>([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[2,3,5,6,4,7,1,8]=>([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4),(6,7)],8)
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[2,3,6,5,7,4,1,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>([(0,7),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8)
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>([(0,7),(1,3),(1,5),(2,7),(3,6),(4,7),(5,2),(5,6),(6,4)],8)
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>([(0,7),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6),(6,7)],8)
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[2,5,4,7,3,6,1,8]=>([(0,7),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[2,5,6,3,4,7,1,8]=>([(0,7),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2),(6,7)],8)
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[2,6,4,5,7,3,1,8]=>([(0,7),(1,2),(1,4),(1,5),(2,7),(3,6),(4,6),(5,3),(6,7)],8)
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[2,6,4,7,3,5,1,8]=>([(0,7),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>([(0,7),(1,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[6,5,3,4,7,2,1,8]=>[2,7,5,3,6,4,1,8]=>([(0,7),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,2),(5,6),(6,7)],8)
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[2,7,6,3,5,4,1,8]=>([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[2,7,6,3,4,5,1,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[3,4,2,5,6,7,1,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[3,4,2,5,7,6,1,8]=>([(0,7),(1,6),(2,3),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[3,4,2,6,7,5,1,8]=>([(0,7),(1,5),(1,6),(2,4),(3,7),(4,5),(4,6),(5,7),(6,3)],8)
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>([(0,7),(1,5),(1,6),(2,4),(3,7),(4,5),(4,6),(5,7),(6,3)],8)
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>([(0,4),(1,3),(1,7),(2,6),(2,7),(3,6),(5,4),(6,5),(7,5)],8)
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>([(0,7),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>([(0,7),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>([(0,7),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[3,7,2,5,4,6,1,8]=>([(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[4,3,6,2,7,5,1,8]=>([(0,7),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,7),(6,7)],8)
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[4,3,7,2,6,5,1,8]=>([(0,7),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>([(0,7),(1,6),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>([(0,7),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>([(0,7),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>([(0,7),(1,4),(2,3),(2,5),(2,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>([(0,7),(1,4),(2,3),(2,6),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[5,3,4,6,2,7,1,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[5,3,4,7,2,6,1,8]=>([(0,7),(1,6),(2,5),(2,7),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>([(0,7),(1,7),(2,5),(3,4),(3,7),(4,6),(6,5),(7,6)],8)
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[5,4,2,7,3,6,1,8]=>([(0,6),(1,5),(1,7),(2,5),(2,7),(3,4),(3,5),(4,7),(5,6),(7,6)],8)
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>([(0,6),(1,5),(2,4),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[5,3,7,2,4,6,1,8]=>([(0,7),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[6,4,2,5,7,3,1,8]=>([(0,6),(1,7),(2,5),(3,4),(3,5),(4,7),(5,6),(6,7)],8)
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>([(0,7),(1,6),(2,5),(2,7),(3,4),(3,5),(4,7),(5,6),(7,6)],8)
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>([(0,7),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,7),(6,7)],8)
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[7,3,2,4,5,6,1,8]=>[6,3,7,2,4,5,1,8]=>([(0,6),(1,7),(2,5),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[6,7,2,3,4,5,1,8]=>([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8)
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,3,4,6,5,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[7,5,4,6,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[7,4,2,5,6,3,1,8]=>([(0,7),(1,7),(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[7,5,2,6,4,3,1,8]=>([(0,7),(1,7),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,6,2,4,5,3,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[7,3,6,2,5,4,1,8]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[7,6,2,3,5,4,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>([(0,7),(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,4,2,5,3,6,1,8]=>([(0,7),(1,7),(2,5),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>([(0,7),(1,7),(2,5),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>([(0,7),(1,7),(2,6),(3,4),(4,6),(5,7),(6,5)],8)
