Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00064: Permutations —reverse⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
=>
Cc0010;cc-rep-0Cc0014;cc-rep-3
[.,.]=>[1]=>[1]=>([],1)
[.,[.,.]]=>[2,1]=>[1,2]=>([(0,1)],2)
[[.,.],.]=>[1,2]=>[2,1]=>([],2)
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>([(0,2),(2,1)],3)
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>([(0,1),(0,2)],3)
[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>([(0,2),(1,2)],3)
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>([(1,2)],3)
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>([],3)
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>([(0,3),(3,1),(3,2)],4)
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>([(0,2),(0,3),(3,1)],4)
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>([(0,1),(0,2),(0,3)],4)
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4)
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4)
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4)
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>([(1,2),(2,3)],4)
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>([(1,2),(1,3)],4)
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>([(1,3),(2,3)],4)
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>([(2,3)],4)
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>([],4)
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>([(0,3),(3,4),(4,1),(4,2)],5)
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>([(0,4),(3,2),(4,1),(4,3)],5)
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>([(0,4),(4,1),(4,2),(4,3)],5)
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>([(0,2),(0,4),(3,1),(4,3)],5)
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>([(0,3),(0,4),(4,1),(4,2)],5)
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>([(0,2),(0,3),(0,4),(4,1)],5)
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4)],5)
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>([(0,4),(1,4),(4,2),(4,3)],5)
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>([(0,4),(1,3),(2,3),(3,4)],5)
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>([(1,4),(4,2),(4,3)],5)
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>([(1,2),(1,3),(2,4),(3,4)],5)
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>([(1,3),(1,4),(4,2)],5)
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>([(1,2),(1,3),(1,4)],5)
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>([(1,4),(2,4),(4,3)],5)
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>([(1,3),(1,4),(2,3),(2,4)],5)
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>([(1,4),(2,3),(3,4)],5)
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>([(1,4),(2,4),(3,4)],5)
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>([(2,3),(3,4)],5)
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>([(2,3),(2,4)],5)
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>([(2,4),(3,4)],5)
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>([(3,4)],5)
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>([],5)
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>([(1,4),(4,5),(5,2),(5,3)],6)
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>([(1,5),(4,3),(5,2),(5,4)],6)
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>([(1,5),(5,2),(5,3),(5,4)],6)
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>([(1,3),(1,5),(4,2),(5,4)],6)
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>([(1,4),(1,5),(5,2),(5,3)],6)
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>([(1,3),(1,4),(1,5),(5,2)],6)
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5)],6)
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>([(1,5),(2,5),(3,4),(5,3)],6)
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>([(1,5),(2,5),(5,3),(5,4)],6)
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>([(1,5),(2,5),(3,5),(5,4)],6)
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>([(1,5),(2,3),(3,4),(4,5)],6)
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>([(1,5),(2,4),(3,4),(4,5)],6)
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>([(2,3),(3,5),(5,4)],6)
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>([(2,3),(3,4),(3,5)],6)
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>([(2,3),(2,4),(3,5),(4,5)],6)
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>([(2,3),(2,4),(4,5)],6)
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>([(2,3),(2,4),(2,5)],6)
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>([(2,5),(3,5),(5,4)],6)
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>([(2,4),(2,5),(3,4),(3,5)],6)
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>([(2,5),(3,4),(4,5)],6)
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>([(2,5),(3,5),(4,5)],6)
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>([(3,4),(4,5)],6)
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>([(3,4),(3,5)],6)
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>([(3,5),(4,5)],6)
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>([(4,5)],6)
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>([],6)
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7)
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(3,5),(3,6),(4,1)],7)
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7)
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7)
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(5,2),(6,3)],7)
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7)
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7)
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>([(0,6),(1,4),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>([(1,6),(5,3),(5,4),(6,2),(6,5)],7)
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>([(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>([(1,4),(1,5),(5,6),(6,2),(6,3)],7)
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>([(1,4),(1,6),(5,3),(6,2),(6,5)],7)
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>([(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>([(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>([(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>([(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>([(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>([(2,6),(4,5),(5,3),(6,4)],7)
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>([(2,5),(5,6),(6,3),(6,4)],7)
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>([(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>([(2,6),(5,4),(6,3),(6,5)],7)
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>([(2,6),(6,3),(6,4),(6,5)],7)
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>([(2,4),(2,6),(5,3),(6,5)],7)
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>([(2,5),(2,6),(6,3),(6,4)],7)
