Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Images
=>
Cc0010;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[.,.]=>[1]=>{{1}}=>{{1}}
[.,[.,.]]=>[2,1]=>{{1,2}}=>{{1,2}}
[[.,.],.]=>[1,2]=>{{1},{2}}=>{{1},{2}}
[.,[.,[.,.]]]=>[3,2,1]=>{{1,3},{2}}=>{{1,3},{2}}
[.,[[.,.],.]]=>[2,3,1]=>{{1,2,3}}=>{{1,2,3}}
[[.,.],[.,.]]=>[1,3,2]=>{{1},{2,3}}=>{{1,2},{3}}
[[.,[.,.]],.]=>[2,1,3]=>{{1,2},{3}}=>{{1},{2,3}}
[[[.,.],.],.]=>[1,2,3]=>{{1},{2},{3}}=>{{1},{2},{3}}
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>{{1,4},{2,3}}=>{{1,4},{2,3}}
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>{{1,3},{2,4}}=>{{1,3},{2,4}}
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>{{1,2,4},{3}}=>{{1,3,4},{2}}
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>{{1,3,4},{2}}=>{{1,2,4},{3}}
[.,[[[.,.],.],.]]=>[2,3,4,1]=>{{1,2,3,4}}=>{{1,2,3,4}}
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>{{1},{2,4},{3}}=>{{1,3},{2},{4}}
[[.,.],[[.,.],.]]=>[1,3,4,2]=>{{1},{2,3,4}}=>{{1,2,3},{4}}
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2},{3,4}}
[[[.,.],.],[.,.]]=>[1,2,4,3]=>{{1},{2},{3,4}}=>{{1,2},{3},{4}}
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>{{1,3},{2},{4}}=>{{1},{2,4},{3}}
[[.,[[.,.],.]],.]=>[2,3,1,4]=>{{1,2,3},{4}}=>{{1},{2,3,4}}
[[[.,.],[.,.]],.]=>[1,3,2,4]=>{{1},{2,3},{4}}=>{{1},{2,3},{4}}
[[[.,[.,.]],.],.]=>[2,1,3,4]=>{{1,2},{3},{4}}=>{{1},{2},{3,4}}
[[[[.,.],.],.],.]=>[1,2,3,4]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}}
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}=>{{1,5},{2,4},{3}}
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>{{1,4},{2,5},{3}}=>{{1,4},{2,5},{3}}
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>{{1,3,4},{2,5}}=>{{1,4},{2,3,5}}
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>{{1,4},{2,3,5}}=>{{1,3,4},{2,5}}
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}=>{{1,3,5},{2,4}}
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}=>{{1,4,5},{2,3}}
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>{{1,2,4},{3,5}}=>{{1,3},{2,4,5}}
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}=>{{1,3,5},{2},{4}}
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}=>{{1,3,4,5},{2}}
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}=>{{1,2,5},{3,4}}
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>{{1,3},{2,4,5}}=>{{1,2,4},{3,5}}
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}=>{{1,2,4,5},{3}}
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}=>{{1,2,3,5},{4}}
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}}
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}=>{{1,4},{2,3},{5}}
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>{{1},{2,4},{3,5}}=>{{1,3},{2,4},{5}}
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}=>{{1,3,4},{2},{5}}
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}=>{{1,2,4},{3},{5}}
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}=>{{1,2,3,4},{5}}
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}=>{{1,3},{2},{4,5}}
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}=>{{1,2,3},{4,5}}
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}=>{{1,3},{2},{4},{5}}
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}=>{{1,2,3},{4},{5}}
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}=>{{1,2},{3,5},{4}}
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}=>{{1,2},{3,4,5}}
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}=>{{1,2},{3,4},{5}}
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}=>{{1,2},{3},{4,5}}
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}=>{{1,2},{3},{4},{5}}
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}=>{{1},{2,5},{3,4}}
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>{{1,3},{2,4},{5}}=>{{1},{2,4},{3,5}}
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}=>{{1},{2,4,5},{3}}
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}=>{{1},{2,3,5},{4}}
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}=>{{1},{2,3,4,5}}
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}=>{{1},{2,4},{3},{5}}
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}=>{{1},{2,3,4},{5}}
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}=>{{1},{2,3},{4,5}}
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}=>{{1},{2,3},{4},{5}}
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}=>{{1},{2},{3,5},{4}}
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}=>{{1},{2},{3,4,5}}
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}=>{{1},{2},{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}}=>{{1},{2},{3},{4},{5}}
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}=>{{1,6},{2,5},{3,4}}
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>{{1,5},{2,6},{3,4}}=>{{1,5},{2,6},{3,4}}
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>{{1,4},{2,6},{3,5}}=>{{1,5},{2,4},{3,6}}
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>{{1,5},{2,4},{3,6}}=>{{1,4},{2,6},{3,5}}
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}=>{{1,4},{2,5},{3,6}}
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>{{1,3,5},{2,6},{4}}=>{{1,5},{2,4,6},{3}}
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}=>{{1,4,6},{2,5},{3}}
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>{{1,4,5},{2,3,6}}=>{{1,4,5},{2,3,6}}
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}=>{{1,4,6},{2,3,5}}
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>{{1,5},{2,4,6},{3}}=>{{1,3,5},{2,6},{4}}
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}=>{{1,3,6},{2,5},{4}}
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}=>{{1,3,4,6},{2,5}}
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}=>{{1,3,6},{2,4,5}}
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>{{1,3,5},{2,4,6}}=>{{1,3,5},{2,4,6}}
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}=>{{1,5,6},{2,4},{3}}
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>{{1,2,5},{3,6},{4}}=>{{1,4},{2,5,6},{3}}
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>{{1,2,4,5},{3,6}}=>{{1,4},{2,3,5,6}}
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>{{1,2,5},{3,4,6}}=>{{1,3,4},{2,5,6}}
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}=>{{1,3,5,6},{2,4}}
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}=>{{1,4,6},{2,3},{5}}
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>{{1,3,5},{2},{4,6}}=>{{1,3},{2,4,6},{5}}
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}=>{{1,4,5,6},{2,3}}
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>{{1,2,3,5},{4,6}}=>{{1,3},{2,4,5,6}}
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}=>{{1,3,6},{2},{4,5}}
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>{{1,3},{2,4,6},{5}}=>{{1,3,5},{2},{4,6}}
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}=>{{1,3,5,6},{2},{4}}
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}=>{{1,3,4,6},{2},{5}}
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}=>{{1,3,4,5,6},{2}}
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}=>{{1,2,6},{3,5},{4}}
