Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ 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}}
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>{{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}}
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,2,4,1]=>{{1,3,4},{2}}
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}}
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}}
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,4,2]=>{{1},{2,3,4}}
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}}
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}}
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>{{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}}
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>{{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}}
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}
[.,[.,[[.,[.,.]],.]]]=>[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}}
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[.,[[.,[.,[.,.]]],.]]=>[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}}
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>{{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}}
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{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}}
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{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}}
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{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}}
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{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}}
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}
[.,[.,[.,[[.,[.,.]],.]]]]=>[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}}
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}
[.,[.,[[.,[.,[.,.]]],.]]]=>[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}}
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>{{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}}
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[.,[[.,[.,[.,[.,.]]]],.]]=>[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}}
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[.,[[.,[[.,[.,.]],.]],.]]=>[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}}
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>{{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}}
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>{{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}}
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{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}}
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{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}}
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{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}}
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>{{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}}
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{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}}
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{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}}
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{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}}
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{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}}
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[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}}
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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}}
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>{{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}}
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[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}}
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[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}}
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>{{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}}
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>{{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}}
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[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}}
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[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}}
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[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}}
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>{{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}}
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>{{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}}
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{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}}
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>{{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}}
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>{{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}}
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{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}}
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{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}}
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{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}}
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>{{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}}
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{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}}
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{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}}
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>{{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}}
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>{{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}}
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{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}}
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{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}}
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{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}}
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>{{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}}
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{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}}
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{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}}
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{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}}
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{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}}
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[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}}
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>{{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}}
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>{{1,2,3,7,8},{4},{5},{6}}
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[2,4,3,7,6,5,8,1]=>{{1,2,4,7,8},{3},{5,6}}
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}}
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}}
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[2,5,4,3,6,8,7,1]=>{{1,2,5,6,8},{3,4},{7}}
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[2,5,4,3,7,6,8,1]=>{{1,2,5,7,8},{3,4},{6}}
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[2,5,4,3,8,7,6,1]=>{{1,2,5,8},{3,4},{6,7}}
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>{{1,2,5,8},{3,4},{6},{7}}
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[3,2,4,7,6,5,8,1]=>{{1,3,4,7,8},{2},{5,6}}
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[3,2,4,8,7,6,5,1]=>{{1,3,4,8},{2},{5,7},{6}}
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[4,3,2,7,6,5,8,1]=>{{1,4,7,8},{2,3},{5,6}}
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>{{1,4,7,8},{2,3},{5},{6}}
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[4,3,2,8,7,6,5,1]=>{{1,4,8},{2,3},{5,7},{6}}
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]=>{{1,4,7,8},{2},{3},{5,6}}
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[4,2,3,8,7,6,5,1]=>{{1,4,8},{2},{3},{5,7},{6}}
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}}
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>{{1,5,6,8},{2,4},{3},{7}}
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[5,4,3,2,7,6,8,1]=>{{1,5,7,8},{2,4},{3},{6}}
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[3,4,2,7,6,8,5,1]=>[5,4,3,2,8,7,6,1]=>{{1,5,8},{2,4},{3},{6,7}}
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[5,4,3,2,8,6,7,1]=>{{1,5,8},{2,4},{3},{6},{7}}
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}}
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>{{1},{2,3,8},{4,5,6,7}}
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}}
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}}
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]=>{{1},{2,7,8},{3,5},{4},{6}}
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>{{1},{2,8},{3,5},{4},{6},{7}}
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}}
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}}
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}}
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[1,2,4,8,7,6,5,3]=>{{1},{2},{3,4,8},{5,7},{6}}
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>{{1},{2},{3,8},{4,5},{6},{7}}
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>{{1,2,3},{4,8},{5,6,7}}
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}}
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}}
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>{{1,3},{2},{4,5,6,8},{7}}
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}}
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}}
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>{{1,3},{2},{4,5,8},{6},{7}}
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}}
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}}
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}}
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[3,2,1,7,5,6,8,4]=>{{1,3},{2},{4,7,8},{5},{6}}
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>{{1,3},{2},{4,8},{5,6,7}}
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}}
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>{{1,3},{2},{4,8},{5},{6,7}}
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>{{1,3},{2},{4,8},{5,6},{7}}
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>{{1,3},{2},{4,8},{5},{6},{7}}
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}}
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}}
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}}
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}}
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>{{1},{2},{3},{4,8},{5,6,7}}
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}}
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>{{1},{2},{3},{4,8},{5},{6,7}}
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>{{1},{2},{3},{4,8},{5,6},{7}}
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}}
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}}
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}}
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}}
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>{{1,2},{3,4},{5,7,8},{6}}
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>{{1,2},{3,4},{5,8},{6},{7}}
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}}
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}}
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}}
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[3,2,1,4,7,6,8,5]=>{{1,3},{2},{4},{5,7,8},{6}}
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>{{1},{2,3},{4},{5,7,8},{6}}
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}}
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}}
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}}
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}}
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[4,5,3,2,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[4,3,5,2,1,7,8,6]=>[2,5,4,3,1,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[2,5,3,4,1,8,7,6]=>{{1,2,5},{3},{4},{6,8},{7}}
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[3,2,4,5,1,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>{{1,3,5},{2},{4},{6,8},{7}}
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}}
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[4,2,3,5,1,8,7,6]=>{{1,4,5},{2},{3},{6,8},{7}}
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}}
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>{{1,5},{2,4},{3},{6,7,8}}
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}}
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>{{1,5},{2},{3,4},{6,8},{7}}
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>{{1,5},{2,3},{4},{6,8},{7}}
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}}
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}}
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}}
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}}
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]=>{{1,5,6},{2,4},{3},{7,8}}
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}}
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}}
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>{{1,2},{3,5},{4},{6},{7,8}}
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}}
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>{{1,3,4},{2},{5},{6},{7,8}}
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}}
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}}
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{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}}
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>{{1,7},{2},{3},{4,6},{5},{8}}
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>{{1,3},{2},{4,7},{5},{6},{8}}
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}}
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}}
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}}
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}}
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>{{1,5},{2,4},{3},{6,7},{8}}
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}}
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}}
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}}
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>{{1,6},{2},{3},{4,5},{7},{8}}
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{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}}
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{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}}
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{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}}
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{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}}
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
searching the database
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