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>([(2,4),(2,5),(2,6),(6,3)],7)
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>([(2,3),(2,4),(2,5),(2,6)],7)
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>([(2,6),(3,6),(4,5),(6,4)],7)
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>([(2,6),(3,6),(6,4),(6,5)],7)
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>([(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7)
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>([(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>([(2,6),(3,6),(4,6),(6,5)],7)
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>([(2,6),(3,4),(4,5),(5,6)],7)
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>([(2,6),(3,5),(4,5),(5,6)],7)
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>([(3,4),(4,6),(6,5)],7)
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>([(3,4),(4,5),(4,6)],7)
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>([(3,4),(3,5),(4,6),(5,6)],7)
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>([(3,4),(3,5),(5,6)],7)
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>([(3,4),(3,5),(3,6)],7)
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>([(3,6),(4,6),(6,5)],7)
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>([(3,5),(3,6),(4,5),(4,6)],7)
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>([(3,6),(4,5),(5,6)],7)
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>([(3,6),(4,6),(5,6)],7)
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>([(4,5),(5,6)],7)
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>([(4,5),(4,6)],7)
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>([(4,6),(5,6)],7)
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>([(5,6)],7)
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>([],7)
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>([(0,6),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],8)
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>([(0,6),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],8)
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(5,1),(5,2)],8)
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>([(0,6),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],8)
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>([(0,5),(4,7),(5,4),(6,2),(6,3),(7,1),(7,6)],8)
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>([(0,5),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>([(0,6),(4,7),(5,3),(6,4),(7,1),(7,2),(7,5)],8)
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>([(0,6),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],8)
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2),(5,7),(6,7)],8)
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3),(7,1)],8)
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,1),(4,2)],8)
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,2),(4,5),(5,1),(5,3)],8)
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>([(0,5),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],8)
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>([(0,4),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>([(0,5),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],8)
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>([(0,5),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>([(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>([(0,5),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>([(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>([(0,6),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],8)
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>([(0,5),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>([(0,5),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>([(0,6),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],8)
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>([(0,6),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>([(0,6),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,5)],8)
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>([(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,4),(7,5)],8)
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8)
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>([(0,1),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(5,3),(7,4)],8)
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,1),(7,2)],8)
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>([(0,1),(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4),(7,1)],8)
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,2),(4,1),(4,3)],8)
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>([(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,2),(5,1),(5,3)],8)
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>([(0,7),(3,4),(4,6),(5,3),(6,1),(7,2),(7,5)],8)
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>([(0,7),(4,5),(5,6),(6,2),(6,3),(7,1),(7,4)],8)
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>([(0,6),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4)],8)
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>([(0,6),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5)],8)
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>([(0,7),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],8)
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>([(0,5),(3,7),(4,7),(5,2),(5,6),(6,1),(6,3),(6,4)],8)
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>([(0,6),(5,4),(6,3),(6,7),(7,1),(7,2),(7,5)],8)
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>([(0,6),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>([(0,6),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,5)],8)
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>([(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2),(4,3)],8)
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>([(0,6),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>([(0,6),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>([(0,5),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8)
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>([(0,6),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>([(0,7),(6,3),(6,4),(6,5),(7,1),(7,2),(7,6)],8)
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>([(0,6),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>([(0,7),(6,4),(6,5),(7,1),(7,2),(7,3),(7,6)],8)
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>([(0,6),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>([(0,7),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>([(0,3),(0,4),(3,7),(4,7),(5,2),(6,1),(6,5),(7,6)],8)
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(7,1),(7,2)],8)
