Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00073: Permutations —major-index to inversion-number bijection⟶ 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]=>[3,2,1]=>([],3)
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>([(1,2)],3)
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>([(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]=>[4,3,2,1]=>([],4)
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>([(2,3)],4)
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>([(2,3)],4)
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>([(1,3),(2,3)],4)
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>([(1,2),(2,3)],4)
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[3,4,2,1]=>([(2,3)],4)
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4)
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,4,1]=>([(1,3),(2,3)],4)
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,4,1]=>([(1,2),(2,3)],4)
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4)
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4)
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,3,1,4]=>([(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]=>[5,4,3,2,1]=>([],5)
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>([(3,4)],5)
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,3,1]=>([(3,4)],5)
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>([(2,4),(3,4)],5)
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>([(2,3),(3,4)],5)
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,3,4,2,1]=>([(3,4)],5)
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,4,1,3]=>([(1,4),(2,3),(2,4)],5)
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>([(2,4),(3,4)],5)
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>([(2,3),(3,4)],5)
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>([(1,4),(2,4),(3,4)],5)
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>([(1,4),(2,3),(3,4)],5)
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,3,1,4]=>([(1,4),(2,3),(3,4)],5)
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>([(1,4),(2,4),(4,3)],5)
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[4,5,3,2,1]=>([(3,4)],5)
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,5,4,1,2]=>([(0,4),(1,2),(1,3)],5)
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,5,2,4,1]=>([(1,4),(2,3),(2,4)],5)
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,5,2,1,4]=>([(0,4),(1,4),(2,3),(2,4)],5)
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5)
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[4,3,5,2,1]=>([(2,4),(3,4)],5)
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,5,1,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>([(2,3),(3,4)],5)
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5)
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,5,1]=>([(1,4),(2,4),(3,4)],5)
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,5,1]=>([(1,4),(2,3),(3,4)],5)
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5)
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5)
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>([(0,4),(1,3),(2,3),(3,4)],5)
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,4,1,3,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5)
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3,1,4,5]=>([(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]=>[6,5,4,3,2,1]=>([],6)
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>([(4,5)],6)
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>([(4,5)],6)
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>([(3,5),(4,5)],6)
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>([(3,4),(4,5)],6)
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>([(4,5)],6)
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>([(2,5),(3,4),(3,5)],6)
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>([(3,5),(4,5)],6)
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>([(3,4),(4,5)],6)
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>([(2,5),(3,5),(4,5)],6)
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>([(2,5),(3,4),(4,5)],6)
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>([(2,5),(3,4),(4,5)],6)
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>([(2,5),(3,5),(5,4)],6)
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>([(2,3),(3,5),(5,4)],6)
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>([(4,5)],6)
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>([(1,5),(2,3),(2,4)],6)
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>([(2,5),(3,4),(3,5)],6)
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>([(1,5),(2,5),(3,4),(3,5)],6)
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>([(1,5),(2,3),(2,5),(5,4)],6)
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>([(3,5),(4,5)],6)
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>([(3,4),(4,5)],6)
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>([(1,5),(2,3),(3,4),(3,5)],6)
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>([(2,5),(3,5),(4,5)],6)
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>([(2,5),(3,4),(4,5)],6)
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>([(2,5),(3,4),(4,5)],6)
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>([(2,5),(3,5),(5,4)],6)
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>([(2,3),(3,5),(5,4)],6)
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>([(1,5),(2,5),(3,5),(4,5)],6)
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6)
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>([(1,5),(2,4),(3,4),(4,5)],6)
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>([(1,5),(2,3),(3,4),(4,5)],6)
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6)
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>([(1,5),(2,4),(3,4),(4,5)],6)
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>([(1,5),(2,3),(3,4),(4,5)],6)
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>([(1,5),(2,5),(3,5),(5,4)],6)
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>([(1,5),(2,5),(3,4),(5,3)],6)
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>([(4,5)],6)
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>([(1,5),(2,3),(2,4)],6)
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>([(1,5),(2,3),(2,4)],6)
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>([(0,5),(1,5),(2,3),(2,4)],6)
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>([(0,4),(1,2),(1,3),(1,5),(4,5)],6)
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>([(2,5),(3,4),(3,5)],6)
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>([(1,5),(2,5),(3,4),(3,5)],6)
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>([(1,5),(2,3),(2,5),(5,4)],6)
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>([(0,5),(1,4),(2,3),(2,4),(4,5)],6)
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6)
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6)
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>([(0,4),(1,5),(5,2),(5,3)],6)
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>([(1,5),(2,3),(3,4),(3,5)],6)
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>([(2,5),(3,5),(4,5)],6)
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>([(2,5),(3,4),(4,5)],6)
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>([(2,5),(3,4),(4,5)],6)
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>([(2,5),(3,5),(5,4)],6)
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>([(2,3),(3,5),(5,4)],6)
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6)
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6)
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>([(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]=>[7,6,5,4,3,2,1]=>([],7)
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>([(5,6)],7)
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>([(5,6)],7)
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>([(4,6),(5,6)],7)
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>([(4,5),(5,6)],7)
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>([(5,6)],7)
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>([(3,6),(4,5),(4,6)],7)
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>([(4,6),(5,6)],7)
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>([(4,5),(5,6)],7)
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>([(3,6),(4,6),(5,6)],7)
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>([(3,6),(4,5),(5,6)],7)
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>([(3,6),(4,5),(5,6)],7)
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>([(3,6),(4,6),(6,5)],7)
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>([(3,4),(4,6),(6,5)],7)
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>([(5,6)],7)
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>([(2,6),(3,4),(3,5)],7)
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>([(3,6),(4,5),(4,6)],7)
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>([(2,6),(3,6),(4,5),(4,6)],7)
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>([(2,6),(3,4),(3,6),(6,5)],7)
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>([(4,6),(5,6)],7)
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>([(4,5),(5,6)],7)
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>([(2,6),(3,4),(4,5),(4,6)],7)
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>([(3,6),(4,6),(5,6)],7)
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>([(3,6),(4,5),(5,6)],7)
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>([(3,6),(4,5),(5,6)],7)
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>([(3,6),(4,6),(6,5)],7)
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>([(3,4),(4,6),(6,5)],7)
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>([(2,6),(3,6),(4,6),(5,6)],7)
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>([(2,6),(3,5),(4,5),(5,6)],7)
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>([(2,6),(3,5),(4,5),(5,6)],7)
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>([(2,6),(3,6),(4,6),(6,5)],7)
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>([(2,6),(3,6),(4,5),(6,4)],7)
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>([(2,6),(4,5),(5,3),(6,4)],7)
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>([(5,6)],7)
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>([(2,6),(3,4),(3,5)],7)
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>([(2,6),(3,4),(3,5)],7)
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>([(1,6),(2,6),(3,4),(3,5)],7)
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>([(3,6),(4,5),(4,6)],7)
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>([(2,6),(3,6),(4,5),(4,6)],7)
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>([(2,6),(3,4),(3,6),(6,5)],7)
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7)
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>([(1,5),(2,3),(2,4),(4,6),(5,6)],7)
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7)
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>([(1,6),(2,6),(3,4),(3,6),(6,5)],7)
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>([(4,6),(5,6)],7)
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7)
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>([(4,5),(5,6)],7)
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>([(1,5),(2,6),(6,3),(6,4)],7)
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>([(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>([(1,6),(2,3),(3,5),(3,6),(6,4)],7)
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>([(3,6),(4,6),(5,6)],7)
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>([(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>([(3,6),(4,5),(5,6)],7)
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>([(3,6),(4,6),(6,5)],7)
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>([(1,6),(2,6),(3,5),(6,4),(6,5)],7)
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>([(3,4),(4,6),(6,5)],7)
