Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0010;cc-rep-0Cc0009;cc-rep-3
[.,.]=>[1]=>[1]=>{{1}}
[.,[.,.]]=>[2,1]=>[2,1]=>{{1,2}}
[[.,.],.]=>[1,2]=>[1,2]=>{{1},{2}}
[.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>{{1,2,3}}
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>{{1,3},{2}}
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>{{1,2,3}}
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}}
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>{{1,2,3,4}}
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>{{1,2,4},{3}}
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>{{1,2,3,4}}
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}}
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}}
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>{{1,2,3,4}}
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>{{1,2,4},{3}}
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>{{1,2,3,4}}
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>{{1,2,3,4}}
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>{{1,2,3},{4}}
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}}
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>{{1,2,3},{4}}
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}}
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>{{1,2,3,4,5}}
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}}
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>{{1,2,3,4,5}}
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>{{1,2,3,5},{4}}
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>{{1,2,3,4,5}}
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>{{1,2,3,4,5}}
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}}
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>{{1,2,3,4,5}}
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>{{1,2,3,5},{4}}
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>{{1,2,3,4,5}}
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>{{1,2,5},{3,4}}
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>{{1,2,5},{3},{4}}
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>{{1,2,3,4,5}}
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>{{1,2,3,5},{4}}
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>{{1,2,3,4,5}}
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>{{1,2,3,5},{4}}
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>{{1,2,3,4,5}}
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>{{1,2,3,4,5}}
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>{{1,2,3,4,5}}
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>{{1,2,3,4,5}}
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}}
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>{{1,2,3,4},{5}}
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>{{1,2,4},{3},{5}}
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>{{1,2,3,4},{5}}
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}}
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}}
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>{{1,2,3,4,5,6}}
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>{{1,2,3,4,5,6}}
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>{{1,2,3,4,6},{5}}
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>{{1,2,3,4,5,6}}
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>{{1,2,3,4,5,6}}
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}}
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}}
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>{{1,2,3,4,5,6}}
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>{{1,2,3,6},{4,5}}
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>{{1,2,3,4,5,6}}
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>{{1,2,3,4,6},{5}}
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>{{1,2,3,4,5,6}}
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>{{1,2,3,4,5,6}}
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}}
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>{{1,2,3,4,6},{5}}
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>{{1,2,3,4,5,6}}
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>{{1,2,3,6},{4,5}}
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>{{1,2,3,6},{4},{5}}
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>{{1,2,3,4,5,6}}
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>{{1,2,3,4,6},{5}}
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>{{1,2,3,4,5,6}}
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>{{1,2,3,4,5,6}}
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}}
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}}
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}}
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>{{1,2,6},{3,4},{5}}
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}}
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>{{1,2,3,4,6},{5}}
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>{{1,2,3,6},{4,5}}
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>{{1,2,3,6},{4},{5}}
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>{{1,2,3,4,6},{5}}
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>{{1,2,3,4,5,6}}
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}}
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}}
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>{{1,2,3,4,6},{5}}
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>{{1,2,3,4,5,6}}
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>{{1,2,3,4,6},{5}}
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>{{1,2,3,4,6},{5}}
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>{{1,2,3,4,6},{5}}