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,2,8]=>([(0,7),(1,3),(1,7),(2,6),(3,6),(4,5),(5,2),(7,4)],8)
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[3,1,4,5,7,6,2,8]=>([(0,6),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(6,5)],8)
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[3,1,4,7,6,5,2,8]=>([(0,6),(1,2),(1,6),(2,7),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>([(0,6),(1,3),(1,6),(2,7),(3,7),(4,7),(5,2),(6,4),(6,5)],8)
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(4,2),(5,4),(6,7)],8)
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,4)],8)
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[4,1,7,3,6,5,2,8]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[6,7,4,3,5,1,2,8]=>[5,1,4,7,3,6,2,8]=>([(0,5),(0,7),(1,2),(1,3),(1,4),(2,7),(3,6),(4,5),(4,7),(5,6),(7,6)],8)
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,1,5,7,4,3,2,8]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[7,1,5,6,4,3,2,8]=>([(0,7),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2)],8)
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[5,4,6,3,7,1,2,8]=>[7,1,6,5,4,3,2,8]=>([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>([(0,7),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,2),(5,6),(6,7)],8)
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[7,1,6,3,5,4,2,8]=>([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[2,4,1,5,6,7,3,8]=>([(0,6),(0,7),(1,3),(1,7),(2,5),(3,6),(4,2),(6,4),(7,5)],8)
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,2),(6,7)],8)
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[2,5,1,6,4,7,3,8]=>([(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(4,3),(5,4),(6,4),(7,3)],8)
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[2,6,1,5,7,4,3,8]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(3,7),(4,7),(5,7),(6,3)],8)
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[2,7,1,5,6,4,3,8]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2)],8)
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,7),(7,4)],8)
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>([(0,6),(1,5),(2,7),(3,7),(4,7),(5,2),(5,6),(6,3),(6,4)],8)
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>([(0,5),(0,6),(1,4),(2,7),(3,7),(4,3),(4,5),(4,6),(5,7),(6,2)],8)
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>([(0,5),(0,6),(1,4),(2,7),(3,7),(4,3),(4,5),(4,6),(5,7),(6,2)],8)
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>([(0,7),(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>([(0,5),(0,6),(1,4),(2,7),(3,7),(4,3),(4,5),(4,6),(5,7),(6,2)],8)
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[3,6,2,1,7,5,4,8]=>([(0,3),(0,5),(0,6),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,7),(5,4),(6,4),(7,4)],8)
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,2),(6,7)],8)
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[2,5,1,3,7,6,4,8]=>([(0,6),(1,3),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,2),(6,4),(6,5)],8)
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[2,6,1,3,7,5,4,8]=>([(0,6),(1,4),(1,6),(2,7),(3,7),(4,5),(5,7),(6,2),(6,3),(6,5)],8)
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>([(0,6),(1,3),(1,6),(2,7),(3,7),(4,7),(5,2),(6,4),(6,5)],8)
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>([(0,7),(1,5),(2,6),(3,6),(4,3),(4,7),(5,4),(7,2)],8)
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>([(0,5),(0,6),(1,3),(2,7),(3,4),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>([(0,6),(1,4),(2,7),(3,7),(4,5),(5,2),(5,3),(5,6),(6,7)],8)
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>([(0,6),(0,7),(1,3),(2,7),(3,4),(4,2),(4,6),(6,5),(7,5)],8)
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>([(0,5),(0,6),(1,3),(2,7),(3,4),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>([(0,6),(0,7),(1,4),(1,7),(2,3),(3,6),(3,7),(4,5),(6,4),(7,5)],8)
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,7),(3,4),(3,7),(4,6),(6,5),(7,5)],8)
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[4,3,7,2,1,6,5,8]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[4,6,2,3,1,7,5,8]=>([(0,6),(0,7),(1,4),(2,3),(2,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,7),(6,5),(7,5)],8)