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>([(1,3),(2,6),(3,5),(5,4),(5,6)],7)
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>([(2,6),(3,6),(4,6),(5,6)],7)
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7)
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7)
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>([(2,6),(3,6),(4,6),(6,5)],7)
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>([(2,6),(3,6),(4,5),(6,4)],7)
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>([(2,6),(4,5),(5,3),(6,4)],7)
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>([(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>([(5,6)],7)
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>([(2,6),(3,4),(3,5)],7)
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>([(2,6),(3,4),(3,5)],7)
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>([(1,6),(2,6),(3,4),(3,5)],7)
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>([(0,6),(1,3),(1,4),(1,5),(6,2)],7)
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>([(2,6),(3,4),(3,5)],7)
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6)],7)
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>([(1,6),(2,6),(3,4),(3,5)],7)
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5)],7)
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7)
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>([(0,5),(1,2),(1,3),(1,6),(5,6),(6,4)],7)
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>([(3,6),(4,5),(4,6)],7)
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>([(0,5),(0,6),(1,3),(2,4),(2,5),(2,6)],7)
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(6,4)],7)
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>([(2,6),(3,6),(4,5),(4,6)],7)
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>([(2,6),(3,4),(3,6),(6,5)],7)
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>([(0,6),(1,5),(2,4),(2,6),(6,3),(6,5)],7)
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7)
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>([(1,5),(2,3),(2,4),(4,6),(5,6)],7)
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7)
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>([(1,6),(2,6),(3,4),(3,6),(6,5)],7)
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>([(0,6),(1,5),(2,3),(2,4),(4,6),(5,6)],7)
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>([(0,6),(1,5),(2,3),(2,4),(4,6),(5,6)],7)
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7)
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>([(0,4),(1,2),(1,3),(1,5),(3,6),(4,5),(5,6)],7)
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7)
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>([(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7)
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7)
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7)
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>([(0,5),(1,2),(1,3),(3,6),(5,6),(6,4)],7)
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>([(0,6),(1,5),(2,4),(2,5),(5,6),(6,3)],7)
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>([(4,6),(5,6)],7)
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7)
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7)
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7)
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,6)],7)
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7)
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7)
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>([(4,5),(5,6)],7)
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>([(1,5),(2,6),(6,3),(6,4)],7)
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>([(1,5),(2,6),(6,3),(6,4)],7)
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>([(0,3),(1,6),(2,6),(3,4),(3,5)],7)
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>([(0,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>([(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>([(1,6),(2,3),(3,5),(3,6),(6,4)],7)
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>([(0,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7)
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>([(0,6),(1,5),(2,3),(3,4),(3,6),(6,5)],7)
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7)
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7)
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>([(0,5),(0,6),(1,3),(2,4),(4,5),(4,6)],7)
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>([(0,5),(0,6),(1,3),(2,4),(4,5),(4,6)],7)
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>([(3,6),(4,6),(6,5)],7)
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>([(0,6),(1,6),(2,3),(6,4),(6,5)],7)
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>([(1,6),(2,6),(3,5),(6,4),(6,5)],7)
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7)
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7)
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>([(3,4),(4,6),(6,5)],7)
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>([(0,4),(1,5),(5,6),(6,2),(6,3)],7)
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>([(1,3),(2,6),(3,5),(5,4),(5,6)],7)
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7)
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>([(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>([(2,6),(3,6),(4,6),(6,5)],7)
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7)
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>([(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7)
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7)
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>([(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>([(0,6),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>([(0,4),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>([(0,4),(1,2),(1,3),(1,5),(2,6),(3,6),(4,5),(5,6)],7)
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>([(0,4),(1,2),(1,3),(2,6),(3,5),(4,5),(5,6)],7)
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>([(0,5),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7)
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7)
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7)
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>([(0,6),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7)
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>([(0,4),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(5,6),(6,4)],7)
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[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]=>[8,7,6,5,4,3,2,1]=>([],8)
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>([(6,7)],8)
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>([(6,7)],8)
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>([(5,7),(6,7)],8)
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>([(5,6),(6,7)],8)
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>([(6,7)],8)
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>([(4,7),(5,6),(5,7)],8)
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>([(5,7),(6,7)],8)
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>([(5,6),(6,7)],8)
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>([(4,7),(5,7),(6,7)],8)
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>([(4,7),(5,6),(6,7)],8)
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>([(4,7),(5,6),(6,7)],8)
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>([(4,7),(5,7),(7,6)],8)
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>([(4,5),(5,7),(7,6)],8)
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>([(6,7)],8)
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[8,7,6,3,5,4,1,2]=>([(3,7),(4,5),(4,6)],8)
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>([(4,7),(5,6),(5,7)],8)
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>([(3,7),(4,7),(5,6),(5,7)],8)
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[8,7,6,2,5,1,3,4]=>([(3,7),(4,5),(4,7),(7,6)],8)
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>([(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>([(5,6),(6,7)],8)
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>([(4,7),(5,7),(6,7)],8)
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>([(4,7),(5,6),(6,7)],8)
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>([(4,5),(5,7),(7,6)],8)
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>([(3,7),(4,7),(5,7),(6,7)],8)
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>([(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>([(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>([(3,7),(4,6),(5,6),(6,7)],8)
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>([(3,7),(4,5),(5,6),(6,7)],8)
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>([(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[8,7,6,2,4,1,3,5]=>([(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>([(3,7),(4,6),(5,6),(6,7)],8)
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>([(3,7),(4,5),(5,6),(6,7)],8)
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>([(3,7),(4,7),(5,7),(7,6)],8)
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>([(3,7),(4,5),(5,7),(7,6)],8)
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>([(3,7),(4,5),(5,7),(7,6)],8)
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>([(3,7),(4,7),(5,6),(7,5)],8)
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>([(3,4),(4,7),(6,5),(7,6)],8)
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,5,6,4,3,2,1]=>([(6,7)],8)
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[8,7,4,6,5,3,1,2]=>([(3,7),(4,5),(4,6)],8)
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[8,7,4,6,5,2,3,1]=>([(3,7),(4,5),(4,6)],8)
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,7,4,6,5,2,1,3]=>([(2,7),(3,7),(4,5),(4,6)],8)
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>([(4,7),(5,6),(5,7)],8)
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>([(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[3,5,7,6,8,4,2,1]=>[8,7,3,6,2,4,1,5]=>([(2,7),(3,6),(4,5),(4,6),(6,7)],8)
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,7,2,6,1,3,4,5]=>([(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,7,5,4,6,3,2,1]=>([(5,7),(6,7)],8)
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>([(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,7,3,2,6,1,4,5]=>([(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,4,5,6,3,2,1]=>([(5,6),(6,7)],8)
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,7,2,3,6,1,4,5]=>([(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>([(4,7),(5,7),(6,7)],8)
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>([(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[8,7,3,2,4,6,1,5]=>([(2,7),(3,7),(4,6),(7,5),(7,6)],8)
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>([(4,5),(5,7),(7,6)],8)
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[8,7,2,3,4,6,1,5]=>([(2,4),(3,7),(4,6),(6,5),(6,7)],8)
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[8,7,5,4,3,2,6,1]=>([(3,7),(4,7),(5,7),(6,7)],8)
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[8,7,5,4,2,3,6,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,4,3,5,2,6,1]=>([(3,7),(4,6),(5,6),(6,7)],8)
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[8,7,4,3,2,5,6,1]=>([(3,7),(4,7),(5,7),(7,6)],8)
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[8,7,2,3,4,5,6,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[8,7,3,5,2,4,1,6]=>([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[8,7,2,5,1,3,4,6]=>([(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>[8,7,3,4,2,1,5,6]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[8,7,2,4,1,3,5,6]=>([(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>([(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,6,7,5,4,3,2,1]=>([(6,7)],8)
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[8,5,7,6,4,3,1,2]=>([(3,7),(4,5),(4,6)],8)
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,5,7,6,4,2,3,1]=>([(3,7),(4,5),(4,6)],8)