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>{{1,4},{2,5,6},{3}}=>{{1,2,5},{3,6},{4}}
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>{{1,3,4},{2,5,6}}=>{{1,2,5},{3,4,6}}
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>{{1,4},{2,3,5,6}}=>{{1,2,4,5},{3,6}}
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}=>{{1,2,4,6},{3,5}}
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}=>{{1,2,5,6},{3,4}}
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>{{1,2,4},{3,5,6}}=>{{1,2,4},{3,5,6}}
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}=>{{1,2,4,6},{3},{5}}
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}=>{{1,2,4,5,6},{3}}
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}=>{{1,2,3,6},{4,5}}
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>{{1,3},{2,4,5,6}}=>{{1,2,3,5},{4,6}}
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}=>{{1,2,3,5,6},{4}}
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}=>{{1,2,3,4,6},{5}}
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}}
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}=>{{1,5},{2,4},{3},{6}}
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>{{1},{2,5},{3,6},{4}}=>{{1,4},{2,5},{3},{6}}
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>{{1},{2,4,5},{3,6}}=>{{1,4},{2,3,5},{6}}
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>{{1},{2,5},{3,4,6}}=>{{1,3,4},{2,5},{6}}
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}=>{{1,3,5},{2,4},{6}}
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}=>{{1,4,5},{2,3},{6}}
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>{{1},{2,3,5},{4,6}}=>{{1,3},{2,4,5},{6}}
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}=>{{1,3,5},{2},{4},{6}}
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}=>{{1,3,4,5},{2},{6}}
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}=>{{1,2,5},{3,4},{6}}
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>{{1},{2,4},{3,5,6}}=>{{1,2,4},{3,5},{6}}
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}=>{{1,2,4,5},{3},{6}}
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}=>{{1,2,3,5},{4},{6}}
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}=>{{1,2,3,4,5},{6}}
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}=>{{1,4},{2,3},{5,6}}
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>{{1,2},{3,5},{4,6}}=>{{1,3},{2,4},{5,6}}
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}=>{{1,3,4},{2},{5,6}}
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}=>{{1,2,4},{3},{5,6}}
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}=>{{1,2,3,4},{5,6}}
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}=>{{1,4},{2,3},{5},{6}}
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>{{1},{2},{3,5},{4,6}}=>{{1,3},{2,4},{5},{6}}
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}=>{{1,3,4},{2},{5},{6}}
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}=>{{1,2,4},{3},{5},{6}}
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}=>{{1,2,3,4},{5},{6}}
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}=>{{1,3},{2},{4,6},{5}}
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}=>{{1,2,3},{4,6},{5}}
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}=>{{1,3},{2},{4,5,6}}
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}=>{{1,2,3},{4,5,6}}
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}=>{{1,3},{2},{4,5},{6}}
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}=>{{1,2,3},{4,5},{6}}
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}=>{{1,3},{2},{4},{5,6}}
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}=>{{1,2,3},{4},{5,6}}
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}=>{{1,3},{2},{4},{5},{6}}
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}=>{{1,2,3},{4},{5},{6}}
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}=>{{1,2},{3,6},{4,5}}
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,2},{3,5},{4,6}}
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}=>{{1,2},{3,5,6},{4}}
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}=>{{1,2},{3,4,6},{5}}
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}=>{{1,2},{3,4,5,6}}
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}=>{{1,2},{3,5},{4},{6}}
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}=>{{1,2},{3,4,5},{6}}
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}}
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}=>{{1,2},{3,4},{5},{6}}
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}=>{{1,2},{3},{4,6},{5}}
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}=>{{1,2},{3},{4,5,6}}
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}=>{{1,2},{3},{4,5},{6}}
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5,6}}
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}=>{{1,2},{3},{4},{5},{6}}
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}=>{{1},{2,6},{3,5},{4}}
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>{{1,4},{2,5},{3},{6}}=>{{1},{2,5},{3,6},{4}}
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>{{1,3,4},{2,5},{6}}=>{{1},{2,5},{3,4,6}}
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>{{1,4},{2,3,5},{6}}=>{{1},{2,4,5},{3,6}}
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}=>{{1},{2,4,6},{3,5}}
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}=>{{1},{2,5,6},{3,4}}
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>{{1,2,4},{3,5},{6}}=>{{1},{2,4},{3,5,6}}
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}=>{{1},{2,4,6},{3},{5}}
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}=>{{1},{2,4,5,6},{3}}
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}=>{{1},{2,3,6},{4,5}}
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>{{1,3},{2,4,5},{6}}=>{{1},{2,3,5},{4,6}}
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}=>{{1},{2,3,5,6},{4}}
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}=>{{1},{2,3,4,6},{5}}
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}=>{{1},{2,3,4,5,6}}
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}=>{{1},{2,5},{3,4},{6}}
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>{{1},{2,4},{3,5},{6}}=>{{1},{2,4},{3,5},{6}}
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}=>{{1},{2,4,5},{3},{6}}
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}=>{{1},{2,3,5},{4},{6}}
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}=>{{1},{2,3,4,5},{6}}
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}=>{{1},{2,4},{3},{5,6}}
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}=>{{1},{2,3,4},{5,6}}
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}=>{{1},{2,4},{3},{5},{6}}
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}=>{{1},{2,3,4},{5},{6}}
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}=>{{1},{2,3},{4,6},{5}}
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}=>{{1},{2,3},{4,5,6}}
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}=>{{1},{2,3},{4,5},{6}}
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}=>{{1},{2,3},{4},{5,6}}
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}=>{{1},{2,3},{4},{5},{6}}