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}}
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>{{1,2,3,4,5,6}}
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>{{1,2,3,4,5,6}}
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>{{1,2,3,4,5,6}}
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}}
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}}
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>{{1,2,3,5},{4},{6}}
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>{{1,2,5},{3,4},{6}}
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>{{1,2,5},{3},{4},{6}}
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>{{1,2,3,5},{4},{6}}
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>{{1,2,3,5},{4},{6}}
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>{{1,2,4},{3},{5},{6}}
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>{{1,2,7},{3,4,5,6}}
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>{{1,2,7},{3,4,5,6}}
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>{{1,2,7},{3,4,6},{5}}
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>{{1,2,7},{3,4,5,6}}
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}}
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>{{1,2,7},{3,4,5},{6}}
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>{{1,2,3,4,7},{5,6}}
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>{{1,7},{2,3,6},{4,5}}
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>{{1,7},{2,3,6},{4},{5}}
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>{{1,7},{2,3,5},{4},{6}}
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>{{1,2,3,4,5,7},{6}}
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>{{1,2,3,4,7},{5,6}}
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>{{1,2,3,4,5,7},{6}}
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>{{1,2,3,7},{4,5,6}}
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>{{1,2,3,7},{4,5,6}}
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>{{1,2,3,4,5,7},{6}}
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>{{1,2,3,4,7},{5,6}}
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>{{1,2,3,4,5,7},{6}}
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>{{1,2,3,4,5,7},{6}}
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>{{1,2,7},{3,4,5,6}}
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>{{1,2,7},{3,4,6},{5}}
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>{{1,2,7},{3,4,5,6}}
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>{{1,2,7},{3,6},{4,5}}
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>{{1,2,7},{3,6},{4},{5}}
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>{{1,2,7},{3,4,5,6}}
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>{{1,2,7},{3,4,6},{5}}
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>{{1,2,7},{3,4,5,6}}
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>{{1,2,7},{3,4,5,6}}
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>{{1,2,7},{3,4,5},{6}}
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>{{1,2,7},{3,5},{4},{6}}
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>{{1,2,7},{3,4,5},{6}}
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>{{1,2,7},{3,4},{5},{6}}
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}}
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>{{1,2,3,4,5,7},{6}}
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7}}
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>{{1,2,3,4,7},{5,6}}
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>{{1,2,3,4,5,7},{6}}
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>{{1,2,3,4,5,7},{6}}
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>{{1,2,3,4,5,6,7}}
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>{{1,2,3,4,5,7},{6}}
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>{{1,2,3,4,5,7},{6}}
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>{{1,2,6},{3,4,5},{7}}
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>{{1,6},{2,3,5},{4},{7}}
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>{{1,2,6},{3,4,5},{7}}
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>{{1,2,6},{3,5},{4},{7}}
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>{{1,2,6},{3,4,5},{7}}
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>{{1,2,6},{3,4},{5},{7}}
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>{{1,2,6},{3},{4},{5},{7}}
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>{{1,2,5},{3,4},{6},{7}}
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[2,3,4,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[2,3,4,7,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[2,3,5,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[2,3,5,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[2,3,6,5,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[2,3,6,7,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>{{1,2,3,8},{4,5,6,7}}
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>{{1,2,3,8},{4,5,7},{6}}
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>{{1,2,3,8},{4,5,6,7}}
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>{{1,2,3,8},{4,5,6,7}}
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>{{1,2,3,8},{4,5,6},{7}}
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>{{1,2,3,8},{4,6},{5},{7}}
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]=>{{1,2,3,8},{4,5,6},{7}}
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>{{1,2,3,8},{4,5},{6},{7}}
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>{{1,2,3,8},{4},{5},{6},{7}}