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[4,1,7,3,2,6,5,8]=>([(0,2),(0,3),(0,4),(1,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[2,3,6,1,4,7,5,8]=>([(0,7),(1,4),(2,6),(3,5),(4,3),(4,7),(5,6),(7,2),(7,5)],8)
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>([(0,7),(1,7),(2,4),(2,7),(3,6),(4,5),(5,6),(7,3),(7,5)],8)
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[3,1,6,2,4,7,5,8]=>([(0,3),(0,7),(1,6),(1,7),(2,4),(3,6),(5,4),(6,2),(6,5),(7,5)],8)
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]=>([(0,7),(1,5),(2,6),(3,4),(4,2),(4,7),(5,3),(7,6)],8)
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>([(0,7),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]=>([(0,7),(1,5),(2,6),(3,4),(4,2),(4,7),(5,3),(7,6)],8)
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[2,5,7,3,4,1,6,8]=>([(0,7),(1,4),(1,5),(2,7),(3,6),(4,2),(5,3),(5,7),(7,6)],8)
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[7,4,5,2,3,1,6,8]=>[3,5,2,7,4,1,6,8]=>([(0,7),(1,4),(1,6),(2,3),(2,4),(3,6),(3,7),(4,7),(6,5),(7,5)],8)
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[4,3,5,2,7,1,6,8]=>([(0,4),(1,4),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>([(0,7),(1,4),(2,3),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[5,3,4,7,2,1,6,8]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[5,4,2,7,3,1,6,8]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,7),(6,5),(7,5)],8)
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[5,3,7,2,4,1,6,8]=>([(0,7),(1,5),(2,4),(2,7),(3,4),(3,5),(4,6),(5,7),(7,6)],8)
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>([(0,7),(1,3),(2,4),(2,7),(3,5),(4,6),(5,7),(7,6)],8)
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[2,5,1,7,4,3,6,8]=>([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,6),(2,7),(4,7),(5,7),(6,3),(7,3)],8)
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>([(0,7),(1,4),(2,6),(3,5),(4,3),(4,7),(5,6),(7,2),(7,5)],8)
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4),(6,5),(7,4)],8)
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[2,5,1,3,7,4,6,8]=>([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(5,4),(6,4),(7,2),(7,5)],8)
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>([(0,7),(1,5),(2,6),(3,6),(4,3),(4,7),(5,4),(7,2)],8)
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>([(0,7),(1,5),(1,7),(2,4),(3,6),(4,5),(4,7),(5,6),(7,3)],8)
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>([(0,7),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(7,4)],8)
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>([(0,6),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,5),(6,5),(7,4)],8)
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>([(0,6),(0,7),(1,4),(2,7),(3,5),(4,2),(4,6),(6,5),(7,3)],8)
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,7),(7,4)],8)
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>([(0,6),(0,7),(1,3),(1,7),(2,5),(3,6),(4,2),(6,4),(7,5)],8)
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>([(0,7),(1,3),(1,7),(2,6),(3,6),(4,5),(5,2),(7,4)],8)
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>([(0,7),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[2,3,5,6,4,1,7,8]=>([(0,7),(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>([(0,7),(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[5,3,4,6,2,1,7,8]=>[2,6,5,3,4,1,7,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[3,4,2,5,6,1,7,8]=>([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>([(0,7),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[4,3,5,2,6,1,7,8]=>([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>([(0,7),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[6,3,4,2,5,1,7,8]=>[5,4,6,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[5,4,2,6,3,1,7,8]=>([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>([(0,7),(1,6),(2,5),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[5,6,2,3,4,1,7,8]=>([(0,7),(1,5),(2,6),(3,7),(5,7),(6,3),(7,4)],8)
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>([(0,7),(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[6,3,5,2,4,1,7,8]=>([(0,7),(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>([(0,6),(1,2),(1,6),(2,7),(4,7),(5,7),(6,4),(6,5),(7,3)],8)
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[3,1,5,6,4,2,7,8]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(7,4)],8)