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}=>{{1},{2},{3,6},{4,5}}
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>{{1,3},{2,4},{5},{6}}=>{{1},{2},{3,5},{4,6}}
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}=>{{1},{2},{3,5,6},{4}}
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}=>{{1},{2},{3,4,6},{5}}
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}=>{{1},{2},{3,4,5,6}}
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}=>{{1},{2},{3,5},{4},{6}}
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}=>{{1},{2},{3,4,5},{6}}
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5,6}}
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}=>{{1},{2},{3,4},{5},{6}}
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}=>{{1},{2},{3},{4,6},{5}}
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}=>{{1},{2},{3},{4,5,6}}
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}=>{{1},{2},{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}}=>{{1},{2},{3},{4},{5},{6}}
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}=>{{1,7},{2,6},{3,5},{4}}
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>{{1,6},{2,7},{3,5},{4}}=>{{1,6},{2,7},{3,5},{4}}
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>{{1,5},{2,7},{3,6},{4}}=>{{1,6},{2,5},{3,7},{4}}
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>{{1,6},{2,5},{3,7},{4}}=>{{1,5},{2,7},{3,6},{4}}
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>{{1,5},{2,6},{3,7},{4}}=>{{1,5},{2,6},{3,7},{4}}
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>{{1,4,5},{2,7},{3,6}}=>{{1,6},{2,5},{3,4,7}}
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>{{1,4,5},{2,6},{3,7}}=>{{1,5},{2,6},{3,4,7}}
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>{{1,5},{2,4,6},{3,7}}=>{{1,5},{2,4,6},{3,7}}
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>{{1,4,6},{2,5},{3,7}}=>{{1,5},{2,4,7},{3,6}}
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>{{1,6},{2,5},{3,4,7}}=>{{1,4,5},{2,7},{3,6}}
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>{{1,5},{2,6},{3,4,7}}=>{{1,4,5},{2,6},{3,7}}
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>{{1,4,7},{2,6},{3,5}}=>{{1,4,7},{2,6},{3,5}}
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>{{1,5},{2,4,7},{3,6}}=>{{1,4,6},{2,5},{3,7}}
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,5},{3,6}}=>{{1,4,7},{2,5},{3,6}}
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>{{1,3,6},{2,7},{4,5}}=>{{1,6},{2,5,7},{3,4}}
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}}=>{{1,5,7},{2,6},{3,4}}
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>{{1,3,7},{2,5},{4,6}}=>{{1,5,7},{2,4},{3,6}}
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>{{1,3,5},{2,6},{4,7}}=>{{1,4},{2,6},{3,5,7}}
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>{{1,3,6},{2,5},{4,7}}=>{{1,4},{2,5,7},{3,6}}
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>{{1,4,6},{2,3,7},{5}}=>{{1,5,6},{2,4,7},{3}}
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>{{1,4,7},{2,3,6},{5}}=>{{1,4,7},{2,5,6},{3}}
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}}=>{{1,5,7},{2,4,6},{3}}
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>{{1,3,6},{2,4,7},{5}}=>{{1,4,6},{2,5,7},{3}}
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>{{1,5,6},{2,4,7},{3}}=>{{1,4,6},{2,3,7},{5}}
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>{{1,4,7},{2,5,6},{3}}=>{{1,4,7},{2,3,6},{5}}
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}}=>{{1,4,5,7},{2,3,6}}
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>{{1,4,7},{2,3,5,6}}=>{{1,4,7},{2,3,5,6}}
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>{{1,3,5,6},{2,4,7}}=>{{1,4,6},{2,3,5,7}}
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>{{1,6},{2,5,7},{3,4}}=>{{1,3,6},{2,7},{4,5}}
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}=>{{1,3,7},{2,6},{4,5}}
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>{{1,4},{2,6},{3,5,7}}=>{{1,3,5},{2,6},{4,7}}
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,4},{3,6}}=>{{1,3,7},{2,5},{4,6}}
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>{{1,4},{2,5,7},{3,6}}=>{{1,3,6},{2,5},{4,7}}
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>{{1,3,5,7},{2,6},{4}}=>{{1,3,5,7},{2,6},{4}}
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>{{1,3,6},{2,5,7},{4}}=>{{1,3,6},{2,5,7},{4}}
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>{{1,4,5,7},{2,3,6}}=>{{1,3,4,7},{2,5,6}}
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>{{1,3,6},{2,4,5,7}}=>{{1,3,4,6},{2,5,7}}
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}=>{{1,3,7},{2,4,6},{5}}
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>{{1,4,6},{2,5,7},{3}}=>{{1,3,6},{2,4,7},{5}}
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>{{1,3,4,6},{2,5,7}}=>{{1,3,6},{2,4,5,7}}
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>{{1,4,6},{2,3,5,7}}=>{{1,3,5,6},{2,4,7}}
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}=>{{1,3,5,7},{2,4,6}}
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}=>{{1,6,7},{2,5},{3,4}}
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>{{1,2,6},{3,7},{4,5}}=>{{1,5},{2,6,7},{3,4}}
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>{{1,2,5},{3,7},{4,6}}=>{{1,5},{2,4},{3,6,7}}
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>{{1,2,6},{3,5},{4,7}}=>{{1,4},{2,6,7},{3,5}}
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>{{1,2,5},{3,6},{4,7}}=>{{1,4},{2,5},{3,6,7}}
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>{{1,2,4,6},{3,7},{5}}=>{{1,5},{2,4,6,7},{3}}
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}}=>{{1,4,6,7},{2,5},{3}}
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>{{1,2,5,6},{3,4,7}}=>{{1,4,5},{2,3,6,7}}
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}}=>{{1,4,6,7},{2,3,5}}
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>{{1,2,6},{3,5,7},{4}}=>{{1,3,5},{2,6,7},{4}}
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>{{1,2,5,7},{3,6},{4}}=>{{1,3,6,7},{2,5},{4}}
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}}=>{{1,3,4,6,7},{2,5}}
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}=>{{1,3,6,7},{2,4,5}}
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>{{1,2,4,6},{3,5,7}}=>{{1,3,5},{2,4,6,7}}
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}=>{{1,5,7},{2,4},{3},{6}}
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>{{1,3,6},{2},{4,7},{5}}=>{{1,4},{2,5,7},{3},{6}}
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>{{1,3,5,6},{2},{4,7}}=>{{1,4},{2,3,5,7},{6}}
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>{{1,3,6},{2},{4,5,7}}=>{{1,3,4},{2,5,7},{6}}
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>{{1,3,5,7},{2},{4,6}}=>{{1,3,5,7},{2,4},{6}}
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}=>{{1,5,6,7},{2,4},{3}}
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>{{1,2,3,6},{4,7},{5}}=>{{1,4},{2,5,6,7},{3}}
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>{{1,2,3,5,6},{4,7}}=>{{1,4},{2,3,5,6,7}}