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>([(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,2),(7,6)],8)
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],8)
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>([(0,4),(0,5),(2,6),(3,6),(4,7),(5,7),(7,1),(7,2),(7,3)],8)
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>([(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(5,1),(6,4),(6,5),(7,4),(7,5)],8)
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>([(0,2),(0,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,4)],8)
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>([(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,1),(6,2)],8)
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(4,1),(5,4),(7,5)],8)
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(7,1),(7,2)],8)
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>([(0,3),(0,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,1),(7,5)],8)
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>([(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(6,4),(7,4)],8)
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>([(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(7,4)],8)
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(7,1)],8)
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>([(0,4),(0,5),(3,7),(4,7),(5,3),(6,1),(6,2),(7,6)],8)
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8)
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>([(0,5),(0,6),(1,7),(5,7),(6,1),(7,2),(7,3),(7,4)],8)
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(5,7),(6,7),(7,1)],8)
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>([(0,1),(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(7,4)],8)
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>([(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,1),(7,2)],8)
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>([(0,1),(0,3),(1,2),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>([(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(7,1)],8)
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>([(0,1),(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>([(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>([(0,2),(0,3),(0,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>([(0,4),(0,6),(1,7),(4,7),(5,1),(6,5),(7,2),(7,3)],8)
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3),(5,7),(6,7)],8)
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4),(7,1)],8)
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>([(0,2),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,1),(4,3)],8)
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>([(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(7,5)],8)
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>([(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2),(7,3),(7,4)],8)
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>([(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(4,2),(6,5),(7,5)],8)
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(7,1)],8)
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2)],8)
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>([(0,2),(0,3),(0,4),(2,7),(3,6),(4,6),(5,1),(6,7),(7,5)],8)
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>([(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7),(7,1),(7,2)],8)
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>([(0,1),(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7),(7,1)],8)
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>([(0,1),(0,2),(0,3),(1,7),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>([(0,4),(0,5),(0,6),(1,7),(4,7),(5,7),(6,1),(7,2),(7,3)],8)
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>([(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(7,1)],8)
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1)],8)
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8)
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>([(0,2),(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,1),(5,3)],8)
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,7),(6,2),(7,1)],8)
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>([(0,3),(0,4),(0,5),(2,6),(3,7),(4,6),(5,2),(6,7),(7,1)],8)
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(3,7),(4,1),(5,6),(5,7)],8)
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>([(0,2),(0,3),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(5,4)],8)
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,1),(4,2),(5,7),(6,7)],8)
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>([(0,2),(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(7,5)],8)
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>([(0,2),(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,1),(6,4)],8)
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>([(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1)],8)
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,6),(5,1),(6,7)],8)
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>([(0,4),(0,6),(5,7),(6,5),(7,1),(7,2),(7,3)],8)
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>([(0,4),(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3)],8)
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>([(0,3),(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4)],8)
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>([(0,4),(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3)],8)
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>([(0,4),(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3)],8)
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>([(0,5),(0,6),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>([(0,4),(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,5)],8)
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2),(5,7),(6,7)],8)
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(5,2),(5,3),(7,1)],8)
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>([(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5),(7,3)],8)
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>([(0,3),(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4)],8)
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>([(0,4),(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5)],8)
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[1,8,2,6,5,3,4,7]=>([(0,4),(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5)],8)
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>([(0,4),(0,6),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5)],8)
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8)
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>([(0,5),(0,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>([(0,5),(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4)],8)