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7),(7,2)],8)
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>([(0,5),(0,6),(1,2),(1,4),(1,6),(2,7),(4,5),(5,7),(6,7),(7,3)],8)
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[5,1,6,3,4,2,7,8]=>([(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(5,2),(6,7),(7,4)],8)
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[2,4,1,5,6,3,7,8]=>([(0,5),(0,7),(1,2),(1,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,7),(6,7),(7,2)],8)
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(4,7),(5,7),(6,7),(7,2)],8)
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7),(7,2)],8)
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[4,5,6,2,1,3,7,8]=>[2,6,1,4,5,3,7,8]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(7,4)],8)
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>([(0,7),(1,5),(2,6),(3,6),(5,3),(5,7),(6,4),(7,2)],8)
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[4,1,2,6,5,3,7,8]=>([(0,5),(0,6),(1,4),(2,7),(4,2),(4,5),(4,6),(5,7),(6,7),(7,3)],8)
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[2,3,5,1,6,4,7,8]=>([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(5,7),(6,7),(7,2)],8)
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>([(0,5),(0,6),(1,4),(2,7),(4,2),(4,5),(4,6),(5,7),(6,7),(7,3)],8)
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[3,1,6,2,5,4,7,8]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(4,7),(5,7),(6,7),(7,2)],8)
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[6,5,2,1,3,4,7,8]=>[2,5,1,3,6,4,7,8]=>([(0,7),(1,2),(1,7),(2,5),(3,6),(5,6),(6,4),(7,3),(7,5)],8)
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>([(0,6),(1,2),(1,6),(2,7),(4,7),(5,7),(6,4),(6,5),(7,3)],8)
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>([(0,6),(1,4),(2,7),(4,5),(5,2),(5,6),(6,7),(7,3)],8)
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>([(0,7),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>([(0,6),(1,4),(2,7),(4,5),(5,2),(5,6),(6,7),(7,3)],8)
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[4,6,2,3,1,5,7,8]=>([(0,7),(1,3),(2,4),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[4,1,6,3,2,5,7,8]=>([(0,5),(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,6),(6,2),(7,6)],8)
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(4,2),(5,4),(6,4),(7,5)],8)
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>([(0,7),(1,5),(2,6),(3,6),(5,3),(5,7),(6,4),(7,2)],8)
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>([(0,5),(0,7),(1,2),(1,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>([(0,6),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5),(7,2)],8)
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>([(0,7),(1,6),(2,3),(2,6),(3,7),(4,5),(6,7),(7,4)],8)
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>([(0,7),(1,5),(2,4),(4,7),(5,7),(6,3),(7,6)],8)
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>([(0,7),(1,4),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3)],8)
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,5)],8)
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5),(7,6)],8)
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5),(7,6)],8)
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>([(0,7),(1,7),(2,3),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>([(0,7),(1,4),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3)],8)
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>([(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,6)],8)
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>([(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,6)],8)
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>([(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],9)
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>([(1,7),(4,5),(5,8),(6,2),(7,4),(8,3),(8,6)],9)
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>([(1,7),(4,8),(5,6),(6,2),(7,4),(8,3),(8,5)],9)
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>([(1,7),(4,6),(5,4),(6,2),(7,8),(8,3),(8,5)],9)
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>([(1,8),(4,5),(5,7),(6,4),(7,2),(8,3),(8,6)],9)
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>([(1,3),(1,8),(4,5),(5,7),(6,4),(7,2),(8,6)],9)
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>([(2,8),(4,5),(5,7),(6,4),(7,3),(8,6)],9)
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[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)