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>{{1,2,3,6},{4,5,7}}=>{{1,3,4},{2,5,6,7}}
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}=>{{1,3,5,6,7},{2,4}}
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}=>{{1,4,7},{2,3},{5,6}}
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>{{1,4,6},{2,3},{5,7}}=>{{1,3},{2,4,7},{5,6}}
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>{{1,3},{2,4,7},{5,6}}=>{{1,4,6},{2,3},{5,7}}
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>{{1,3},{2,4,6},{5,7}}=>{{1,3},{2,4,6},{5,7}}
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}=>{{1,4,6,7},{2,3},{5}}
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>{{1,2,4,6},{3},{5,7}}=>{{1,3},{2,4,6,7},{5}}
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}=>{{1,4,5,7},{2,3},{6}}
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>{{1,3,4,6},{2},{5,7}}=>{{1,3},{2,4,5,7},{6}}
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}=>{{1,4,5,6,7},{2,3}}
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,6},{5,7}}=>{{1,3},{2,4,5,6,7}}
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}=>{{1,3,7},{2},{4,6},{5}}
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>{{1,4},{2,5,7},{3},{6}}=>{{1,3,6},{2},{4,7},{5}}
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>{{1,3,4},{2,5,7},{6}}=>{{1,3,6},{2},{4,5,7}}
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>{{1,4},{2,3,5,7},{6}}=>{{1,3,5,6},{2},{4,7}}
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}}=>{{1,3,5,7},{2},{4,6}}
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}=>{{1,3,6,7},{2},{4,5}}
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>{{1,2,4},{3,5,7},{6}}=>{{1,3,5},{2},{4,6,7}}
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}=>{{1,3,5,7},{2},{4},{6}}
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}=>{{1,3,5,6,7},{2},{4}}
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}=>{{1,3,4,7},{2},{5,6}}
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>{{1,3},{2,4,5,7},{6}}=>{{1,3,4,6},{2},{5,7}}
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}=>{{1,3,4,6,7},{2},{5}}
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}=>{{1,3,4,5,7},{2},{6}}
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}=>{{1,3,4,5,6,7},{2}}
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}=>{{1,2,7},{3,6},{4,5}}
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>{{1,5},{2,6,7},{3,4}}=>{{1,2,6},{3,7},{4,5}}
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>{{1,4},{2,6,7},{3,5}}=>{{1,2,6},{3,5},{4,7}}
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>{{1,5},{2,4},{3,6,7}}=>{{1,2,5},{3,7},{4,6}}
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>{{1,4},{2,5},{3,6,7}}=>{{1,2,5},{3,6},{4,7}}
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>{{1,3,5},{2,6,7},{4}}=>{{1,2,6},{3,5,7},{4}}
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>{{1,3,6,7},{2,5},{4}}=>{{1,2,5,7},{3,6},{4}}
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>{{1,4,5},{2,3,6,7}}=>{{1,2,5,6},{3,4,7}}
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}}=>{{1,2,5,7},{3,4,6}}
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>{{1,5},{2,4,6,7},{3}}=>{{1,2,4,6},{3,7},{5}}
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}=>{{1,2,4,7},{3,6},{5}}
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}}=>{{1,2,4,5,7},{3,6}}
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}=>{{1,2,4,7},{3,5,6}}
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>{{1,3,5},{2,4,6,7}}=>{{1,2,4,6},{3,5,7}}
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}=>{{1,2,6,7},{3,5},{4}}
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>{{1,2,5},{3,6,7},{4}}=>{{1,2,5},{3,6,7},{4}}
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>{{1,2,4,5},{3,6,7}}=>{{1,2,5},{3,4,6,7}}
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>{{1,2,5},{3,4,6,7}}=>{{1,2,4,5},{3,6,7}}
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}=>{{1,2,4,6,7},{3,5}}
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}=>{{1,2,5,7},{3,4},{6}}
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>{{1,3,5},{2},{4,6,7}}=>{{1,2,4},{3,5,7},{6}}
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}=>{{1,2,5,6,7},{3,4}}
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>{{1,2,3,5},{4,6,7}}=>{{1,2,4},{3,5,6,7}}
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}=>{{1,2,4,7},{3},{5,6}}
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>{{1,3},{2,4,6,7},{5}}=>{{1,2,4,6},{3},{5,7}}
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}=>{{1,2,4,6,7},{3},{5}}
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}=>{{1,2,4,5,7},{3},{6}}
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}=>{{1,2,4,5,6,7},{3}}
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}=>{{1,2,3,7},{4,6},{5}}
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>{{1,4},{2,5,6,7},{3}}=>{{1,2,3,6},{4,7},{5}}
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>{{1,3,4},{2,5,6,7}}=>{{1,2,3,6},{4,5,7}}
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>{{1,4},{2,3,5,6,7}}=>{{1,2,3,5,6},{4,7}}
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}=>{{1,2,3,5,7},{4,6}}
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}=>{{1,2,3,6,7},{4,5}}
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>{{1,2,4},{3,5,6,7}}=>{{1,2,3,5},{4,6,7}}
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}=>{{1,2,3,5,7},{4},{6}}
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}=>{{1,2,3,5,6,7},{4}}
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}=>{{1,2,3,4,7},{5,6}}
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>{{1,3},{2,4,5,6,7}}=>{{1,2,3,4,6},{5,7}}
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}=>{{1,2,3,4,6,7},{5}}
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}=>{{1,2,3,4,5,7},{6}}
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}=>{{1,6},{2,5},{3,4},{7}}
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>{{1},{2,6},{3,7},{4,5}}=>{{1,5},{2,6},{3,4},{7}}
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>{{1},{2,5},{3,7},{4,6}}=>{{1,5},{2,4},{3,6},{7}}
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>{{1},{2,6},{3,5},{4,7}}=>{{1,4},{2,6},{3,5},{7}}
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>{{1},{2,5},{3,6},{4,7}}=>{{1,4},{2,5},{3,6},{7}}
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>{{1},{2,4,6},{3,7},{5}}=>{{1,5},{2,4,6},{3},{7}}
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}}=>{{1,4,6},{2,5},{3},{7}}
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>{{1},{2,5,6},{3,4,7}}=>{{1,4,5},{2,3,6},{7}}
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}}=>{{1,4,6},{2,3,5},{7}}
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>{{1},{2,6},{3,5,7},{4}}=>{{1,3,5},{2,6},{4},{7}}
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>{{1},{2,5,7},{3,6},{4}}=>{{1,3,6},{2,5},{4},{7}}
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>{{1},{2,4,5,7},{3,6}}=>{{1,3,4,6},{2,5},{7}}
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>{{1},{2,5,7},{3,4,6}}=>{{1,3,6},{2,4,5},{7}}