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,4,5,3,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[2,4,5,3,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[2,4,7,3,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[2,4,7,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[2,4,8,3,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[2,5,4,7,3,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[2,5,6,3,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[2,6,4,5,7,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[2,6,5,7,4,3,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[2,6,5,3,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,6,4,8,3,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[2,7,4,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[2,7,6,3,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[2,7,4,6,3,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[2,7,4,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[2,7,4,8,3,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[2,7,8,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>{{1,2,8},{3,4,5,6,7}}
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>{{1,2,8},{3,4,7},{5,6}}
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[2,8,5,7,4,6,3,1]=>{{1,2,8},{3,4,5,7},{6}}
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>{{1,2,8},{3,7},{4,5,6}}
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>{{1,2,8},{3,7},{4,6},{5}}
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>{{1,2,8},{3,7},{4,5,6}}
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>{{1,2,8},{3,7},{4,5},{6}}
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>{{1,2,8},{3,7},{4},{5},{6}}
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[2,8,4,5,7,3,6,1]=>{{1,2,8},{3,4,5,6,7}}
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[7,4,3,5,6,8,2,1]=>[2,8,4,7,3,5,6,1]=>{{1,2,8},{3,4,5,6,7}}
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[2,8,7,3,4,5,6,1]=>{{1,2,8},{3,4,5,6,7}}
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[2,8,4,6,5,3,7,1]=>{{1,2,8},{3,4,6},{5},{7}}
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[2,8,5,3,6,4,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[2,8,6,3,4,5,7,1]=>{{1,2,8},{3,4,5,6},{7}}
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>{{1,2,8},{3,4,5},{6},{7}}
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>{{1,2,8},{3,5},{4},{6},{7}}
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>{{1,2,8},{3,4,5},{6},{7}}
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>{{1,2,8},{3,4},{5},{6},{7}}
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>{{1,2,8},{3},{4},{5},{6},{7}}
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[3,4,2,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[3,4,2,5,7,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[3,4,2,5,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[3,4,2,6,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[3,4,2,6,8,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[3,5,2,6,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[3,6,2,5,7,4,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[3,7,2,8,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>{{1,2,3,8},{4,5,6,7}}
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>{{1,2,3,8},{4,7},{5,6}}
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[3,8,2,5,7,4,6,1]=>{{1,2,3,8},{4,5,6,7}}
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>{{1,2,3,8},{4,5},{6},{7}}
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>{{1,2,3,8},{4},{5},{6},{7}}
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[4,3,6,2,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>{{1,2,3,4,8},{5,6,7}}
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[4,8,2,3,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[5,4,6,3,2,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[5,4,6,3,2,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[5,4,8,3,2,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[5,4,2,6,3,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[5,3,6,2,4,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[5,7,2,3,4,8,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>{{1,2,3,4,5,8},{6,7}}
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>{{1,2,3,4,5,8},{6},{7}}
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[6,3,4,5,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[6,5,4,7,3,2,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[6,5,4,8,3,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1]=>[6,5,8,3,4,2,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[6,4,2,5,8,3,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[6,4,7,3,2,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]=>{{1,2,3,4,5,6,8},{7}}
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[6,7,2,3,4,5,8,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[7,6,4,8,3,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[7,6,8,3,4,5,2,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[7,6,2,5,8,4,3,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[7,6,2,3,4,8,5,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[7,3,5,8,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[8,4,3,5,2,6,7,1]=>[7,5,4,8,3,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[7,3,8,2,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[7,8,2,3,4,5,6,1]=>{{1,2,3,4,5,6,7,8}}
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>{{1,8},{2,3,4,7},{5,6}}
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,3,5,6,4,7,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[8,3,6,5,7,4,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>{{1,8},{2,3,7},{4,5,6}}