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>([(1,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(9,3)],10)
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,9,7,1]=>([(1,7),(4,5),(5,8),(6,2),(7,4),(8,3),(8,6)],9)
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>([(1,8),(4,6),(5,4),(6,9),(7,2),(8,5),(9,3),(9,7)],10)
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[2,3,4,5,7,9,6,8,1]=>([(1,5),(3,8),(4,7),(5,4),(6,2),(6,8),(7,3),(7,6)],9)
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>([(1,8),(4,5),(5,9),(6,7),(7,2),(8,4),(9,3),(9,6)],10)
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[2,3,4,6,9,5,7,8,1]=>([(1,5),(3,8),(5,7),(6,2),(6,8),(7,3),(7,6),(8,4)],9)
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>([(1,8),(4,7),(5,9),(6,4),(7,2),(8,5),(9,3),(9,6)],10)
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[2,3,5,9,4,6,7,8,1]=>([(1,7),(4,8),(5,3),(5,8),(6,2),(7,4),(7,5),(8,6)],9)
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>([(1,8),(4,5),(5,7),(6,4),(7,2),(8,9),(9,3),(9,6)],10)
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[2,4,9,3,5,6,7,8,1]=>([(1,4),(1,6),(4,8),(5,3),(6,2),(6,8),(7,5),(8,7)],9)
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>([(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(9,3),(9,7)],10)
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[3,9,2,4,5,6,7,8,1]=>([(1,8),(2,4),(2,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>([(1,3),(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>([(1,3),(1,8),(4,5),(5,7),(6,4),(7,2),(8,6)],9)
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>([(2,9),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7)],10)
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[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)
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>([(1,7),(5,6),(6,8),(7,5),(8,2),(8,3),(8,4)],9)
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>([(1,7),(5,8),(6,4),(7,5),(8,2),(8,3),(8,6)],9)
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>([(1,7),(5,6),(6,4),(7,8),(8,2),(8,3),(8,5)],9)
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>([(1,8),(5,7),(6,4),(7,6),(8,2),(8,3),(8,5)],9)
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>([(1,3),(1,4),(1,8),(5,7),(6,5),(7,2),(8,6)],9)
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[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)
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>([(1,8),(5,7),(6,5),(7,9),(8,6),(9,2),(9,3),(9,4)],10)
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>([(1,8),(5,6),(6,9),(7,2),(8,5),(9,3),(9,4),(9,7)],10)
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>([(1,8),(5,9),(6,7),(7,2),(8,5),(9,3),(9,4),(9,6)],10)
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>([(1,8),(5,7),(6,5),(7,2),(8,9),(9,3),(9,4),(9,6)],10)
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>([(1,9),(5,6),(6,8),(7,5),(8,2),(9,3),(9,4),(9,7)],10)
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>([(1,3),(1,4),(1,9),(5,6),(6,8),(7,5),(8,2),(9,7)],10)
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,2,9]=>([(0,8),(1,3),(1,8),(2,7),(3,7),(4,6),(5,4),(6,2),(8,5)],9)
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>([(3,9),(5,6),(6,8),(7,5),(8,4),(9,7)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[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)
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[6,7,5,8,4,9,3,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9)],10)
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[7,5,6,4,8,3,9,2,10,1]=>[10,9,8,6,7,5,4,3,2,1]=>([(8,9)],10)
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[2,4,1,6,3,8,5,10,7,9]=>([(0,2),(0,9),(1,8),(1,9),(2,7),(2,8),(5,4),(6,3),(6,4),(7,3),(7,5),(8,5),(8,6),(9,6),(9,7)],10)
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>([(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>([(1,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],11)
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>([(0,9),(1,3),(1,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>([(0,7),(0,8),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(8,5)],9)
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>([(2,8),(3,8),(4,8),(5,7),(7,6),(8,5)],9)
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>([(2,9),(3,9),(5,7),(6,5),(7,4),(8,6),(9,8)],10)
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>([(2,10),(4,5),(5,7),(6,4),(7,9),(8,6),(9,3),(10,8)],11)