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>([(0,4),(0,6),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5)],8)
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>([(0,5),(0,6),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4)],8)
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>([(0,4),(0,7),(5,6),(6,3),(7,1),(7,2),(7,5)],8)
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>([(0,5),(0,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>([(0,5),(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4)],8)
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>([(0,6),(0,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>([(0,2),(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>([(0,2),(0,3),(0,4),(1,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,1)],8)
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>([(0,3),(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,5)],8)
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>([(0,4),(0,5),(0,6),(1,7),(5,7),(6,1),(7,2),(7,3)],8)
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>([(0,3),(0,4),(0,5),(2,6),(2,7),(4,6),(4,7),(5,2),(7,1)],8)
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(3,5),(3,6),(3,7),(4,1)],8)
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>([(0,2),(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>([(0,2),(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>([(0,2),(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4)],8)
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(3,7),(4,7),(5,6),(7,1)],8)
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(3,7),(4,6),(5,1),(6,7)],8)
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>([(0,2),(0,3),(0,7),(4,6),(5,4),(6,1),(7,5)],8)
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>([(0,3),(0,4),(0,6),(5,2),(6,7),(7,1),(7,5)],8)
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>([(0,4),(0,5),(0,6),(6,7),(7,1),(7,2),(7,3)],8)
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>([(0,3),(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5)],8)
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>([(0,3),(0,4),(0,7),(5,6),(6,2),(7,1),(7,5)],8)
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>([(0,4),(0,5),(0,7),(6,2),(6,3),(7,1),(7,6)],8)
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>([(0,5),(0,6),(0,7),(7,1),(7,2),(7,3),(7,4)],8)
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>([(0,2),(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,6)],8)
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>([(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2)],8)
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1)],8)
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>([(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1),(7,2)],8)
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1)],8)
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>([(0,2),(0,3),(0,4),(0,6),(1,7),(4,7),(5,1),(6,5)],8)
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7)],8)
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(3,7),(4,7),(5,7),(6,7)],8)
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2)],8)
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>([(0,4),(0,5),(0,6),(0,7),(7,1),(7,2),(7,3)],8)
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1)],8)
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7)],8)
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1)],8)
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7)],8)
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(7,1),(7,2)],8)
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8)
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>([(0,6),(1,6),(3,7),(4,7),(5,3),(5,4),(6,5),(7,2)],8)
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(7,4)],8)
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>([(0,7),(1,7),(4,5),(5,3),(6,2),(6,4),(7,6)],8)
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>([(0,7),(1,7),(5,3),(5,4),(6,2),(6,5),(7,6)],8)
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>([(0,7),(1,7),(3,6),(4,6),(5,2),(5,3),(5,4),(7,5)],8)
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>([(0,7),(1,7),(5,4),(6,2),(6,3),(6,5),(7,6)],8)
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>([(0,7),(1,7),(6,2),(6,3),(6,4),(6,5),(7,6)],8)
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>([(0,7),(1,7),(2,6),(3,6),(6,4),(6,5),(7,2),(7,3)],8)
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,3)],8)
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>([(0,7),(1,7),(4,5),(5,2),(6,4),(7,3),(7,6)],8)
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>([(0,7),(1,7),(5,6),(6,2),(6,3),(7,4),(7,5)],8)
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>([(0,7),(1,7),(5,3),(6,2),(6,5),(7,4),(7,6)],8)
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>([(0,7),(1,7),(6,2),(6,3),(6,4),(7,5),(7,6)],8)
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>([(0,7),(1,7),(3,5),(3,6),(4,5),(4,6),(7,2),(7,3),(7,4)],8)
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>([(0,7),(1,7),(5,2),(6,5),(7,3),(7,4),(7,6)],8)
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>([(0,7),(1,7),(6,2),(6,3),(7,4),(7,5),(7,6)],8)
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>([(0,7),(1,7),(4,6),(5,6),(7,2),(7,3),(7,4),(7,5)],8)
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>([(0,7),(1,7),(6,2),(7,3),(7,4),(7,5),(7,6)],8)
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>([(0,7),(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,7),(6,7),(7,3)],8)
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,4),(6,5),(7,5)],8)
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>([(0,6),(0,7),(1,6),(1,7),(4,3),(5,3),(6,2),(6,4),(6,5),(7,2),(7,4),(7,5)],8)
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>([(0,5),(0,6),(1,5),(1,6),(4,7),(5,7),(6,4),(7,2),(7,3)],8)
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2),(7,3)],8)
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,4),(3,5),(6,2),(7,4),(7,5)],8)
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(4,6),(5,6),(6,2),(6,3),(7,2),(7,3)],8)
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,3),(5,7),(6,2),(6,4)],8)
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>([(0,6),(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(7,4)],8)
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(5,4),(7,5)],8)
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(7,2),(7,3)],8)
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,5),(4,3),(7,2),(7,4)],8)
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>([(0,6),(0,7),(1,6),(1,7),(4,5),(5,3),(7,2),(7,4)],8)
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>([(0,6),(0,7),(1,6),(1,7),(5,3),(5,4),(7,2),(7,5)],8)