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[8,5,7,6,4,2,1,3]=>([(2,7),(3,7),(4,5),(4,6)],8)
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[8,4,7,6,5,1,2,3]=>([(1,7),(2,4),(2,5),(2,6),(7,3)],8)
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[8,4,7,6,3,1,2,5]=>([(1,7),(2,6),(3,4),(3,5),(3,7),(6,7)],8)
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>([(1,6),(2,6),(3,4),(3,5),(3,7),(6,7)],8)
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,3,7,6,1,2,4,5]=>([(1,5),(2,3),(2,4),(2,7),(5,7),(7,6)],8)
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,5,7,4,6,3,2,1]=>([(4,7),(5,6),(5,7)],8)
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[8,4,7,3,6,5,1,2]=>([(1,6),(1,7),(2,5),(3,4),(3,6),(3,7)],8)
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[8,3,7,2,6,1,4,5]=>([(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(7,5)],8)
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[8,5,7,4,3,6,2,1]=>([(3,7),(4,7),(5,6),(5,7)],8)
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[8,4,7,3,2,6,1,5]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[8,3,7,2,4,6,1,5]=>([(1,7),(2,6),(3,5),(3,7),(7,4),(7,6)],8)
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[8,5,7,4,3,2,6,1]=>([(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[8,4,7,5,2,3,6,1]=>([(2,6),(3,4),(3,5),(5,7),(6,7)],8)
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,4,7,3,5,2,6,1]=>([(2,7),(3,6),(4,5),(4,6),(6,7)],8)
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[8,3,7,2,4,5,6,1]=>([(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[8,5,7,4,3,2,1,6]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>[8,3,7,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(2,6),(4,7),(5,6),(6,7)],8)
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[8,4,7,3,5,2,1,6]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(6,7)],8)
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[8,3,7,2,5,1,4,6]=>([(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(5,6),(7,6)],8)
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[8,4,7,3,2,5,1,6]=>([(1,7),(2,7),(3,6),(4,5),(4,7),(7,6)],8)
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[8,4,7,3,2,1,5,6]=>([(1,7),(2,7),(3,7),(4,5),(4,7),(7,6)],8)
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[8,3,7,4,1,2,5,6]=>([(1,5),(2,3),(2,4),(4,7),(5,7),(7,6)],8)
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[8,3,7,2,4,1,5,6]=>([(1,7),(2,6),(3,5),(3,6),(6,7),(7,4)],8)
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[2,5,4,6,7,8,3,1]=>[8,3,7,2,1,4,5,6]=>([(1,7),(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,6,5,7,4,3,2,1]=>([(5,7),(6,7)],8)
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[8,5,4,7,6,3,1,2]=>([(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[8,4,3,7,5,1,2,6]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(6,7)],8)
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[8,3,2,7,1,4,5,6]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,5,6,7,4,3,2,1]=>([(5,6),(6,7)],8)
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[8,3,4,7,6,1,2,5]=>([(1,5),(2,6),(5,7),(6,3),(6,4),(6,7)],8)
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[8,4,5,7,3,6,2,1]=>([(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[8,3,4,7,2,6,1,5]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[8,4,5,7,3,2,6,1]=>([(2,7),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,3,4,7,2,5,6,1]=>([(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,2,3,7,1,4,5,6]=>([(1,7),(2,5),(5,4),(5,7),(6,3),(7,6)],8)
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,6,5,4,7,3,2,1]=>([(4,7),(5,7),(6,7)],8)
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[8,5,4,3,7,6,1,2]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[8,5,4,3,7,2,6,1]=>([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,6,4,5,7,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[8,5,6,4,7,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,4,5,3,7,2,6,1]=>([(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,4,5,6,7,3,2,1]=>([(4,5),(5,7),(7,6)],8)
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[8,3,4,5,7,6,1,2]=>([(1,5),(2,6),(6,7),(7,3),(7,4)],8)
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>[8,3,4,5,7,2,1,6]=>([(1,4),(2,7),(3,7),(4,6),(6,5),(6,7)],8)
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,7,1,5,6]=>([(1,7),(2,5),(5,6),(6,3),(6,7),(7,4)],8)
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,6,5,4,3,7,2,1]=>([(3,7),(4,7),(5,7),(6,7)],8)
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[8,5,4,3,2,7,1,6]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[3,5,4,2,7,8,6,1]=>[8,5,3,4,2,7,1,6]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,6,4,3,5,7,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[8,3,5,2,4,7,1,6]=>([(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[8,3,4,5,2,7,1,6]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,5,4,3,6,7,2,1]=>([(3,7),(4,7),(5,7),(7,6)],8)
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[8,4,3,2,5,7,1,6]=>([(1,7),(2,7),(3,7),(4,6),(7,5),(7,6)],8)
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[8,5,3,4,6,7,2,1]=>([(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[8,4,2,3,5,7,1,6]=>([(1,7),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[3,2,4,5,7,8,6,1]=>[8,3,2,4,5,7,1,6]=>([(1,7),(2,6),(3,6),(4,5),(4,7),(6,4)],8)
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[8,3,4,5,6,7,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[8,2,3,4,5,7,1,6]=>([(1,7),(2,5),(4,6),(5,4),(6,3),(6,7)],8)
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[8,6,5,3,4,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[8,6,5,3,2,4,7,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[8,6,4,5,3,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[8,6,4,3,2,5,7,1]=>([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,6,4,2,3,5,7,1]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[8,6,2,3,4,5,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[8,5,6,4,3,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,4,6,3,5,2,7,1]=>([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[8,3,6,2,4,5,7,1]=>([(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,5,4,6,3,2,7,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[8,5,4,3,6,2,7,1]=>([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,4,5,3,6,2,7,1]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[8,4,3,5,6,2,7,1]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,3,4,5,6,2,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,5,4,3,2,6,7,1]=>([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[8,5,4,2,3,6,7,1]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,4,5,3,2,6,7,1]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[8,4,2,3,5,6,7,1]=>([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,3,4,2,5,6,7,1]=>([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,7,1]=>([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,7,1]=>([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>([(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[8,6,2,5,1,3,4,7]=>([(1,7),(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[8,6,2,3,5,1,4,7]=>([(1,7),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,6,2,4,1,3,5,7]=>([(1,5),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[8,5,6,4,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[8,3,6,5,1,2,4,7]=>([(1,5),(2,3),(2,4),(2,6),(3,7),(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[8,3,6,2,5,1,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,3,6,2,4,1,5,7]=>([(1,6),(2,5),(3,4),(3,5),(4,7),(5,6),(6,7)],8)
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[8,3,6,2,1,4,5,7]=>([(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(7,5)],8)
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[8,4,3,6,5,1,2,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,7)],8)
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[8,4,3,6,2,5,1,7]=>([(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,4,3,6,2,1,5,7]=>([(1,7),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[8,3,2,6,1,4,5,7]=>([(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(7,4)],8)
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[8,4,5,6,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[8,2,3,6,1,4,5,7]=>([(1,7),(2,3),(3,5),(3,7),(4,6),(5,6),(7,4)],8)
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[8,4,2,3,6,1,5,7]=>([(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,4,5,3,6,2,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[8,4,3,5,6,2,1,7]=>([(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,3,4,5,6,2,1,7]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,6,1,5,7]=>([(1,3),(2,6),(3,5),(4,7),(5,4),(5,6),(6,7)],8)
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[8,5,4,3,2,6,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,3,2,4,6,1,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[8,5,2,3,4,6,1,7]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,4,3,5,2,6,1,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[8,3,4,2,5,6,1,7]=>([(1,7),(2,6),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,6,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,6,1,7]=>([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>[8,5,2,3,4,1,6,7]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>([(1,7),(2,6),(3,6),(5,7),(6,5),(7,4)],8)
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[8,4,5,3,2,1,6,7]=>([(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[2,4,6,5,3,7,8,1]=>[8,3,5,2,4,1,6,7]=>([(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,3,5,2,1,4,6,7]=>([(1,7),(2,7),(3,4),(3,7),(4,6),(6,5),(7,6)],8)
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[3,2,5,6,4,7,8,1]=>[8,3,2,5,1,4,6,7]=>([(1,7),(2,5),(2,7),(3,5),(3,7),(5,6),(6,4),(7,6)],8)
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[8,2,3,5,1,4,6,7]=>([(1,7),(2,3),(3,5),(3,7),(5,6),(6,4),(7,6)],8)
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>([(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[8,4,2,3,1,5,6,7]=>([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,3,4,2,1,5,6,7]=>([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[8,2,4,1,3,5,6,7]=>([(1,6),(2,3),(2,6),(3,7),(4,5),(6,7),(7,4)],8)
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[7,8,6,5,4,3,2,1]=>([(6,7)],8)
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[6,8,7,5,4,3,1,2]=>([(3,7),(4,5),(4,6)],8)
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[6,8,7,5,4,2,1,3]=>([(2,7),(3,7),(4,5),(4,6)],8)
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[5,8,7,6,4,1,2,3]=>([(1,7),(2,4),(2,5),(2,6),(7,3)],8)
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[6,8,7,5,3,4,2,1]=>([(3,7),(4,5),(4,6)],8)
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[6,8,7,5,3,2,4,1]=>([(2,7),(3,7),(4,5),(4,6)],8)
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[6,8,7,5,3,2,1,4]=>([(1,7),(2,7),(3,7),(4,5),(4,6)],8)
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[5,8,7,6,3,1,2,4]=>([(0,7),(1,6),(2,3),(2,4),(2,5),(6,7)],8)
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[5,8,7,6,2,3,1,4]=>([(0,7),(1,6),(2,3),(2,4),(2,5),(6,7)],8)
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[5,8,7,6,2,1,3,4]=>([(0,7),(1,7),(2,3),(2,4),(2,5),(7,6)],8)
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[4,8,7,6,1,2,3,5]=>([(0,6),(1,2),(1,3),(1,4),(1,7),(5,7),(6,5)],8)
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[6,8,7,4,5,3,2,1]=>([(3,7),(4,5),(4,6)],8)
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[5,8,7,3,6,2,4,1]=>([(1,6),(2,6),(2,7),(3,4),(3,5),(3,7)],8)
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[4,8,7,2,6,1,3,5]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(2,7),(5,7)],8)
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[5,8,7,3,2,6,1,4]=>([(0,6),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7)],8)