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>([(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],9)
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>([(1,7),(4,5),(5,8),(6,2),(7,4),(8,3),(8,6)],9)
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,7]=>([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9)
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>([(1,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(9,3)],10)
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,8,7,6]=>([(1,7),(5,6),(6,8),(7,5),(8,2),(8,3),(8,4)],9)
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>([(1,8),(4,7),(5,9),(6,4),(7,2),(8,5),(9,3),(9,6)],10)
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>([(1,3),(1,9),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],10)
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,2]=>([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>([(0,8),(1,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,2),(7,3)],9)
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,2]=>([(0,9),(1,3),(1,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>([(0,9),(1,7),(2,9),(3,9),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],10)
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,11,2]=>([(0,10),(1,3),(1,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>([],10)
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[7,6,8,4,3,5,9,2,10,1]=>[10,9,4,8,3,7,6,5,2,1]=>([(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[7,6,8,5,9,4,10,2,1,3]=>[2,10,1,9,8,7,6,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9)],10)
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[10,5,4,6,3,7,2,8,1,9]=>[8,7,6,5,10,4,3,2,1,9]=>([(0,9),(1,9),(2,9),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>([],12)
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[6,4,5,7,3,8,2,9,1,10]=>[9,8,7,6,4,5,3,2,1,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,3]=>([(0,7),(0,8),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(8,5)],9)
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,4]=>([(0,7),(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(6,7),(8,4)],9)
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,5]=>([(0,7),(0,8),(1,5),(3,8),(4,2),(5,6),(6,3),(6,7),(8,4)],9)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,6]=>([(0,7),(0,8),(1,5),(2,8),(4,6),(5,4),(6,2),(6,7),(8,3)],9)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,7]=>([(0,7),(0,8),(1,5),(2,8),(3,4),(4,6),(5,3),(6,2),(6,7)],9)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]=>([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9)
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,3]=>([(0,8),(1,6),(4,5),(5,2),(6,3),(6,8),(7,4),(8,7)],9)
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,10,3]=>([(0,8),(0,9),(1,3),(1,8),(3,9),(4,5),(5,7),(6,4),(7,2),(9,6)],10)
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,10,4]=>([(0,8),(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(7,8),(9,5)],10)
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,10,5]=>([(0,8),(0,9),(1,6),(3,9),(4,5),(5,2),(6,7),(7,3),(7,8),(9,4)],10)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,10,6]=>([(0,8),(0,9),(1,6),(3,9),(4,7),(5,2),(6,4),(7,3),(7,8),(9,5)],10)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,10,7]=>([(0,8),(0,9),(1,6),(2,9),(4,5),(5,7),(6,4),(7,2),(7,8),(9,3)],10)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,10,8]=>([(0,8),(0,9),(1,6),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>([(0,9),(1,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(8,9)],10)
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>([(0,7),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(7,8),(8,5)],9)
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,9,1]=>([(1,6),(2,8),(3,8),(5,3),(6,7),(7,2),(7,5),(8,4)],9)
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,9,1]=>([(1,7),(3,8),(4,8),(5,4),(6,2),(7,3),(7,5),(8,6)],9)
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,9,1]=>([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>([(1,3),(1,7),(2,7),(2,9),(3,8),(3,9),(6,5),(7,6),(7,8),(8,4),(8,5),(9,4),(9,6)],10)
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>([(1,3),(1,9),(2,9),(2,11),(3,10),(3,11),(6,5),(7,4),(7,6),(8,4),(8,5),(9,7),(9,10),(10,6),(10,8),(11,7),(11,8)],12)
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[8,9,2,3,4,5,6,7,1]=>([(1,8),(2,4),(5,7),(6,5),(7,3),(8,6)],9)