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>{{1,8},{2,3,7},{4,6},{5}}
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>{{1,8},{2,3,7},{4},{5},{6}}
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>{{1,8},{2,3,4,7},{5,6}}
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,4,7,3,5,6,2,1]=>{{1,8},{2,3,4,7},{5},{6}}
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[8,5,4,7,3,6,2,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[8,6,7,3,4,5,2,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>{{1,8},{2,7},{3,4,6},{5}}
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>{{1,8},{2,7},{3,6},{4},{5}}
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>{{1,8},{2,7},{3,4,6},{5}}
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>{{1,8},{2,7},{3,4,5,6}}
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>{{1,8},{2,7},{3,5},{4},{6}}
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>{{1,8},{2,7},{3,4,5},{6}}
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>{{1,8},{2,7},{3,4},{5},{6}}
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>{{1,8},{2,7},{3},{4},{5},{6}}
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,4,2,5,6,7,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>{{1,8},{2,3,7},{4,5,6}}
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>{{1,8},{2,3,7},{4,5,6}}
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>{{1,8},{2,3,7},{4},{5},{6}}
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[8,3,6,2,7,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>{{1,8},{2,3,4,7},{5,6}}
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[8,6,2,3,7,5,4,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>{{1,8},{2,3,4,5,7},{6}}
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,3,6,2,4,7,5,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[7,4,5,3,2,6,8,1]=>[8,3,5,7,4,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[8,4,5,3,7,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[8,4,2,5,7,3,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[8,3,4,7,2,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[8,4,7,3,2,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,4,2,7,3,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,7,2,4,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,7,2,3,4,5,6,1]=>{{1,8},{2,3,4,5,6,7}}
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,3,4,5,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,3,6,5,4,2,7,1]=>{{1,8},{2,3,6},{4,5},{7}}
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>{{1,8},{2,3,6},{4},{5},{7}}
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[8,4,5,3,6,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,4,6,3,5,2,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[8,5,4,6,3,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>{{1,8},{2,6},{3,5},{4},{7}}
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[8,6,5,3,4,2,7,1]=>{{1,8},{2,6},{3,4,5},{7}}
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>{{1,8},{2,6},{3,4},{5},{7}}
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>{{1,8},{2,6},{3},{4},{5},{7}}
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,4,2,5,6,3,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[8,4,2,6,5,3,7,1]=>{{1,8},{2,3,4,6},{5},{7}}
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,6,2,5,4,3,7,1]=>{{1,8},{2,3,6},{4,5},{7}}
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>{{1,8},{2,3,6},{4},{5},{7}}
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[6,3,2,4,5,7,8,1]=>[8,3,6,2,4,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,6,2,3,4,5,7,1]=>{{1,8},{2,3,4,5,6},{7}}
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>{{1,8},{2,3,5},{4},{6},{7}}
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,4,5,3,2,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>{{1,8},{2,5},{3,4},{6},{7}}
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>{{1,8},{2,5},{3},{4},{6},{7}}
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,4,2,5,3,6,7,1]=>{{1,8},{2,3,4,5},{6},{7}}
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>{{1,8},{2,4},{3},{5},{6},{7}}
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>{{1,8},{2,3,4},{5},{6},{7}}
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>{{1,8},{2,3},{4},{5},{6},{7}}
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[3,1,4,5,7,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[3,1,4,6,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[3,1,4,7,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>{{1,2,3,4,8},{5,7},{6}}
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[3,1,5,6,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[3,1,5,7,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>{{1,2,3,8},{4,7},{5,6}}
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>{{1,2,3,8},{4,5,6,7}}
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>{{1,2,3,8},{4,5,6,7}}
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>{{1,2,3,8},{4,5},{6},{7}}
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>{{1,2,3,8},{4},{5},{6},{7}}
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[4,1,5,3,8,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[4,1,7,3,6,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>{{1,2,3,4,8},{5,6,7}}
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>{{1,2,3,4,8},{5,6,7}}
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>{{1,2,3,4,8},{5,6},{7}}
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>{{1,2,3,4,5,8},{6,7}}
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[5,1,6,3,4,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[5,1,8,3,4,6,7,2]=>{{1,2,3,4,5,8},{6},{7}}