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[5,8,7,3,4,6,2,1]=>([(2,6),(3,4),(3,5),(3,7),(6,7)],8)
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>[6,8,7,4,3,2,5,1]=>([(1,7),(2,7),(3,7),(4,5),(4,6)],8)
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[5,8,7,3,4,2,6,1]=>([(1,7),(2,6),(3,4),(3,5),(3,7),(6,7)],8)
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[5,8,7,3,2,4,6,1]=>([(1,6),(2,6),(3,4),(3,5),(3,7),(6,7)],8)
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[6,8,7,4,3,2,1,5]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6)],8)
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[4,8,7,2,5,1,3,6]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(5,7),(6,7)],8)
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[5,8,7,3,2,1,4,6]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(7,6)],8)
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,5,6,4,7,8,3,2]=>[4,8,7,3,1,2,5,6]=>([(0,7),(1,5),(2,3),(2,4),(2,7),(5,7),(7,6)],8)
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[4,8,7,2,1,3,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,7),(6,7),(7,3)],8)
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[3,8,7,1,2,4,5,6]=>([(0,5),(1,3),(1,4),(1,7),(5,7),(6,2),(7,6)],8)
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[6,8,5,7,4,3,2,1]=>([(4,7),(5,6),(5,7)],8)
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[5,8,4,7,6,3,1,2]=>([(1,6),(1,7),(2,5),(3,4),(3,6),(3,7)],8)
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[5,8,4,7,6,2,3,1]=>([(1,6),(1,7),(2,5),(3,4),(3,6),(3,7)],8)
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[4,8,3,7,6,1,2,5]=>([(0,5),(0,6),(0,7),(1,4),(2,3),(2,5),(2,6),(2,7),(4,7)],8)
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[5,8,4,7,3,6,2,1]=>([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[4,8,3,7,2,5,6,1]=>([(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(7,5)],8)
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[4,8,3,7,5,1,2,6]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(2,6),(4,7),(6,7)],8)
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[4,8,3,7,2,5,1,6]=>([(0,7),(1,6),(2,5),(2,7),(3,4),(3,5),(3,7),(7,6)],8)
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[4,8,3,7,2,1,5,6]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(7,5)],8)
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[3,8,2,7,1,4,5,6]=>([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(4,5),(7,4)],8)
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[6,8,5,4,7,3,2,1]=>([(3,7),(4,7),(5,6),(5,7)],8)
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[5,8,4,3,7,6,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(3,6),(3,7)],8)
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[5,8,4,3,7,2,6,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[5,8,4,3,7,2,1,6]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[4,8,3,2,7,1,5,6]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(7,5)],8)
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[3,8,2,4,7,1,5,6]=>([(0,7),(1,6),(2,3),(2,6),(6,4),(6,7),(7,5)],8)
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[6,8,5,4,3,7,2,1]=>([(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[5,8,6,3,4,7,2,1]=>([(2,6),(3,4),(3,5),(5,7),(6,7)],8)
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[4,8,3,5,2,7,1,6]=>([(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(5,6),(5,7)],8)
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[5,8,4,3,6,7,2,1]=>([(2,7),(3,7),(4,5),(4,7),(7,6)],8)
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[4,8,3,5,6,7,2,1]=>([(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[6,8,5,4,3,2,7,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[5,8,4,6,3,2,7,1]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(6,7)],8)
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[5,8,4,3,6,2,7,1]=>([(1,7),(2,7),(3,6),(4,5),(4,7),(7,6)],8)
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[5,8,4,3,2,6,7,1]=>([(1,7),(2,7),(3,7),(4,5),(4,7),(7,6)],8)
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[3,8,2,4,5,6,7,1]=>([(1,7),(2,4),(2,7),(5,3),(6,5),(7,6)],8)
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[6,8,5,4,3,2,1,7]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7)],8)
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[5,8,6,4,2,1,3,7]=>([(0,7),(1,6),(2,6),(3,4),(3,5),(5,7),(6,7)],8)
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,5,6,7,4,3,8,2]=>[4,8,6,5,1,2,3,7]=>([(0,6),(1,2),(1,4),(1,5),(3,7),(4,7),(5,7),(6,3)],8)
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>[4,8,6,2,3,1,5,7]=>([(0,7),(1,4),(2,3),(2,5),(2,7),(4,7),(5,6),(7,6)],8)
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[4,8,6,2,1,3,5,7]=>([(0,5),(1,5),(2,3),(2,4),(2,6),(4,7),(5,6),(6,7)],8)
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[3,8,6,1,2,4,5,7]=>([(0,5),(1,2),(1,4),(1,7),(3,6),(4,6),(5,7),(7,3)],8)
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[4,8,3,6,2,5,1,7]=>([(0,7),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,3,6,5,7,4,8,2]=>[4,8,3,6,2,1,5,7]=>([(0,7),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(5,6),(7,6)],8)
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[3,8,2,6,1,4,5,7]=>([(0,7),(1,5),(1,7),(2,3),(2,5),(2,7),(4,6),(5,6),(7,4)],8)
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[4,8,3,2,6,1,5,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8)
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[4,8,3,5,2,6,1,7]=>([(0,5),(1,6),(2,7),(3,4),(3,5),(5,7),(7,6)],8)
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[5,8,4,3,2,1,6,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,7),(7,6)],8)
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[4,8,5,2,1,3,6,7]=>([(0,6),(1,6),(2,3),(2,4),(4,7),(6,7),(7,5)],8)
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[4,8,3,2,1,5,6,7]=>([(0,7),(1,7),(2,7),(3,4),(3,7),(5,6),(7,5)],8)
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[3,8,2,1,4,5,6,7]=>([(0,7),(1,7),(2,4),(2,7),(5,3),(6,5),(7,6)],8)
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,8,1,3,4,5,6,7]=>([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[7,6,8,5,4,3,2,1]=>([(5,7),(6,7)],8)
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[6,5,8,7,4,3,1,2]=>([(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[6,5,8,7,4,2,3,1]=>([(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[6,5,8,7,4,2,1,3]=>([(1,5),(2,5),(3,6),(3,7),(4,6),(4,7)],8)
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[5,4,8,7,6,1,2,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4)],8)
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[6,5,8,7,3,4,2,1]=>([(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[5,4,8,7,2,6,1,3]=>([(0,4),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[6,5,8,7,3,2,4,1]=>([(1,5),(2,5),(3,6),(3,7),(4,6),(4,7)],8)
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[5,4,8,7,2,3,6,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,7)],8)
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[6,5,8,7,3,2,1,4]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[5,4,8,7,3,1,2,6]=>([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,7)],8)
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[5,4,8,7,2,3,1,6]=>([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,7)],8)
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[5,4,8,7,2,1,3,6]=>([(0,6),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(6,7)],8)
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[4,3,8,7,1,2,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,7),(7,4)],8)
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[6,5,8,4,7,3,2,1]=>([(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[5,4,8,3,7,6,1,2]=>([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4)],8)
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[5,4,8,3,7,2,6,1]=>([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[5,4,8,3,7,2,1,6]=>([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[4,3,8,2,7,1,5,6]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[6,5,8,4,3,7,2,1]=>([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[5,4,8,3,2,7,1,6]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[4,3,8,2,5,7,1,6]=>([(0,7),(1,6),(2,5),(2,7),(3,5),(3,7),(7,4),(7,6)],8)
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[6,5,8,4,3,2,7,1]=>([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>[5,4,8,6,2,3,7,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(6,7)],8)
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[5,4,8,3,6,2,7,1]=>([(1,7),(2,6),(3,5),(3,7),(4,5),(4,7),(7,6)],8)
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[5,4,8,3,2,6,7,1]=>([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[4,3,8,2,5,6,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[6,5,8,4,3,2,1,7]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>[5,4,8,6,3,1,2,7]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(6,7)],8)
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[5,4,8,6,2,3,1,7]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(6,7)],8)
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[5,4,8,6,2,1,3,7]=>([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,7),(6,7)],8)
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[4,3,8,6,1,2,5,7]=>([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(2,3),(3,7),(5,6),(7,6)],8)
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[5,4,8,3,6,2,1,7]=>([(0,7),(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(6,7)],8)
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[4,3,8,2,6,1,5,7]=>([(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8)
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[5,4,8,3,2,6,1,7]=>([(0,7),(1,7),(2,6),(3,5),(3,7),(4,5),(4,7),(7,6)],8)
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[4,3,8,5,1,2,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,7),(6,7),(7,4)],8)
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[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)
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,2,8,1,4,5,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[6,7,8,5,4,3,2,1]=>([(5,6),(6,7)],8)
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[5,6,8,7,4,3,1,2]=>([(2,4),(3,5),(5,6),(5,7)],8)
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[5,6,8,7,4,2,1,3]=>([(1,4),(2,7),(3,7),(4,5),(4,6)],8)
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[4,5,8,7,6,1,2,3]=>([(0,7),(1,6),(6,5),(7,2),(7,3),(7,4)],8)
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[4,5,8,7,2,3,6,1]=>([(1,5),(2,6),(5,7),(6,3),(6,4),(6,7)],8)
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[5,6,8,7,3,2,1,4]=>([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6)],8)
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[4,5,8,7,2,3,1,6]=>([(0,7),(1,5),(2,6),(5,7),(6,3),(6,4),(6,7)],8)
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>([(0,5),(1,6),(5,7),(6,2),(6,3),(6,7),(7,4)],8)
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[5,6,8,4,7,3,2,1]=>([(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[4,5,8,3,7,6,1,2]=>([(0,6),(0,7),(1,3),(2,4),(4,5),(4,6),(4,7)],8)
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[4,5,8,3,7,2,6,1]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[4,5,8,3,7,2,1,6]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,4,8,2,7,1,5,6]=>([(0,7),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[5,6,8,4,3,7,2,1]=>([(2,7),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>[4,5,8,3,2,7,1,6]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[4,5,8,3,6,7,2,1]=>([(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[5,6,8,4,3,2,7,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[3,4,8,2,5,6,7,1]=>([(1,7),(2,5),(5,4),(5,7),(6,3),(7,6)],8)