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>([(0,8),(1,3),(1,8),(2,7),(3,7),(4,6),(5,4),(6,2),(8,5)],9)
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,8,2,3,4,5,6,7,1]=>([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>([(0,7),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(7,8),(8,5)],9)
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>([(0,7),(1,6),(3,8),(4,5),(5,2),(6,3),(6,7),(7,8),(8,4)],9)
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[2,3,4,6,1,5,7,8,9]=>([(0,7),(1,5),(3,8),(4,2),(5,6),(6,3),(6,7),(7,8),(8,4)],9)
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[2,3,4,5,7,1,6,8,9]=>([(0,8),(1,6),(2,7),(4,5),(5,2),(5,8),(6,4),(7,3),(8,7)],9)
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]=>([(0,8),(1,6),(2,7),(3,5),(4,3),(5,2),(5,8),(6,4),(8,7)],9)
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>([(0,8),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>([(0,8),(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>([(0,8),(1,8),(2,6),(4,8),(5,3),(6,4),(7,5),(8,7)],9)
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>([(0,8),(1,8),(2,7),(3,8),(5,6),(6,3),(7,5),(8,4)],9)
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>([(0,9),(1,9),(2,8),(3,9),(4,5),(5,7),(6,4),(7,3),(8,6)],10)
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,9,2,1]=>([(2,4),(3,8),(4,7),(5,8),(6,5),(7,6)],9)
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,9,2,8]=>([(0,8),(1,3),(1,8),(3,7),(4,6),(5,4),(6,2),(6,7),(8,5)],9)
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>([(0,9),(1,7),(4,6),(5,4),(6,2),(7,3),(7,9),(8,5),(9,8)],10)
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>([(0,9),(1,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(8,9)],10)
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>([(3,10),(5,7),(6,5),(7,9),(8,6),(9,4),(10,8)],11)
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>([(0,8),(1,6),(4,5),(5,7),(6,4),(7,2),(7,8),(8,3)],9)
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>([(0,8),(1,5),(4,6),(5,4),(6,2),(6,8),(7,3),(8,7)],9)
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>([(0,8),(1,5),(4,2),(5,6),(6,3),(6,8),(7,4),(8,7)],9)
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>([(0,7),(0,8),(1,5),(2,8),(3,4),(4,6),(5,3),(6,2),(6,7)],9)
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>([(0,9),(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,9),(9,3)],10)
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>([(0,7),(0,8),(1,4),(2,6),(2,8),(3,5),(4,3),(5,2),(5,7),(7,6)],9)
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>([(0,9),(1,6),(4,5),(5,7),(6,4),(7,2),(7,9),(8,3),(9,8)],10)
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>([(0,9),(1,6),(4,7),(5,2),(6,4),(7,3),(7,9),(8,5),(9,8)],10)
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>([(0,9),(1,6),(4,5),(5,2),(6,7),(7,3),(7,9),(8,4),(9,8)],10)
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(6,5),(7,6),(8,4)],9)
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>([(1,9),(4,6),(5,4),(6,8),(7,5),(8,10),(9,7),(10,2),(10,3)],11)
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>([(3,7),(6,8),(7,6),(8,4),(8,5)],9)
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>([(3,8),(6,7),(7,9),(8,6),(9,4),(9,5)],10)
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>([(0,8),(1,3),(1,4),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>([(1,7),(4,8),(5,8),(6,3),(7,2),(7,4),(7,5),(8,6)],9)
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>([(1,6),(3,8),(4,8),(6,7),(7,2),(7,3),(7,4),(8,5)],9)
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>([(0,8),(1,7),(3,8),(4,8),(5,2),(6,5),(7,3),(7,4),(8,6)],9)
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>([(0,8),(1,5),(4,2),(5,6),(6,3),(6,8),(7,4),(8,7)],9)
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>([(0,8),(1,6),(2,7),(3,5),(4,3),(5,2),(5,8),(6,4),(8,7)],9)
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>([(0,8),(1,3),(1,7),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,10,2,9]=>([(0,9),(1,3),(1,9),(3,8),(4,5),(5,7),(6,4),(7,2),(7,8),(9,6)],10)
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>([(0,8),(1,6),(2,8),(3,8),(5,7),(6,5),(7,2),(7,3),(8,4)],9)
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>([(1,6),(3,8),(4,8),(5,7),(6,5),(7,2),(7,3),(7,4)],9)
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
searching the database
Sorry, this map was not found in the database.