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>([(0,6),(0,7),(1,6),(1,7),(3,5),(4,5),(7,2),(7,3),(7,4)],8)
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>([(0,6),(0,7),(1,6),(1,7),(5,4),(7,2),(7,3),(7,5)],8)
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>([(0,6),(0,7),(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(6,4),(7,4)],8)
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(6,3),(6,4),(7,3),(7,4)],8)
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2)],8)
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(4,2),(5,4),(6,4),(7,2)],8)
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(7,3)],8)
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(7,4)],8)
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(7,2),(7,3)],8)
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(3,2),(6,3),(7,3)],8)
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(6,2),(7,3)],8)
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7)],8)
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(7,2)],8)
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(6,2),(7,2)],8)
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>([(0,7),(1,3),(3,7),(5,2),(6,5),(7,4),(7,6)],8)
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>([(0,7),(1,4),(4,7),(6,2),(6,3),(7,5),(7,6)],8)
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>([(0,7),(1,3),(3,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>([(0,7),(1,3),(3,7),(6,2),(7,4),(7,5),(7,6)],8)
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>([(0,7),(1,2),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>([(0,5),(0,6),(1,4),(4,5),(4,6),(5,7),(6,7),(7,2),(7,3)],8)
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>([(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>([(0,3),(1,4),(1,7),(2,5),(2,6),(3,4),(3,7),(4,2),(7,5),(7,6)],8)
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>([(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,2)],8)
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(7,5)],8)
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>([(0,6),(0,7),(1,4),(4,6),(4,7),(5,2),(5,3),(7,5)],8)
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>([(0,6),(0,7),(1,4),(4,6),(4,7),(5,3),(7,2),(7,5)],8)
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>([(0,3),(1,4),(1,5),(1,7),(2,6),(3,4),(3,5),(3,7),(5,2),(7,6)],8)
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>([(0,5),(0,6),(0,7),(1,3),(3,5),(3,6),(3,7),(4,2),(7,4)],8)
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>([(0,5),(0,6),(0,7),(1,4),(4,5),(4,6),(4,7),(7,2),(7,3)],8)
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>([(0,3),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(3,7),(7,2)],8)
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8)
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>([(0,6),(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>([(0,7),(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>([(0,7),(1,7),(2,7),(6,3),(6,4),(7,5),(7,6)],8)
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>([(0,7),(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,3),(6,4),(7,3),(7,4)],8)
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(6,5),(7,3)],8)
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(6,5),(7,3)],8)
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(7,3)],8)
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(4,5),(7,3),(7,4)],8)
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,4),(7,3)],8)
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(5,3),(6,3),(7,3)],8)
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(7,3)],8)
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>([(0,7),(1,5),(4,7),(5,4),(6,2),(6,3),(7,6)],8)
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(7,3),(7,4)],8)
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>([(0,7),(1,5),(3,7),(5,3),(6,2),(7,4),(7,6)],8)
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>([(0,7),(1,6),(2,7),(6,2),(7,3),(7,4),(7,5)],8)
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(5,7),(6,7),(7,2)],8)
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>([(0,2),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>([(0,6),(0,7),(1,4),(2,6),(2,7),(3,5),(4,2),(6,5),(7,3)],8)
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>([(0,6),(0,7),(1,5),(4,6),(4,7),(5,4),(7,2),(7,3)],8)
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>([(0,2),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>([(0,5),(0,6),(0,7),(1,4),(3,5),(3,6),(3,7),(4,3),(7,2)],8)
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(3,4),(3,5),(3,6),(3,7)],8)
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>([(0,6),(0,7),(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>([(0,6),(0,7),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>([(0,7),(1,6),(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>([(0,7),(1,7),(2,5),(2,6),(4,3),(5,4),(6,4),(7,5),(7,6)],8)
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>([(0,7),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8)
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>([(0,6),(0,7),(1,5),(2,5),(3,4),(5,6),(5,7),(7,3)],8)
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,4),(7,5),(7,6)],8)
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(6,3),(7,4),(7,5),(7,6)],8)
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(7,3),(7,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>([(0,7),(1,7),(2,3),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>([(0,7),(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>([(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>([(0,7),(1,7),(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>([(0,7),(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>([(0,7),(1,6),(2,7),(3,7),(6,2),(6,3),(7,4),(7,5)],8)
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>([(0,7),(1,3),(1,4),(3,6),(4,6),(5,2),(6,7),(7,5)],8)
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>([(0,7),(1,4),(1,5),(4,6),(5,6),(6,7),(7,2),(7,3)],8)
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>([(0,6),(0,7),(1,3),(1,4),(3,5),(4,5),(5,6),(5,7),(7,2)],8)
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>([(0,6),(0,7),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,2)],8)
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>([(0,7),(1,6),(2,3),(3,7),(6,4),(6,5),(7,6)],8)
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>([(0,7),(1,5),(1,6),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>([(0,3),(1,7),(2,4),(2,5),(2,6),(3,7),(7,4),(7,5),(7,6)],8)
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(6,4),(7,5),(7,6)],8)