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[5,6,8,4,3,2,1,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[3,4,8,6,1,2,5,7]=>([(0,4),(1,5),(3,7),(4,6),(5,2),(5,3),(5,6),(6,7)],8)
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,2,5,4,7,6,8,3]=>[4,5,8,3,2,6,1,7]=>([(0,7),(1,7),(2,6),(3,4),(4,5),(4,7),(7,6)],8)
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[4,5,8,3,2,1,6,7]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(4,7),(7,5)],8)
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,4,8,2,1,5,6,7]=>([(0,7),(1,7),(2,5),(5,4),(5,7),(6,3),(7,6)],8)
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[2,3,8,1,4,5,6,7]=>([(0,7),(1,5),(4,2),(5,3),(5,7),(6,4),(7,6)],8)
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[7,6,5,8,4,3,2,1]=>([(4,7),(5,7),(6,7)],8)
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[6,5,4,8,7,3,1,2]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[6,5,4,8,7,2,3,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[6,5,4,8,7,2,1,3]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5)],8)
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[6,5,4,8,3,7,2,1]=>([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[5,4,3,8,2,7,1,6]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[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)
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[5,4,3,8,2,6,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[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)
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[5,4,3,8,2,1,6,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,3,2,8,1,5,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[7,5,6,8,4,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[6,4,5,8,7,3,1,2]=>([(1,6),(1,7),(2,4),(3,5),(5,6),(5,7)],8)
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[5,3,4,8,7,1,2,6]=>([(0,5),(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[6,4,5,8,3,2,7,1]=>([(1,7),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[5,3,4,8,2,6,1,7]=>([(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(7,5)],8)
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,2,3,8,1,5,6,7]=>([(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[5,6,4,8,7,2,1,3]=>([(0,5),(1,5),(2,6),(2,7),(3,4),(4,6),(4,7)],8)
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>[4,5,3,8,7,1,2,6]=>([(0,5),(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(4,6),(4,7)],8)
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[5,6,4,8,3,7,2,1]=>([(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[4,5,3,8,2,7,1,6]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[5,6,4,8,3,2,1,7]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[4,5,3,8,6,1,2,7]=>([(0,5),(0,6),(1,3),(2,4),(3,7),(4,5),(4,6),(6,7)],8)
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[4,5,3,8,2,6,1,7]=>([(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(4,7),(7,5)],8)
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[4,5,3,8,2,1,6,7]=>([(0,7),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[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)
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[6,5,7,8,4,3,2,1]=>([(4,7),(5,7),(7,6)],8)
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[5,4,6,8,7,3,1,2]=>([(1,7),(2,7),(3,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[4,3,5,8,7,1,2,6]=>([(0,6),(1,6),(2,3),(3,7),(6,4),(6,5),(6,7)],8)
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[3,2,4,8,1,5,6,7]=>([(0,7),(1,6),(2,6),(4,5),(6,3),(6,7),(7,4)],8)
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[5,6,7,8,4,3,2,1]=>([(4,5),(5,7),(7,6)],8)
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>([(1,5),(2,6),(6,7),(7,3),(7,4)],8)
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,5,6,8,7,2,1,3]=>([(0,7),(1,7),(2,5),(5,6),(6,3),(6,4)],8)
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[3,4,5,8,7,1,2,6]=>([(0,4),(1,5),(4,7),(5,6),(6,2),(6,3),(6,7)],8)
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[4,5,6,8,3,7,2,1]=>([(2,4),(3,7),(4,6),(6,5),(6,7)],8)
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[3,4,5,8,2,7,1,6]=>([(0,3),(1,7),(2,6),(2,7),(3,5),(5,4),(5,6),(5,7)],8)
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[3,4,5,8,2,6,7,1]=>([(1,7),(2,5),(5,6),(6,3),(6,7),(7,4)],8)
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,5,6,8,3,2,1,7]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(6,5),(6,7)],8)
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[3,4,5,8,6,1,2,7]=>([(0,4),(1,5),(3,7),(4,7),(5,6),(6,2),(6,3)],8)
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[2,3,4,8,1,5,6,7]=>([(0,7),(1,4),(4,5),(5,2),(5,7),(6,3),(7,6)],8)
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[7,6,5,4,8,3,2,1]=>([(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[6,5,4,3,8,7,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5)],8)
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[6,5,4,3,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[6,5,4,3,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[7,6,4,5,8,3,2,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[6,5,3,4,8,7,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(5,6),(5,7)],8)
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[6,5,3,4,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[6,5,3,4,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,4,2,3,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[7,5,6,4,8,3,2,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[6,4,5,3,8,7,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(5,6),(5,7)],8)
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[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)
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[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)
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[7,5,4,6,8,3,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[6,4,3,5,8,7,1,2]=>([(0,5),(1,5),(2,6),(2,7),(3,4),(5,6),(5,7)],8)
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[6,4,3,5,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[6,4,3,5,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,3,2,4,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,5),(3,5),(5,6),(5,7),(7,4)],8)
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[7,4,5,6,8,3,2,1]=>([(3,7),(4,5),(5,6),(6,7)],8)
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[6,3,4,5,8,7,1,2]=>([(0,6),(0,7),(1,3),(2,4),(4,5),(5,6),(5,7)],8)
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[6,3,4,5,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[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)
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,2,3,4,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,3),(3,5),(5,6),(5,7),(7,4)],8)
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[6,7,5,4,8,3,2,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[5,6,4,3,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[4,5,3,2,8,1,6,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,7,4,6,8,3,2,1]=>([(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[4,6,3,5,8,7,1,2]=>([(0,5),(1,3),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[4,6,3,5,8,2,7,1]=>([(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[4,6,3,5,8,2,1,7]=>([(0,7),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,5,2,4,8,1,6,7]=>([(0,7),(1,5),(2,3),(2,5),(3,6),(3,7),(5,6),(5,7),(7,4)],8)
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[6,5,7,4,8,3,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,4,6,3,8,7,1,2]=>([(0,5),(1,5),(2,6),(2,7),(3,4),(5,6),(5,7)],8)
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,4,6,3,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,4,6,3,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[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)
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,4,8,3,2,1]=>([(3,7),(4,5),(5,6),(6,7)],8)
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[4,5,6,3,8,7,1,2]=>([(0,6),(0,7),(1,3),(2,4),(4,5),(5,6),(5,7)],8)
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[4,5,6,3,8,2,7,1]=>([(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[4,5,6,3,8,2,1,7]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[6,5,4,7,8,3,2,1]=>([(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,4,3,6,8,7,1,2]=>([(0,7),(1,7),(2,7),(3,4),(7,5),(7,6)],8)
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[6,4,5,7,8,3,2,1]=>([(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,3,4,6,8,2,1,7]=>([(0,7),(1,7),(2,6),(3,4),(4,6),(6,5),(6,7)],8)
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[4,2,3,5,8,1,6,7]=>([(0,7),(1,6),(2,3),(3,7),(6,5),(7,4),(7,6)],8)
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,4,7,8,3,2,1]=>([(3,7),(4,5),(5,7),(7,6)],8)
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[4,5,3,6,8,2,7,1]=>([(1,7),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,4,6,7,8,3,2,1]=>([(3,7),(4,7),(5,6),(7,5)],8)
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[4,3,5,6,8,7,1,2]=>([(0,7),(1,7),(2,5),(6,3),(6,4),(7,6)],8)
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,8,1,6,7]=>([(0,7),(1,6),(2,6),(4,5),(4,7),(6,4),(7,3)],8)
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[4,5,6,7,8,3,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[3,4,5,6,8,7,1,2]=>([(0,6),(1,4),(5,7),(6,5),(7,2),(7,3)],8)
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[3,4,5,6,8,2,7,1]=>([(1,7),(2,5),(4,6),(5,4),(6,3),(6,7)],8)
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,8,1,6,7]=>([(0,7),(1,5),(4,6),(5,4),(6,2),(6,7),(7,3)],8)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[7,6,5,4,3,8,2,1]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[7,6,5,3,4,8,2,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[6,5,3,4,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[7,6,4,3,5,8,2,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[7,6,3,4,5,8,2,1]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[6,5,2,3,4,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[7,5,6,4,3,8,2,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,4,5,3,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[6,3,5,2,4,8,1,7]=>([(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[7,5,4,6,3,8,2,1]=>([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,4,3,5,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[7,4,5,6,3,8,2,1]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[7,5,4,3,6,8,2,1]=>([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,4,3,2,5,8,1,7]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(7,5),(7,6)],8)
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[7,5,3,4,6,8,2,1]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[6,4,2,3,5,8,1,7]=>([(0,6),(1,7),(2,5),(2,7),(3,4),(4,6),(6,5),(6,7)],8)
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[7,3,4,5,6,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,2,3,4,5,8,1,7]=>([(0,3),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[6,7,5,4,3,8,2,1]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[5,6,4,3,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[4,6,3,5,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[5,7,4,3,6,8,2,1]=>([(2,7),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[4,7,3,5,6,8,2,1]=>([(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[2,1,4,5,3,8,7,6]=>[5,4,7,3,6,8,2,1]=>([(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[5,6,7,4,3,8,2,1]=>([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[4,5,6,3,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[4,5,7,3,6,8,2,1]=>([(2,7),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[4,5,3,6,2,8,1,7]=>([(0,6),(1,7),(2,5),(2,7),(3,4),(4,6),(6,5),(6,7)],8)
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[5,4,6,7,3,8,2,1]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>[4,3,5,6,2,8,1,7]=>([(0,7),(1,6),(1,7),(2,5),(3,5),(4,6),(4,7),(5,4)],8)