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>{{1},{2,4,6},{3,5,7}}=>{{1,3,5},{2,4,6},{7}}
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}=>{{1,5,6},{2,4},{3},{7}}
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>{{1},{2,3,6},{4,7},{5}}=>{{1,4},{2,5,6},{3},{7}}
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>{{1},{2,3,5,6},{4,7}}=>{{1,4},{2,3,5,6},{7}}
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>{{1},{2,3,6},{4,5,7}}=>{{1,3,4},{2,5,6},{7}}
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}}=>{{1,3,5,6},{2,4},{7}}
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}=>{{1,4,6},{2,3},{5},{7}}
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>{{1},{2,4,6},{3},{5,7}}=>{{1,3},{2,4,6},{5},{7}}
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}=>{{1,4,5,6},{2,3},{7}}
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,6},{5,7}}=>{{1,3},{2,4,5,6},{7}}
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}=>{{1,3,6},{2},{4,5},{7}}
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>{{1},{2,4},{3,5,7},{6}}=>{{1,3,5},{2},{4,6},{7}}
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}=>{{1,3,5,6},{2},{4},{7}}
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}=>{{1,3,4,6},{2},{5},{7}}
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}=>{{1,3,4,5,6},{2},{7}}
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}=>{{1,2,6},{3,5},{4},{7}}
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>{{1},{2,5},{3,6,7},{4}}=>{{1,2,5},{3,6},{4},{7}}
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>{{1},{2,4,5},{3,6,7}}=>{{1,2,5},{3,4,6},{7}}
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>{{1},{2,5},{3,4,6,7}}=>{{1,2,4,5},{3,6},{7}}
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>{{1},{2,4,6,7},{3,5}}=>{{1,2,4,6},{3,5},{7}}
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}=>{{1,2,5,6},{3,4},{7}}
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>{{1},{2,3,5},{4,6,7}}=>{{1,2,4},{3,5,6},{7}}
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}=>{{1,2,4,6},{3},{5},{7}}
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}=>{{1,2,4,5,6},{3},{7}}
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}=>{{1,2,3,6},{4,5},{7}}
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>{{1},{2,4},{3,5,6,7}}=>{{1,2,3,5},{4,6},{7}}
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}=>{{1,2,3,5,6},{4},{7}}
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}=>{{1,2,3,4,6},{5},{7}}
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}=>{{1,2,3,4,5,6},{7}}
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}=>{{1,5},{2,4},{3},{6,7}}
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>{{1,2},{3,6},{4,7},{5}}=>{{1,4},{2,5},{3},{6,7}}
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>{{1,2},{3,5,6},{4,7}}=>{{1,4},{2,3,5},{6,7}}
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>{{1,2},{3,6},{4,5,7}}=>{{1,3,4},{2,5},{6,7}}
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>{{1,2},{3,5,7},{4,6}}=>{{1,3,5},{2,4},{6,7}}
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}=>{{1,4,5},{2,3},{6,7}}
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>{{1,2},{3,4,6},{5,7}}=>{{1,3},{2,4,5},{6,7}}
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}=>{{1,3,5},{2},{4},{6,7}}
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}=>{{1,3,4,5},{2},{6,7}}
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}=>{{1,2,5},{3,4},{6,7}}
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>{{1,2},{3,5},{4,6,7}}=>{{1,2,4},{3,5},{6,7}}
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}=>{{1,2,4,5},{3},{6,7}}
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}=>{{1,2,3,5},{4},{6,7}}
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}=>{{1,2,3,4,5},{6,7}}
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}=>{{1,5},{2,4},{3},{6},{7}}
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,6},{4,7},{5}}=>{{1,4},{2,5},{3},{6},{7}}
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,5,6},{4,7}}=>{{1,4},{2,3,5},{6},{7}}
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,6},{4,5,7}}=>{{1,3,4},{2,5},{6},{7}}
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}}=>{{1,3,5},{2,4},{6},{7}}
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}=>{{1,4,5},{2,3},{6},{7}}
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,6},{5,7}}=>{{1,3},{2,4,5},{6},{7}}
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}=>{{1,3,5},{2},{4},{6},{7}}
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}=>{{1,3,4,5},{2},{6},{7}}
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}=>{{1,2,5},{3,4},{6},{7}}
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,5},{4,6,7}}=>{{1,2,4},{3,5},{6},{7}}
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}=>{{1,2,4,5},{3},{6},{7}}
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}=>{{1,2,3,5},{4},{6},{7}}
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}=>{{1,2,3,4,5},{6},{7}}
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}=>{{1,4},{2,3},{5,7},{6}}
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>{{1,3},{2},{4,6},{5,7}}=>{{1,3},{2,4},{5,7},{6}}
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}=>{{1,3,4},{2},{5,7},{6}}
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}=>{{1,2,4},{3},{5,7},{6}}
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}=>{{1,2,3,4},{5,7},{6}}
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}=>{{1,4},{2,3},{5,6,7}}
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>{{1,2,3},{4,6},{5,7}}=>{{1,3},{2,4},{5,6,7}}
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}=>{{1,3,4},{2},{5,6,7}}
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}=>{{1,2,4},{3},{5,6,7}}
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,4},{5,6,7}}
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}=>{{1,4},{2,3},{5,6},{7}}
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,6},{5,7}}=>{{1,3},{2,4},{5,6},{7}}
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}=>{{1,3,4},{2},{5,6},{7}}
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}=>{{1,2,4},{3},{5,6},{7}}
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}=>{{1,2,3,4},{5,6},{7}}
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}=>{{1,4},{2,3},{5},{6,7}}
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>{{1,2},{3},{4,6},{5,7}}=>{{1,3},{2,4},{5},{6,7}}
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}=>{{1,3,4},{2},{5},{6,7}}
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}=>{{1,2,4},{3},{5},{6,7}}
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,3,4},{5},{6,7}}
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}=>{{1,4},{2,3},{5},{6},{7}}
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,6},{5,7}}=>{{1,3},{2,4},{5},{6},{7}}
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}=>{{1,3,4},{2},{5},{6},{7}}
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}=>{{1,2,4},{3},{5},{6},{7}}
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}=>{{1,2,3,4},{5},{6},{7}}