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>{{1,2,3,4,5,6,8},{7}}
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[7,1,4,5,6,8,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,1,4,6,3,8,5,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>{{1,2,3,4,5,6,7,8}}
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[8,1,4,5,7,6,3,2]=>{{1,2,8},{3,4,5,7},{6}}
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[8,1,4,7,6,5,3,2]=>{{1,2,8},{3,4,7},{5,6}}
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,3,8,1,2]=>[8,1,5,6,4,7,3,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>{{1,2,8},{3,4,5,7},{6}}
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>{{1,2,8},{3,7},{4,5,6}}
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>{{1,2,8},{3,7},{4,6},{5}}
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>{{1,2,8},{3,7},{4,5,6}}
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[8,1,7,3,6,5,4,2]=>{{1,2,8},{3,4,7},{5,6}}
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[8,1,7,3,5,6,4,2]=>{{1,2,8},{3,4,7},{5},{6}}
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[8,1,4,6,3,7,5,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>{{1,2,8},{3,4,5,7},{6}}
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>{{1,2,8},{3,4,5,6,7}}
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[8,1,4,6,5,3,7,2]=>{{1,2,8},{3,4,6},{5},{7}}
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[8,1,5,3,6,4,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>{{1,2,8},{3,4,6},{5},{7}}
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>{{1,2,8},{3,4,5,6},{7}}
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>{{1,2,8},{3,4,5},{6},{7}}
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>{{1,2,8},{3,5},{4},{6},{7}}
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]=>{{1,2,8},{3,4},{5},{6},{7}}
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>{{1,2,8},{3},{4},{5},{6},{7}}
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[2,4,1,7,6,8,5,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>{{1,2,3,4,8},{5,6,7}}
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[2,5,1,8,4,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[2,6,1,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[2,7,1,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[2,8,1,7,5,6,4,3]=>{{1,2,3,8},{4,7},{5},{6}}
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[2,8,1,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[2,8,1,5,6,4,7,3]=>{{1,2,3,8},{4,5,6},{7}}
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>{{1,2,3,8},{4,5},{6},{7}}
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>{{1,2,3,8},{4},{5},{6},{7}}
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[4,1,2,5,8,7,6,3]=>{{1,2,3,4,5,8},{6,7}}
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>{{1,2,3,4,8},{5,7},{6}}
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>{{1,2,3,4,8},{5,6,7}}
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>{{1,2,3,4,8},{5},{6},{7}}
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>{{1,2,3,8},{4,5,6,7}}
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>{{1,2,3,8},{4,5,6,7}}
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>{{1,2,3,8},{4,7},{5,6}}
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>{{1,2,3,8},{4,5,6,7}}
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>{{1,2,3,8},{4,5,7},{6}}
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>{{1,2,3,8},{4,5,6,7}}
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>{{1,2,3,8},{4,5,6,7}}
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>{{1,2,3,8},{4,5,6},{7}}
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>{{1,2,3,8},{4},{5},{6},{7}}
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[3,1,5,2,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[3,1,5,2,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[2,5,1,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>{{1,2,3,4,5,8},{6,7}}
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>{{1,2,3,4,5,8},{6},{7}}
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>{{1,2,3,4,8},{5,6,7}}
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>{{1,2,3,4,8},{5,7},{6}}
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>{{1,2,3,4,8},{5,6,7}}
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>{{1,2,3,4,8},{5,6},{7}}
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>{{1,2,3,4,8},{5},{6},{7}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[3,4,2,8,1,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>{{1,2,3,4,5,6,8},{7}}
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>{{1,2,3,4,5,8},{6,7}}
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>{{1,2,3,4,5,8},{6},{7}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[4,3,5,2,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[4,5,2,3,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[5,4,2,7,3,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[5,4,2,8,3,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[5,3,8,2,4,1,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[5,1,4,8,3,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[4,3,7,2,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[3,7,2,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>{{1,2,3,4,5,6,8},{7}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[2,3,4,6,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[2,3,6,5,8,4,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[2,4,5,3,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[2,6,4,5,8,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[3,4,2