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[4,5,6,7,3,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[3,4,5,6,2,8,1,7]=>([(0,3),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,5,4,3,7,8,2,1]=>([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,8,1,7]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(7,5),(7,6)],8)
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[6,5,3,4,7,8,2,1]=>([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[5,3,2,4,6,8,1,7]=>([(0,7),(1,5),(2,5),(3,6),(5,7),(7,4),(7,6)],8)
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,3,4,5,7,8,2,1]=>([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[5,2,3,4,6,8,1,7]=>([(0,7),(1,6),(2,4),(4,5),(5,7),(7,3),(7,6)],8)
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[4,6,3,5,7,8,2,1]=>([(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[3,5,2,4,6,8,1,7]=>([(0,5),(1,6),(2,3),(2,5),(3,7),(5,7),(7,4),(7,6)],8)
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[4,3,5,2,6,8,1,7]=>([(0,7),(1,5),(2,5),(3,6),(5,7),(7,4),(7,6)],8)
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[5,4,3,6,7,8,2,1]=>([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,8,1,7]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(7,4)],8)
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[4,2,3,5,6,8,1,7]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[3,4,2,5,6,8,1,7]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[4,3,5,6,7,8,2,1]=>([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[3,2,4,5,6,8,1,7]=>([(0,7),(1,6),(2,6),(3,5),(5,4),(5,7),(6,3)],8)
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[3,4,5,6,7,8,2,1]=>([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[2,3,4,5,6,8,1,7]=>([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,6,5,4,2,3,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[7,6,5,3,4,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,6,5,3,2,4,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,6,5,2,3,4,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,6,4,5,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,6,3,5,2,4,8,1]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,6,4,3,5,2,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[7,6,3,4,5,2,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,6,4,2,3,5,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,6,3,2,4,5,8,1]=>([(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,6,2,3,4,5,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,5,6,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[7,4,6,3,5,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[7,4,3,6,2,5,8,1]=>([(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,4,5,6,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>[7,5,4,3,6,2,8,1]=>([(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[7,5,3,4,6,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,4,5,3,6,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,5,4,3,2,6,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,5,4,2,3,6,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,5,3,2,4,6,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[7,5,2,3,4,6,8,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,4,3,5,2,6,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[7,4,3,2,5,6,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,2,3,4,5,6,8,1]=>([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[6,7,5,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[5,7,6,3,2,4,8,1]=>([(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[6,5,7,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[5,4,7,6,2,3,8,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,7)],8)
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[5,4,7,3,6,2,8,1]=>([(1,7),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[5,4,7,3,2,6,8,1]=>([(1,7),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[4,3,7,2,5,6,8,1]=>([(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(7,4)],8)
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[6,4,5,7,3,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[2,1,3,5,6,4,8,7]=>[4,3,5,7,2,6,8,1]=>([(1,6),(2,6),(3,5),(4,7),(5,7),(6,4),(6,5)],8)
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[4,5,6,7,3,2,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[3,4,5,7,2,6,8,1]=>([(1,3),(2,6),(3,5),(4,7),(5,4),(5,6),(6,7)],8)
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[6,5,4,3,7,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[6,5,3,4,7,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[6,4,5,3,7,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[6,4,3,5,7,2,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[6,3,4,5,7,2,8,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[4,6,3,5,7,2,8,1]=>([(1,5),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[5,4,6,3,7,2,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[4,5,6,3,7,2,8,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[4,5,3,6,7,2,8,1]=>([(1,7),(2,6),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[3,4,5,6,7,2,8,1]=>([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[6,5,4,3,2,7,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[6,5,4,2,3,7,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[6,5,3,4,2,7,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[6,5,3,2,4,7,8,1]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[6,5,2,3,4,7,8,1]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[6,3,5,2,4,7,8,1]=>([(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[6,3,4,5,2,7,8,1]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[6,2,3,4,5,7,8,1]=>([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[4,6,3,5,2,7,8,1]=>([(1,7),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[5,4,6,3,2,7,8,1]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[4,3,6,2,5,7,8,1]=>([(1,7),(2,5),(2,7),(3,5),(3,7),(5,6),(6,4),(7,6)],8)
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[4,5,6,3,2,7,8,1]=>([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[4,3,5,6,2,7,8,1]=>([(1,7),(2,6),(3,6),(5,7),(6,5),(7,4)],8)
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[3,4,5,6,2,7,8,1]=>([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>[5,4,2,3,6,7,8,1]=>([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[5,3,2,4,6,7,8,1]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[5,2,3,4,6,7,8,1]=>([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[4,5,3,2,6,7,8,1]=>([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[3,5,2,4,6,7,8,1]=>([(1,6),(2,3),(2,6),(3,7),(4,5),(6,7),(7,4)],8)
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[4,3,5,2,6,7,8,1]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[3,4,5,2,6,7,8,1]=>([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[4,3,2,5,6,7,8,1]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[4,2,3,5,6,7,8,1]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[3,4,2,5,6,7,8,1]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,8,1]=>([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,8,1]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,6,3,5,2,4,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[7,6,4,3,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>[7,6,4,3,2,5,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[7,6,3,4,2,1,5,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[4,3,6,5,7,2,1,8]=>[7,6,3,2,4,1,5,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,5,6,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,3,6,2,5,1,4,8]=>([(0,7),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[7,3,6,2,1,4,5,8]=>([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,5,4,6,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[3,2,6,5,7,4,1,8]=>[7,4,3,6,2,1,5,8]=>([(0,7),(1,7),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[7,3,2,6,1,4,5,8]=>([(0,7),(1,6),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,4,5,6,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[7,3,4,6,2,1,5,8]=>([(0,7),(1,7),(2,6),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[7,3,2,4,6,1,5,8]=>([(0,6),(1,6),(2,7),(3,5),(4,7),(5,7),(6,4),(6,5)],8)
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,3,4,5,6,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,5,4,3,2,6,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[3,4,2,5,7,6,1,8]=>[7,4,2,3,5,6,1,8]=>([(0,7),(1,7),(2,6),(3,4),(4,6),(5,7),(6,5)],8)
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,6,1,8]=>([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,3,5,2,1,4,6,8]=>([(0,7),(1,7),(2,5),(3,4),(3,7),(4,6),(6,5),(7,6)],8)
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[7,4,2,3,5,1,6,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[7,2,3,4,1,5,6,8]=>([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[2,4,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[6,7,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[5,7,6,4,2,1,3,8]=>([(0,7),(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>[5,7,6,3,4,2,1,8]=>([(0,7),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>[5,7,6,3,2,4,1,8]=>([(0,7),(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[4,7,6,2,3,1,5,8]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(3,7),(4,7),(5,6),(6,7)],8)
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[3,7,6,1,2,4,5,8]=>([(0,5),(1,2),(1,3),(1,6),(2,7),(3,7),(4,7),(5,6),(6,4)],8)
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[5,7,4,6,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[4,7,3,6,5,1,2,8]=>([(0,5),(0,6),(1,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>([(0,7),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[3,7,2,6,1,4,5,8]=>([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(4,7),(5,7),(6,4)],8)
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[4,7,3,5,2,6,1,8]=>([(0,6),(1,7),(2,5),(3,4),(3,5),(4,7),(5,6),(6,7)],8)
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[4,7,3,2,5,6,1,8]=>([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(5,7),(6,5)],8)
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[4,7,5,2,1,3,6,8]=>([(0,5),(1,5),(2,3),(2,4),(3,7),(4,6),(5,6),(6,7)],8)
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[3,7,5,1,2,4,6,8]=>([(0,4),(1,2),(1,3),(1,5),(2,6),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[4,7,3,5,2,1,6,8]=>([(0,7),(1,7),(2,5),(3,4),(3,5),(4,6),(5,7),(7,6)],8)
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[3,7,2,5,1,4,6,8]=>([(0,7),(1,4),(1,7),(2,3),(2,4),(2,7),(3,6),(4,5),(5,6),(7,5)],8)
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[4,7,3,2,5,1,6,8]=>([(0,7),(1,7),(2,5),(3,4),(3,7),(4,6),(5,6),(7,5)],8)
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>[3,7,2,4,5,1,6,8]=>([(0,5),(1,6),(2,3),(2,5),(3,7),(4,6),(5,4),(6,7)],8)
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[4,7,3,2,1,5,6,8]=>([(0,7),(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(7,5)],8)
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[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)
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[6,5,7,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>[5,4,7,6,3,1,2,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,7)],8)
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>([(0,7),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[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)
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[5,6,7,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[3,4,7,6,1,2,5,8]=>([(0,4),(1,5),(2,7),(3,7),(4,6),(5,2),(5,3),(5,6),(6,7)],8)
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[3,4,7,2,5,1,6,8]=>([(0,7),(1,5),(2,3),(3,4),(3,7),(4,6),(5,6),(7,5)],8)
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[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)
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[6,5,4,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>[5,4,3,7,6,1,2,8]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,7)],8)