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>([(0,7),(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>([(0,6),(0,7),(1,5),(2,6),(2,7),(3,4),(4,2),(5,3)],8)
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>([(0,6),(0,7),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6),(5,7)],8)
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>([(0,6),(0,7),(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4)],8)
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>([(0,6),(0,7),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>([(0,7),(1,5),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(7,4)],8)
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(7,5),(7,6)],8)
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>([(0,7),(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,2),(6,5)],8)
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>([(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>([(0,6),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,2),(7,6)],8)
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>([(0,7),(1,4),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,5)],8)
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>([(0,7),(1,2),(1,4),(1,5),(2,7),(3,6),(4,6),(5,3),(6,7)],8)
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>([(0,7),(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>([(0,7),(1,6),(2,3),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>([(0,7),(1,5),(1,6),(2,4),(3,7),(4,5),(4,6),(5,7),(6,3)],8)
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>([(0,7),(1,6),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>([(0,5),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>([(0,7),(1,7),(2,6),(3,4),(4,7),(5,6),(7,5)],8)
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>([(0,3),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>([(0,7),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>([(0,7),(1,7),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>([(0,7),(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>([(0,7),(1,7),(2,3),(2,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>([(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3)],8)
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>([(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>([(1,6),(2,7),(3,7),(6,2),(6,3),(7,4),(7,5)],8)
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>([(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>([(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>([(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>([(1,7),(5,4),(6,3),(6,5),(7,2),(7,6)],8)
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>([(1,6),(6,5),(6,7),(7,2),(7,3),(7,4)],8)
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[8,1,2,7,5,3,4,6]=>([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>([(1,6),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>([(1,2),(1,3),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>([(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>([(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>([(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[8,1,3,2,7,6,4,5]=>([(1,3),(1,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,2)],8)
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>([(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>([(1,3),(1,6),(2,7),(3,7),(6,2),(7,4),(7,5)],8)
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>([(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>([(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>([(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>([(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>([(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>([(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(6,7),(7,2)],8)
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>([(1,2),(1,3),(1,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>([(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>([(1,4),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,5)],8)
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>([(1,2),(1,3),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>([(1,2),(1,4),(1,5),(2,7),(3,6),(4,6),(5,3),(6,7)],8)
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>([(1,4),(1,6),(5,3),(6,7),(7,2),(7,5)],8)
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>([(1,5),(1,6),(6,7),(7,2),(7,3),(7,4)],8)
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>([(1,2),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>([(1,2),(1,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>([(1,2),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>([(1,4),(1,7),(5,6),(6,3),(7,2),(7,5)],8)
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>([(1,5),(1,7),(6,3),(6,4),(7,2),(7,6)],8)
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>([(1,3),(1,6),(4,7),(5,7),(6,2),(6,4),(6,5)],8)
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>([(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>([(1,2),(1,3),(1,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>([(1,2),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[6,4,3,2,5,7,1,8]=>[8,1,7,5,2,3,4,6]=>([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>([(1,2),(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(6,7)],8)
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>([(1,2),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3)],8)
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>([(1,2),(1,3),(1,6),(4,7),(5,7),(6,4),(6,5)],8)
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>([(1,2),(1,3),(1,4),(1,5),(4,7),(5,7),(7,6)],8)
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7)],8)
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>([(1,3),(1,4),(1,5),(1,7),(6,2),(7,6)],8)
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>([(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>([(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,3),(7,4)],8)
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(7,3)],8)
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>([(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>([(1,6),(2,3),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>([(1,6),(1,7),(2,4),(4,6),(4,7),(5,3),(6,5),(7,5)],8)
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>([(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>([(1,5),(1,7),(2,4),(3,6),(4,5),(4,7),(5,6),(7,3)],8)
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>([(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>([(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>([(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>([(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>([(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>([(1,7),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>([(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>([(1,7),(2,6),(3,6),(6,7),(7,4),(7,5)],8)