,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[4,3,5,2,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[5,3,4,6,2,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[8,5,3,4,2,6,1,7]=>[6,4,5,3,8,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[6,5,4,8,3,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[6,5,2,8,4,3,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[6,4,2,8,3,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[6,3,8,2,4,5,1,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[4,1,5,3,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[5,1,6,3,4,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[6,1,4,5,8,3,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[6,1,8,3,4,5,2,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[2,5,1,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[2,6,1,8,4,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[5,1,2,6,4,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[2,6,1,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[3,6,2,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[4,3,5,2,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[8,3,2,4,5,1,6,7]=>[5,3,8,2,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[8,5,4,3,1,2,6,7]=>[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[8,4,3,5,1,2,6,7]=>[5,1,4,8,3,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[2,3,4,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[2,3,6,5,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>{{1,2,3,7},{4,5,6},{8}}
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>{{1,2,3,7},{4,6},{5},{8}}
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>{{1,2,3,7},{4,5},{6},{8}}
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[2,5,4,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[2,6,4,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[2,6,4,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>{{1,2,7},{3,4,6},{5},{8}}
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>{{1,2,7},{3,6},{4,5},{8}}
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[6,5,3,4,7,2,1,8]=>[2,7,5,3,6,4,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[2,7,6,3,5,4,1,8]=>{{1,2,7},{3,4,6},{5},{8}}
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[2,7,6,3,4,5,1,8]=>{{1,2,7},{3,4,5,6},{8}}
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>{{1,2,7},{3},{4},{5},{6},{8}}
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[3,4,2,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[3,4,2,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[3,4,2,6,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>{{1,2,3,7},{4,5,6},{8}}
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>{{1,2,3,7},{4,6},{5},{8}}
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[3,7,2,5,4,6,1,8]=>{{1,2,3,7},{4,5},{6},{8}}
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[4,3,6,2,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[4,3,7,2,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>{{1,2,3,4,7},{5,6},{8}}
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[5,3,4,6,2,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[5,3,4,7,2,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[5,4,2,7,3,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[5,3,7,2,4,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[6,4,2,5,7,3,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[7,3,2,4,5,6,1,8]=>[6,3,7,2,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[6,7,2,3,4,5,1,8]=>{{1,2,3,4,5,6,7},{8}}
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,3,4,5,6,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,3,4,6,5,2,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>{{1,7},{2,3,6},{4,5},{8}}
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[7,5,4,6,3,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>{{1,7},{2,6},{3,4},{5},{8}}
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>{{1,7},{2,6},{3},{4},{5},{8}}
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[7,4,2,5,6,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[7,5,2,6,4,3,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>{{1,7},{2,3,6},{4,5},{8}}
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,6,2,4,5,3,1,8]=>{{1,7},{2,3,6},{4},{5},{8}}
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[7,3,6,2,5,4,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[7,6,2,3,5,4,1,8]=>{{1,7},{2,3,4,6},{5},{8}}
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>{{1,7},{2,3,4,5,6},{8}}
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>{{1,7},{2,3,5},{4},{6},{8}}
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>{{1,7},{2,5},{3,4},{6},{8}}
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,4,2,5,3,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>{{1,7},{2,3,4,5},{6},{8}}
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>{{1,7},{2,3,4},{5},{6},{8}}
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[3,1,4,5,7,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[3,1,4,7,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[4,1,7,3,6,5,2,8]=>{{1,2,3,4,7},{5,6},{8}}
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[6,7,4,3,5,1,2,8]=>[5,1,4,7,3,6,2,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,1,5,7,4,3,2,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>{{1,2,7},{3,4,6},{5},{8}}
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[7,1,5,6,4,3,2,8]=>{{1,2,7},{3,4,5,6},{8}}
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[5,4,6,3,7,1,2,8]=>[7,1,6,5,4,3,2,8]=>{{1,2,7},{3,6},{4,5},{8}}
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>{{1,2,7},{3,4,5,6},{8}}