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[5,4,3,7,2,6,1,8]=>([(0,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>[5,4,3,7,2,1,6,8]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[4,3,2,7,1,5,6,8]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[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)
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[5,6,4,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[4,5,3,7,2,6,1,8]=>([(0,7),(1,6),(2,5),(2,7),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[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)
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[4,5,6,7,3,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[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)
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[6,5,4,3,7,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,7,1,6,8]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[5,3,2,4,7,1,6,8]=>([(0,4),(1,4),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[5,2,3,4,7,1,6,8]=>([(0,7),(1,5),(1,7),(2,3),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[5,6,4,3,7,2,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[4,5,3,2,7,1,6,8]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,5,2,4,7,1,6,8]=>([(0,7),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[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)
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[3,4,5,2,7,1,6,8]=>([(0,7),(1,5),(1,7),(2,3),(3,4),(4,5),(4,7),(5,6),(7,6)],8)
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[5,4,3,6,7,2,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[3,4,5,6,7,2,1,8]=>([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[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)
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[6,5,4,3,2,7,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[6,3,4,5,2,7,1,8]=>([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[6,4,2,3,5,7,1,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[6,2,3,4,5,7,1,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[5,6,4,3,2,7,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[4,6,3,5,2,7,1,8]=>([(0,7),(1,5),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]=>[5,4,6,3,2,7,1,8]=>([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>[3,4,6,2,5,7,1,8]=>([(0,6),(1,7),(2,3),(3,4),(3,7),(4,5),(5,6),(7,5)],8)
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[5,4,3,6,2,7,1,8]=>([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[5,3,4,6,2,7,1,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[4,5,3,6,2,7,1,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[3,4,5,6,2,7,1,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,7,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[5,2,3,4,6,7,1,8]=>([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[4,3,2,5,6,7,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[4,2,3,5,6,7,1,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[3,4,2,5,6,7,1,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[3,2,4,5,6,7,1,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,7,1,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[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)
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[5,6,4,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[4,6,5,3,1,2,7,8]=>([(0,7),(1,5),(2,3),(2,4),(3,7),(4,7),(5,7),(7,6)],8)
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[4,6,5,2,1,3,7,8]=>([(0,6),(1,6),(2,3),(2,4),(3,7),(4,7),(6,7),(7,5)],8)
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,7),(5,7),(6,7),(7,4)],8)
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>([(0,7),(1,6),(2,6),(3,4),(3,6),(4,7),(6,7),(7,5)],8)
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>[3,6,4,1,2,5,7,8]=>([(0,5),(1,3),(1,4),(3,7),(4,6),(5,6),(6,7),(7,2)],8)
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[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)
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[4,3,6,5,1,2,7,8]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,7),(5,7),(6,7),(7,4)],8)
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[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)
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[4,5,6,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[3,4,6,5,1,2,7,8]=>([(0,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3),(7,4)],8)
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[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)
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[5,4,3,6,2,1,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[3,4,5,6,2,1,7,8]=>([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[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)
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,6,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[5,3,2,4,6,1,7,8]=>([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[5,2,3,4,6,1,7,8]=>([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[4,3,5,2,6,1,7,8]=>([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[3,4,5,2,6,1,7,8]=>([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[3,4,2,5,6,1,7,8]=>([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[3,2,4,5,6,1,7,8]=>([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,6,1,7,8]=>([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[5,2,4,1,3,6,7,8]=>([(0,7),(1,6),(2,3),(2,6),(3,7),(4,5),(6,7),(7,4)],8)
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[3,5,4,1,2,6,7,8]=>([(0,5),(1,3),(1,4),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[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)
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[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)
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[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)
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[3,2,5,1,4,6,7,8]=>([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(5,6),(6,3),(7,6)],8)
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[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)
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[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)
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[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]=>[9,8,7,6,5,4,3,2,1]=>([],9)
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>([(7,8)],9)
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>([(6,7),(7,8)],9)
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>([(5,6),(6,8),(8,7)],9)
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>([(4,5),(5,8),(7,6),(8,7)],9)
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>([(2,8),(4,5),(5,7),(6,4),(7,3),(8,6)],9)
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(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]=>[10,9,8,7,6,5,4,3,2,1]=>([],10)
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>([(8,9)],10)
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>([(7,8)],9)
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>([(7,8),(8,9)],10)
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>([(6,7),(7,9),(9,8)],10)
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>([(5,6),(6,9),(8,7),(9,8)],10)
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>([(4,5),(5,9),(7,8),(8,6),(9,7)],10)
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>([(3,9),(5,6),(6,8),(7,5),(8,4),(9,7)],10)
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>([(2,9),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7)],10)
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[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)
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[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)
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[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]=>[9,8,7,6,5,4,2,1,3]=>([(6,8),(7,8)],9)
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>([(5,8),(6,8),(7,8)],9)
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>([(4,8),(5,8),(6,8),(7,8)],9)
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>([(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>([(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>([(7,9),(8,9)],10)
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>([(5,8),(6,7),(7,8)],9)
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>([(6,9),(7,9),(8,9)],10)
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>([(4,8),(5,8),(6,7),(7,8)],9)
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>([(5,9),(6,9),(7,9),(8,9)],10)
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1]=>[9,8,7,4,5,3,2,1,6]=>([(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>([(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1]=>[9,8,5,6,4,3,2,1,7]=>([(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>([(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1]=>[9,6,7,5,4,3,2,1,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[7,8,6,5,4,3,2,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[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)
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,3,5,7,9,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>([(0,9),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9)],10)
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,1,4,6,5,3,8,10,9,7]=>[6,5,8,4,7,3,10,2,9,1]=>([(1,9),(2,8),(2,9),(3,7),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9)],10)
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[6,5,7,4,8,3,9,2,10,1]=>([(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>([(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[2,3,4,5,6,7,8,9,1]=>([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[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)
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[3,2,4,5,6,7,8,9,1]=>([(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>([(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>([(1,10),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],11)
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>[3,2,4,5,6,7,8,9,10,1]=>([(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>[3,4,2,5,6,7,8,9,1]=>([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>[4,2,3,5,6,7,8,9,1]=>([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>[9,2,3,1,4,5,6,7,8]=>([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>([(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>([(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[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)
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[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)
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[2,3,4,5,6,9,1,7,8]=>([(0,8),(1,6),(4,5),(5,7),(6,4),(7,2),(7,8),(8,3)],9)
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[2,3,4,5,9,1,6,7,8]=>([(0,8),(1,5),(4,6),(5,4),(6,2),(6,8),(7,3),(8,7)],9)
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[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)
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[2,3,9,1,4,5,6,7,8]=>([(0,8),(1,6),(4,5),(5,2),(6,3),(6,8),(7,4),(8,7)],9)
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[3,4,5,6,7,8,9,2,1]=>([(2,8),(4,5),(5,7),(6,4),(7,3),(8,6)],9)
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[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)
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[2,3,4,5,6,7,10,1,8,9]=>([(0,9),(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,9),(9,3)],10)
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[2,3,4,5,6,10,1,7,8,9]=>([(0,9),(1,6),(4,5),(5,7),(6,4),(7,2),(7,9),(8,3),(9,8)],10)