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}=>{{1,3},{2},{4,7},{5,6}}
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}=>{{1,2,3},{4,7},{5,6}}
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>{{1,3},{2,4},{5,7},{6}}=>{{1,3},{2},{4,6},{5,7}}
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>{{1,3},{2,4},{5,6,7}}=>{{1,2,3},{4,6},{5,7}}
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}=>{{1,3},{2},{4,6,7},{5}}
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}=>{{1,2,3},{4,6,7},{5}}
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}=>{{1,3},{2},{4,5,7},{6}}
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}=>{{1,2,3},{4,5,7},{6}}
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}=>{{1,3},{2},{4,5,6,7}}
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3},{4,5,6,7}}
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}=>{{1,3},{2},{4,6},{5},{7}}
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}=>{{1,2,3},{4,6},{5},{7}}
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}=>{{1,3},{2},{4,5,6},{7}}
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}=>{{1,2,3},{4,5,6},{7}}
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}=>{{1,3},{2},{4,5},{6,7}}
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,3},{4,5},{6,7}}
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}=>{{1,3},{2},{4,5},{6},{7}}
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}=>{{1,2,3},{4,5},{6},{7}}
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,7},{6}}
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}=>{{1,2,3},{4},{5,7},{6}}
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,6,7}}
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6,7}}
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5,6},{7}}
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}=>{{1,2,3},{4},{5,6},{7}}
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5},{6,7}}
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,3},{4},{5},{6,7}}
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}=>{{1,3},{2},{4},{5},{6},{7}}
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,2,3},{4},{5},{6},{7}}
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}=>{{1,2},{3,7},{4,6},{5}}
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>{{1,4},{2,5},{3},{6,7}}=>{{1,2},{3,6},{4,7},{5}}
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>{{1,3,4},{2,5},{6,7}}=>{{1,2},{3,6},{4,5,7}}
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>{{1,4},{2,3,5},{6,7}}=>{{1,2},{3,5,6},{4,7}}
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>{{1,3,5},{2,4},{6,7}}=>{{1,2},{3,5,7},{4,6}}
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}=>{{1,2},{3,6,7},{4,5}}
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>{{1,2,4},{3,5},{6,7}}=>{{1,2},{3,5},{4,6,7}}
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}=>{{1,2},{3,5,7},{4},{6}}
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}=>{{1,2},{3,5,6,7},{4}}
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}=>{{1,2},{3,4,7},{5,6}}
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>{{1,3},{2,4,5},{6,7}}=>{{1,2},{3,4,6},{5,7}}
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}=>{{1,2},{3,4,6,7},{5}}
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}=>{{1,2},{3,4,5,7},{6}}
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}=>{{1,2},{3,4,5,6,7}}
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}=>{{1,2},{3,6},{4,5},{7}}
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>{{1},{2,4},{3,5},{6,7}}=>{{1,2},{3,5},{4,6},{7}}
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}=>{{1,2},{3,5,6},{4},{7}}
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}=>{{1,2},{3,4,6},{5},{7}}
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}=>{{1,2},{3,4,5,6},{7}}
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6,7}}
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6,7}}
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}=>{{1,2},{3,5},{4},{6},{7}}
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}=>{{1,2},{3,4,5},{6},{7}}
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}=>{{1,2},{3,4},{5,7},{6}}
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}=>{{1,2},{3,4},{5,6,7}}
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}=>{{1,2},{3,4},{5,6},{7}}
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2},{3,4},{5},{6,7}}
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,2},{3,4},{5},{6},{7}}
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}=>{{1,2},{3},{4,7},{5,6}}
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>{{1,3},{2,4},{5},{6,7}}=>{{1,2},{3},{4,6},{5,7}}
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}=>{{1,2},{3},{4,6,7},{5}}
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}=>{{1,2},{3},{4,5,7},{6}}
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}=>{{1,2},{3},{4,5,6,7}}
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}=>{{1,2},{3},{4,6},{5},{7}}
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}=>{{1,2},{3},{4,5,6},{7}}
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2},{3},{4,5},{6,7}}
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,2},{3},{4,5},{6},{7}}
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,7},{6}}
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,6,7}}
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5,6},{7}}
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6,7}}
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,2},{3},{4},{5},{6},{7}}
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}=>{{1},{2,7},{3,6},{4,5}}
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>{{1,5},{2,6},{3,4},{7}}=>{{1},{2,6},{3,7},{4,5}}
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>{{1,4},{2,6},{3,5},{7}}=>{{1},{2,6},{3,5},{4,7}}
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>{{1,5},{2,4},{3,6},{7}}=>{{1},{2,5},{3,7},{4,6}}
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>{{1,4},{2,5},{3,6},{7}}=>{{1},{2,5},{3,6},{4,7}}
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>{{1,3,5},{2,6},{4},{7}}=>{{1},{2,6},{3,5,7},{4}}
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>{{1,3,6},{2,5},{4},{7}}=>{{1},{2,5,7},{3,6},{4}}
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>{{1,4,5},{2,3,6},{7}}=>{{1},{2,5,6},{3,4,7}}
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>{{1,3,6},{2,4,5},{7}}=>{{1},{2,5,7},{3,4,6}}
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>{{1,5},{2,4,6},{3},{7}}=>{{1},{2,4,6},{3,7},{5}}
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}=>{{1},{2,4,7},{3,6},{5}}
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}}=>{{1},{2,4,5,7},{3,6}}
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}=>{{1},{2,4,7},{3,5,6}}
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>{{1,3,5},{2,4,6},{7}}=>{{1},{2,4,6},{3,5,7}}
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}=>{{1},{2,6,7},{3,5},{4}}
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>{{1,2,5},{3,6},{4},{7}}=>{{1},{2,5},{3,6,7},{4}}