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[7,1,6,3,5,4,2,8]=>{{1,2,7},{3,4,6},{5},{8}}
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>{{1,2,7},{3},{4},{5},{6},{8}}
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[2,4,1,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[2,5,1,6,4,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[2,6,1,5,7,4,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[2,7,1,5,6,4,3,8]=>{{1,2,3,7},{4,5,6},{8}}
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>{{1,2,3,7},{4,6},{5},{8}}
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>{{1,2,3,7},{4,5,6},{8}}
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>{{1,2,3,7},{4,5},{6},{8}}
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>{{1,2,3,7},{4},{5},{6},{8}}
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[3,6,2,1,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[2,5,1,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[2,6,1,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>{{1,2,3,4,7},{5,6},{8}}
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>{{1,2,3,4,7},{5},{6},{8}}
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[4,3,7,2,1,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[4,6,2,3,1,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[4,1,7,3,2,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[2,3,6,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[3,1,6,2,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>{{1,2,3,4,5,7},{6},{8}}
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[2,5,7,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[7,4,5,2,3,1,6,8]=>[3,5,2,7,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[4,3,5,2,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[5,3,4,7,2,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[5,4,2,7,3,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[5,3,7,2,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[2,5,1,7,4,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[2,5,1,3,7,4,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>{{1,2,3,4,5,6,7},{8}}
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[2,3,5,6,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>{{1,2,3,6},{4},{5},{7},{8}}
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[5,3,4,6,2,1,7,8]=>[2,6,5,3,4,1,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>{{1,2,6},{3},{4},{5},{7},{8}}
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[3,4,2,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[4,3,5,2,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[6,3,4,2,5,1,7,8]=>[5,4,6,3,2,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[5,4,2,6,3,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[5,6,2,3,4,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}}
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>{{1,6},{2,5},{3},{4},{7},{8}}
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[6,3,5,2,4,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>{{1,6},{2,3,4,5},{7},{8}}
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>{{1,6},{2,4},{3},{5},{7},{8}}
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[3,1,5,6,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[5,1,6,3,4,2,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>{{1,2,6},{3,4,5},{7},{8}}
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>{{1,2,6},{3},{4},{5},{7},{8}}
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[2,4,1,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>{{1,2,3,6},{4,5},{7},{8}}
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[4,5,6,2,1,3,7,8]=>[2,6,1,4,5,3,7,8]=>{{1,2,3,6},{4},{5},{7},{8}}
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[4,1,2,6,5,3,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[2,3,5,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[3,1,6,2,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[6,5,2,1,3,4,7,8]=>[2,5,1,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[4,6,2,3,1,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[4,1,6,3,2,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[3,1,6,2,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>{{1,2,5},{3,4},{6},{7},{8}}
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>{{1,2,5},{3},{4},{6},{7},{8}}
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}}
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>{{1,5},{2,3,4},{6},{7},{8}}
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>{{1,5},{2,3},{4},{6},{7},{8}}
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>{{1,2,5},{3,4},{6},{7},{8}}
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>{{1,2,5},{3},{4},{6},{7},{8}}
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>{{1,2,3,5},{4},{6},{7},{8}}
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>{{1,2,4},{3},{5},{6},{7},{8}}
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>{{1,2,4},{3},{5},{6},{7},{8}}
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>{{1,2,3},{4},{5},{6},{7},{8}}
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>{{1,2,3,4,5,6,9},{7},{8}}
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>{{1,2,3,4,5,9},{6},{7},{8}}
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>{{1,2,3,4,9},{5},{6},{7},{8}}
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>{{1,2,3,9},{4},{5},{6},{7},{8}}
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>{{1,2,3,4,5,6,7,8,10},{9}}
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,9,7,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>{{1,2,3,4,5,6,7,10},{8},{9}}