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[2,3,4,5,10,1,6,7,8,9]=>([(0,9),(1,6),(4,7),(5,2),(6,4),(7,3),(7,9),(8,5),(9,8)],10)
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[2,3,4,10,1,5,6,7,8,9]=>([(0,9),(1,6),(4,5),(5,2),(6,7),(7,3),(7,9),(8,4),(9,8)],10)
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[2,3,10,1,4,5,6,7,8,9]=>([(0,9),(1,7),(4,6),(5,4),(6,2),(7,3),(7,9),(8,5),(9,8)],10)
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[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)
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[8,9,7,6,5,4,3,2,1]=>([(7,8)],9)
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[9,10,8,7,6,5,4,3,2,1]=>([(8,9)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>([(9,10)],11)
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>([(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>([(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[8,7,9,6,5,4,3,2,1]=>([(6,8),(7,8)],9)
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[8,7,6,9,5,4,3,2,1]=>([(5,8),(6,8),(7,8)],9)
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[8,7,6,5,9,4,3,2,1]=>([(4,8),(5,8),(6,8),(7,8)],9)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[8,7,6,5,4,9,3,2,1]=>([(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[8,7,6,5,4,3,9,2,1]=>([(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,9,1]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[7,8,9,6,5,4,3,2,1]=>([(6,7),(7,8)],9)
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[9,8,10,7,6,5,4,3,2,1]=>([(7,9),(8,9)],10)
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[8,6,7,9,5,4,3,2,1]=>([(5,8),(6,7),(7,8)],9)
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[9,8,7,10,6,5,4,3,2,1]=>([(6,9),(7,9),(8,9)],10)
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>[8,7,5,6,9,4,3,2,1]=>([(4,8),(5,8),(6,7),(7,8)],9)
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[9,8,7,6,10,5,4,3,2,1]=>([(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>[8,7,6,4,5,9,3,2,1]=>([(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[9,8,7,6,5,10,4,3,2,1]=>([(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[5,6,4,3,2,1,9,8,7]=>[8,7,6,5,3,4,9,2,1]=>([(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[9,8,7,6,5,4,10,3,2,1]=>([(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>[8,7,6,5,4,2,3,9,1]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[9,8,7,6,5,4,3,10,2,1]=>([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[9,8,7,6,5,4,3,2,10,1]=>([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9)
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,6)],9)
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(7,6),(8,5)],9)
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[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)
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[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)
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[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]=>[8,7,6,5,4,3,2,1,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(9,8)],10)
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,7)],10)
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(8,7),(9,6)],10)
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(7,6),(8,7),(9,5)],10)
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(5,7),(6,5),(7,4),(8,6),(9,8)],10)
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[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)
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>([(0,9),(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[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)
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[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)
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>([(7,8)],9)
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,7,8,6,5,4,3,2,1]=>([(7,8)],9)
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,5,8,10,9,7]=>[6,5,7,4,8,3,10,2,9,1]=>([(1,6),(2,6),(3,9),(4,8),(5,7),(5,9),(6,8),(8,7),(8,9)],10)
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,8,1]=>([(2,8),(4,5),(5,7),(6,4),(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)
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>[3,2,4,5,6,7,8,1,9]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[2,1,3,4,5,6,8,9,7]=>[3,2,4,5,6,7,9,1,8]=>([(0,8),(1,8),(2,7),(4,6),(5,4),(6,3),(6,7),(8,5)],9)
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[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)
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>([(0,8),(1,7),(2,7),(4,6),(5,4),(6,3),(7,8),(8,5)],9)
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[3,2,1,5,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>([(0,8),(1,8),(2,8),(3,7),(4,6),(6,5),(7,4),(8,7)],9)
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>[7,6,5,4,3,2,8,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>([(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[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)
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[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)
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[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)
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[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)
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[2,3,5,4,1,6,7,8,9]=>[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)
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[2,3,4,6,5,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>([(0,8),(1,8),(2,6),(4,8),(5,4),(6,5),(7,3),(8,7)],9)
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[2,3,4,5,7,6,1,8,9]=>[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)
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>[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)
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[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)
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[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)
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[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)
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[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)
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[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)
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[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)
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[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)
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[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)
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[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)
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[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)
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[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)
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[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)
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[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)
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>[3,9,2,4,5,6,7,8,1]=>([(1,8),(2,4),(2,8),(5,6),(6,3),(7,5),(8,7)],9)
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[9,7,6,5,4,3,2,8,1]=>([(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,6)],9)
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(8,7)],9)
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(9,8)],10)
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[7,8,6,5,4,3,2,9,1]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[7,6,5,4,3,2,9,1,8]=>([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],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)
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[8,9,10,7,6,5,4,3,2,1]=>([(7,8),(8,9)],10)
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[7,6,8,5,4,3,2,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>[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)
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>[3,2,5,1,4,6,7,8,9]=>([(0,8),(1,6),(1,8),(2,6),(2,8),(3,5),(5,4),(6,7),(7,3),(8,7)],9)
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>([(0,8),(1,7),(2,4),(4,7),(5,3),(6,5),(7,8),(8,6)],9)
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[3,2,9,1,4,5,6,7,8]=>([(0,8),(1,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,4),(8,6)],9)
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[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)
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[3,4,5,6,7,8,9,10,2,1]=>([(2,9),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7)],10)
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[5,4,3,2,1,7,8,9,6]=>[6,5,4,3,2,9,1,7,8]=>([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(8,6)],9)
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[4,5,6,7,8,9,3,2,1]=>([(3,8),(5,7),(6,5),(7,4),(8,6)],9)
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1]=>([(4,5),(5,8),(7,6),(8,7)],9)
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[6,7,8,9,5,4,3,2,1]=>([(5,6),(6,8),(8,7)],9)
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[3,4,5,6,7,8,2,9,1]=>([(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[4,5,6,7,8,9,10,3,2,1]=>([(3,9),(5,6),(6,8),(7,5),(8,4),(9,7)],10)
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[5,6,7,8,9,10,4,3,2,1]=>([(4,5),(5,9),(7,8),(8,6),(9,7)],10)
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[6,7,8,9,10,5,4,3,2,1]=>([(5,6),(6,9),(8,7),(9,8)],10)
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[7,8,9,10,6,5,4,3,2,1]=>([(6,7),(7,9),(9,8)],10)
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>([(9,10)],11)
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>([(0,8),(1,8),(2,4),(4,8),(5,6),(6,3),(7,5),(8,7)],9)
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>([(0,8),(1,7),(2,4),(4,7),(5,3),(6,5),(7,8),(8,6)],9)
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>([(0,8),(1,8),(2,8),(3,4),(4,8),(5,6),(6,7),(8,5)],9)
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>[7,6,5,4,3,8,2,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(8,7)],9)
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,8)],10)
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[9,6,7,8,5,4,3,2,1]=>([(6,7),(7,8)],9)
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[8,6,7,5,4,3,2,1,9]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[8,2,3,4,5,6,7,9,1]=>([(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5)],9)
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[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)
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(9,8)],10)
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[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)
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,8),(6,7),(8,6)],9)
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,5),(5,9),(6,7),(7,8),(9,6)],10)
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,6,5,4,3,1,2,8,9,10,11]=>([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,10),(7,8),(8,9),(10,7)],11)
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,9),(7,8),(9,7)],10)
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[7,5,4,3,1,2,6,8,9]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,8),(7,6),(8,7)],9)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>[8,7,6,5,4,3,2,10,1,9]=>([(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this 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 minimal element of this Sylvester class.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
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.