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>{{1,2,4,5},{3,6},{7}}=>{{1},{2,5},{3,4,6,7}}
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>{{1,2,5},{3,4,6},{7}}=>{{1},{2,4,5},{3,6,7}}
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}}=>{{1},{2,4,6,7},{3,5}}
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}=>{{1},{2,5,7},{3,4},{6}}
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>{{1,3,5},{2},{4,6},{7}}=>{{1},{2,4},{3,5,7},{6}}
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}=>{{1},{2,5,6,7},{3,4}}
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>{{1,2,3,5},{4,6},{7}}=>{{1},{2,4},{3,5,6,7}}
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}=>{{1},{2,4,7},{3},{5,6}}
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>{{1,3},{2,4,6},{5},{7}}=>{{1},{2,4,6},{3},{5,7}}
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}=>{{1},{2,4,6,7},{3},{5}}
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}=>{{1},{2,4,5,7},{3},{6}}
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}=>{{1},{2,4,5,6,7},{3}}
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}=>{{1},{2,3,7},{4,6},{5}}
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>{{1,4},{2,5,6},{3},{7}}=>{{1},{2,3,6},{4,7},{5}}
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>{{1,3,4},{2,5,6},{7}}=>{{1},{2,3,6},{4,5,7}}
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>{{1,4},{2,3,5,6},{7}}=>{{1},{2,3,5,6},{4,7}}
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}=>{{1},{2,3,5,7},{4,6}}
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}=>{{1},{2,3,6,7},{4,5}}
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>{{1,2,4},{3,5,6},{7}}=>{{1},{2,3,5},{4,6,7}}
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}=>{{1},{2,3,5,7},{4},{6}}
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}=>{{1},{2,3,5,6,7},{4}}
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}=>{{1},{2,3,4,7},{5,6}}
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>{{1,3},{2,4,5,6},{7}}=>{{1},{2,3,4,6},{5,7}}
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}=>{{1},{2,3,4,6,7},{5}}
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}=>{{1},{2,3,4,5,7},{6}}
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6,7}}
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}=>{{1},{2,6},{3,5},{4},{7}}
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>{{1},{2,5},{3,6},{4},{7}}=>{{1},{2,5},{3,6},{4},{7}}
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>{{1},{2,4,5},{3,6},{7}}=>{{1},{2,5},{3,4,6},{7}}
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>{{1},{2,5},{3,4,6},{7}}=>{{1},{2,4,5},{3,6},{7}}
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>{{1},{2,4,6},{3,5},{7}}=>{{1},{2,4,6},{3,5},{7}}
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}=>{{1},{2,5,6},{3,4},{7}}
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>{{1},{2,3,5},{4,6},{7}}=>{{1},{2,4},{3,5,6},{7}}
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}=>{{1},{2,4,6},{3},{5},{7}}
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}=>{{1},{2,4,5,6},{3},{7}}
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}=>{{1},{2,3,6},{4,5},{7}}
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>{{1},{2,4},{3,5,6},{7}}=>{{1},{2,3,5},{4,6},{7}}
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}=>{{1},{2,3,5,6},{4},{7}}
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}=>{{1},{2,3,4,6},{5},{7}}
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}=>{{1},{2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}=>{{1},{2,5},{3,4},{6,7}}
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>{{1,2},{3,5},{4,6},{7}}=>{{1},{2,4},{3,5},{6,7}}
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}=>{{1},{2,4,5},{3},{6,7}}
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}=>{{1},{2,3,5},{4},{6,7}}
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}=>{{1},{2,3,4,5},{6,7}}
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}=>{{1},{2,5},{3,4},{6},{7}}
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,5},{4,6},{7}}=>{{1},{2,4},{3,5},{6},{7}}
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}=>{{1},{2,4,5},{3},{6},{7}}
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}=>{{1},{2,3,5},{4},{6},{7}}
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}=>{{1},{2,3,4,5},{6},{7}}
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,7},{6}}
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}=>{{1},{2,3,4},{5,7},{6}}
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,6,7}}
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}=>{{1},{2,3,4},{5,6,7}}
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5,6},{7}}
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}=>{{1},{2,3,4},{5,6},{7}}
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5},{6,7}}
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}=>{{1},{2,3,4},{5},{6,7}}
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}=>{{1},{2,4},{3},{5},{6},{7}}
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}=>{{1},{2,3,4},{5},{6},{7}}
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}=>{{1},{2,3},{4,7},{5,6}}
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>{{1,3},{2,4},{5,6},{7}}=>{{1},{2,3},{4,6},{5,7}}
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}=>{{1},{2,3},{4,6,7},{5}}
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}=>{{1},{2,3},{4,5,7},{6}}
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}=>{{1},{2,3},{4,5,6,7}}
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}=>{{1},{2,3},{4,6},{5},{7}}
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}=>{{1},{2,3},{4,5,6},{7}}
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}=>{{1},{2,3},{4,5},{6,7}}
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}=>{{1},{2,3},{4,5},{6},{7}}
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,7},{6}}
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6,7}}
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5,6},{7}}
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5},{6,7}}
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1},{2,3},{4},{5},{6},{7}}
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}=>{{1},{2},{3,7},{4,6},{5}}
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>{{1,4},{2,5},{3},{6},{7}}=>{{1},{2},{3,6},{4,7},{5}}
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>{{1,3,4},{2,5},{6},{7}}=>{{1},{2},{3,6},{4,5,7}}
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>{{1,4},{2,3,5},{6},{7}}=>{{1},{2},{3,5,6},{4,7}}
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}=>{{1},{2},{3,5,7},{4,6}}
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}=>{{1},{2},{3,6,7},{4,5}}
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>{{1,2,4},{3,5},{6},{7}}=>{{1},{2},{3,5},{4,6,7}}
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}=>{{1},{2},{3,5,7},{4},{6}}
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}=>{{1},{2},{3,5,6,7},{4}}
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}=>{{1},{2},{3,4,7},{5,6}}