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>([(1,4),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>([(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>([(1,7),(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[8,5,1,2,4,3,7,6]=>([(1,3),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>([(1,6),(2,3),(2,4),(3,7),(4,7),(6,5),(7,6)],8)
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>([(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>([(1,7),(2,4),(2,6),(3,7),(4,7),(6,3),(7,5)],8)
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>([(1,6),(1,7),(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>([(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>([(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>([(1,7),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>([(1,3),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>([(1,7),(2,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>([(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>([(1,6),(2,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>([(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>([(1,7),(2,4),(2,6),(3,7),(4,7),(5,3),(6,5)],8)
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>([(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>([(1,7),(2,3),(2,4),(2,5),(3,7),(4,6),(5,6),(6,7)],8)
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>([(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>([(1,7),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>([(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[8,6,4,1,2,3,5,7]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>([(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>([(1,4),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>([(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>([(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>([(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>([(2,6),(5,7),(6,5),(7,3),(7,4)],8)
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>([(2,6),(5,4),(6,7),(7,3),(7,5)],8)
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>([(2,3),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>([(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>([(2,7),(5,6),(6,4),(7,3),(7,5)],8)
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>([(2,7),(6,5),(7,3),(7,4),(7,6)],8)
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>([(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>([(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>([(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>([(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>([(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>([(2,4),(2,7),(5,6),(6,3),(7,5)],8)
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>([(2,5),(2,6),(6,7),(7,3),(7,4)],8)
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>([(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>([(2,3),(2,5),(2,6),(4,7),(5,7),(6,4)],8)
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>([(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>([(2,4),(2,5),(2,7),(6,3),(7,6)],8)
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>([(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>([(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>([(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>([(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>([(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>([(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>([(2,7),(3,4),(4,7),(7,5),(7,6)],8)
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>([(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>([(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>([(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>([(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>([(2,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>([(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>([(2,7),(3,6),(4,5),(5,7),(7,6)],8)
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>([(3,4),(4,7),(6,5),(7,6)],8)
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>([(3,4),(4,7),(7,5),(7,6)],8)
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>([(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>([(3,4),(4,6),(4,7),(7,5)],8)
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>([(3,4),(4,5),(4,6),(4,7)],8)
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>([(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>([(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>([(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>([(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>([(3,4),(3,5),(5,6),(6,7)],8)
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>([(3,4),(3,5),(5,6),(5,7)],8)
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>([(3,4),(3,5),(3,6),(6,7)],8)
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>([(3,4),(3,5),(3,6),(3,7)],8)
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>([(3,7),(4,7),(5,6),(7,5)],8)
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>([(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>([(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>([(3,7),(4,7),(5,7),(7,6)],8)
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>([(3,7),(4,5),(5,6),(6,7)],8)
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>([(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>([(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>([(3,7),(4,7),(5,7),(6,7)],8)
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>([(4,5),(5,7),(7,6)],8)
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>([(4,5),(5,6),(5,7)],8)
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>([(4,5),(4,6),(5,7),(6,7)],8)
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>([(4,5),(4,6),(6,7)],8)
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>([(4,5),(4,6),(4,7)],8)
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>([(4,7),(5,7),(7,6)],8)
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>([(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>([(4,7),(5,6),(6,7)],8)
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>([(4,7),(5,7),(6,7)],8)
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>([(5,6),(6,7)],8)
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>([(5,6),(5,7)],8)
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>([(5,7),(6,7)],8)
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>([(6,7)],8)
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>([],8)
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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.