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[2,3,4,5,7,9,6,8,1]=>{{1,2,3,4,5,6,7,9},{8}}
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>{{1,2,3,4,5,6,10},{7},{8},{9}}
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[2,3,4,6,9,5,7,8,1]=>{{1,2,3,4,5,6,9},{7},{8}}
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>{{1,2,3,4,5,10},{6},{7},{8},{9}}
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[2,3,5,9,4,6,7,8,1]=>{{1,2,3,4,5,9},{6},{7},{8}}
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>{{1,2,3,4,10},{5},{6},{7},{8},{9}}
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[2,4,9,3,5,6,7,8,1]=>{{1,2,3,4,9},{5},{6},{7},{8}}
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>{{1,2,3,10},{4},{5},{6},{7},{8},{9}}
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[3,9,2,4,5,6,7,8,1]=>{{1,2,3,9},{4},{5},{6},{7},{8}}
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>{{1,2,3,4,5,6,9},{7,8}}
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>{{1,2,3,4,5,9},{6,7,8}}
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>{{1,2,3,4,9},{5,6,7,8}}
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>{{1,2,3,9},{4,5,6,7,8}}
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>{{1,2,9},{3,4,5,6,7,8}}
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>{{1,9},{2,3,4,5,6,7,8}}
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>{{1,2,3,4,5,6,7,10},{8,9}}
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>{{1,2,3,4,5,6,10},{7,8,9}}
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>{{1,2,3,4,5,10},{6,7,8,9}}
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>{{1,2,3,4,10},{5,6,7,8,9}}
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>{{1,2,3,10},{4,5,6,7,8,9}}
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>{{1,2,10},{3,4,5,6,7,8,9}}
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,2,9]=>{{1,2,3,4,5,6,7,8},{9}}
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>{{1,10},{2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[6,7,5,8,4,9,3,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>{{1,2,10},{3,9},{4,8},{5,7},{6}}
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10}}
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>{{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}}
[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[7,5,6,4,8,3,9,2,10,1]=>[10,9,8,6,7,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,5,6,7}}
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>{{1,9},{2,3},{4},{5},{6},{7},{8}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>{{1,9},{2,4},{3},{5},{6},{7},{8}}
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>{{1,10},{2,3},{4},{5},{6},{7},{8},{9}}
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>{{1,2,3,4,5,6,7,9},{8}}
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>{{1,2,3,4,5,6,9},{7},{8}}
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>{{1,2,3,4,5,6,7,8,10},{9}}
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,8,7,6]=>{{1,2,3,4,5,6,9},{7,8}}
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>{{1,2,3,4,5,10},{6},{7},{8},{9}}
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>{{1,2,3,4,5,6,8},{7},{9}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>{{1,2,3,4,5,6,7,8,9,10},{11}}
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>{{1,2,3,4,5,6,7,9},{8},{10}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[7,6,8,4,3,5,9,2,10,1]=>[10,9,4,8,3,7,6,5,2,1]=>{{1,10},{2,9},{3,4,5,8},{6,7}}
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[7,6,8,5,9,4,10,2,1,3]=>[2,10,1,9,8,7,6,5,4,3]=>{{1,2,3,10},{4,9},{5,8},{6,7}}
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[10,5,4,6,3,7,2,8,1,9]=>[8,7,6,5,10,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[6,4,5,7,3,8,2,9,1,10]=>[9,8,7,6,4,5,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,5,6},{10}}
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[8,9,2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,8,2,3,4,5,6,7,1]=>{{1,9},{2,3,4,5,6,7,8}}
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[2,3,4,6,1,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[2,3,4,5,7,1,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>{{1,5},{2},{3},{4},{6},{7},{8},{9}}
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}}
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>{{1,2,3,4,5,6,7,8},{9},{10}}
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,9,2,1]=>{{1,2,3,4,5,6,7,8,9}}
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>{{1,11},{2,3,4,5,6,7,8,9,10}}
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>{{1,2,3,4,5,6,7,8,9,11},{10}}
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>{{1,9},{2,3,4,5,6,8},{7}}
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>{{1,10},{2,3,4,5,6,7,9},{8}}
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>{{1,2,4},{3},{5},{6},{7},{8},{9}}
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>{{1,2,3,9},{4,5},{6},{7},{8}}
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>{{1,2,3,4,9},{5,6},{7},{8}}
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>{{1,2,3,5},{4},{6},{7},{8},{9}}
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>{{1,2,3,4,5,6,7,8},{9}}
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>{{1,2,8},{3},{4},{5},{6},{7},{9}}
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>{{1,2,3,4,5,7},{6},{8},{9}}
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>{{1,2,3,4,5,9},{6,7},{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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
searching the database
Sorry, this map was not found in the database.