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>{{1,3},{2,4,5},{6},{7}}=>{{1},{2},{3,4,6},{5,7}}
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}=>{{1},{2},{3,4,6,7},{5}}
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}=>{{1},{2},{3,4,5,7},{6}}
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}=>{{1},{2},{3,4,5,6,7}}
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}=>{{1},{2},{3,6},{4,5},{7}}
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>{{1},{2,4},{3,5},{6},{7}}=>{{1},{2},{3,5},{4,6},{7}}
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}=>{{1},{2},{3,5,6},{4},{7}}
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}=>{{1},{2},{3,4,6},{5},{7}}
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}=>{{1},{2},{3,4,5,6},{7}}
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6,7}}
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6,7}}
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}=>{{1},{2},{3,5},{4},{6},{7}}
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}=>{{1},{2},{3,4,5},{6},{7}}
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,7},{6}}
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,6,7}}
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5,6},{7}}
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5},{6,7}}
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1},{2},{3,4},{5},{6},{7}}
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}=>{{1},{2},{3},{4,7},{5,6}}
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}=>{{1},{2},{3},{4,6},{5,7}}
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}=>{{1},{2},{3},{4,6,7},{5}}
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}=>{{1},{2},{3},{4,5,7},{6}}
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5,6,7}}
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}=>{{1},{2},{3},{4,6},{5},{7}}
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5,6},{7}}
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5},{6,7}}
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1},{2},{3},{4,5},{6},{7}}
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5,7},{6}}
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5,6,7}}
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1},{2},{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}}=>{{1},{2},{3},{4},{5},{6},{7}}
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}=>{{1,8},{2,7},{3,6},{4,5}}
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>{{1,7},{2,8},{3,6},{4,5}}=>{{1,7},{2,8},{3,6},{4,5}}
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>{{1,7},{2,6},{3,8},{4,5}}=>{{1,6},{2,8},{3,7},{4,5}}
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>{{1,6},{2,7},{3,8},{4,5}}=>{{1,6},{2,7},{3,8},{4,5}}
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>{{1,5},{2,8},{3,7},{4,6}}=>{{1,7},{2,6},{3,5},{4,8}}
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>{{1,6},{2,5},{3,8},{4,7}}=>{{1,6},{2,5},{3,8},{4,7}}
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>{{1,7},{2,6},{3,5},{4,8}}=>{{1,5},{2,8},{3,7},{4,6}}
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>{{1,6},{2,5},{3,7},{4,8}}=>{{1,5},{2,6},{3,8},{4,7}}
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,5},{2,6},{3,7},{4,8}}
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>{{1,4,6},{2,8},{3,7},{5}}=>{{1,7},{2,6},{3,5,8},{4}}
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>{{1,7},{2,6},{3,5,8},{4}}=>{{1,4,6},{2,8},{3,7},{5}}
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>{{1,6},{2,5,8},{3,7},{4}}=>{{1,4,7},{2,6},{3,8},{5}}
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>{{1,4,5,8},{2,7},{3,6}}=>{{1,4,5,8},{2,7},{3,6}}
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>{{1,4,7},{2,5,8},{3,6}}=>{{1,4,7},{2,5,8},{3,6}}
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>{{1,3,6},{2,7},{4,8},{5}}=>{{1,5},{2,7},{3,6,8},{4}}
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>{{1,3,8},{2,5,6},{4,7}}=>{{1,6,8},{2,5},{3,4,7}}
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>{{1,3,6},{2,5,7},{4,8}}=>{{1,5},{2,4,7},{3,6,8}}
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>{{1,3,6},{2,5,8},{4,7}}=>{{1,4,7},{2,5},{3,6,8}}
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>{{1,3,8},{2,4,7},{5,6}}=>{{1,6,8},{2,5,7},{3,4}}
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>{{1,3,5,7},{2,4,8},{6}}=>{{1,5,7},{2,4,6,8},{3}}
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>{{1,4,5,8},{2,3,6,7}}=>{{1,4,5,8},{2,3,6,7}}
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>{{1,7},{2,6,8},{3,5},{4}}=>{{1,3,7},{2,8},{4,6},{5}}
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>{{1,5},{2,7},{3,6,8},{4}}=>{{1,3,6},{2,7},{4,8},{5}}
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>{{1,5},{2,4,7},{3,6,8}}=>{{1,3,6},{2,5,7},{4,8}}
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>{{1,4,7},{2,5},{3,6,8}}=>{{1,3,6},{2,5,8},{4,7}}
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>{{1,4,6,8},{2,3,5,7}}=>{{1,3,5,8},{2,4,6,7}}
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>{{1,2,7},{3,8},{4,6},{5}}=>{{1,6},{2,7,8},{3,5},{4}}
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>{{1,2,6},{3,8},{4,7},{5}}=>{{1,6},{2,5},{3,7,8},{4}}
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>{{1,2,5,8},{3,6},{4,7}}=>{{1,4,7,8},{2,5},{3,6}}
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>{{1,2,4,7},{3,8},{5,6}}=>{{1,6},{2,5,7,8},{3,4}}
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>{{1,2,4,8},{3,6},{5,7}}=>{{1,5,7,8},{2,4},{3,6}}
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>{{1,2,7},{3,6,8},{4,5}}=>{{1,3,6},{2,7,8},{4,5}}
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>{{1,2,3,5,8},{4,6,7}}=>{{1,4,6,7,8},{2,3,5}}
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>{{1,2,3,5,7},{4,6,8}}=>{{1,3,5},{2,4,6,7,8}}
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>{{1,4,8},{2,3},{5,7},{6}}=>{{1,5,8},{2,4},{3},{6,7}}
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>{{1,3},{2,4,8},{5,7},{6}}=>{{1,5,7},{2,4},{3},{6,8}}
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}}=>{{1,5,7,8},{2,4},{3},{6}}
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>{{1,3,4,8},{2},{5,7},{6}}=>{{1,5,6,8},{2,4},{3},{7}}
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}=>{{1,5,6,7,8},{2,4},{3}}
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>{{1,5,8},{2,4},{3},{6,7}}=>{{1,4,8},{2,3},{5,7},{6}}
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>{{1,5,7},{2,4},{3},{6,8}}=>{{1,3},{2,4,8},{5,7},{6}}
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>{{1,2,5,8},{3,4},{6,7}}=>{{1,4,7,8},{2,3},{5,6}}
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>{{1,2,5,7},{3,4},{6,8}}=>{{1,3},{2,4,7,8},{5,6}}
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>{{1,2,4},{3,5,7},{6,8}}=>{{1,3},{2,4,6},{5,7,8}}
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>{{1,3},{2,4,5,7},{6,8}}=>{{1,3},{2,4,5,7},{6,8}}
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>{{1,4,5},{2,3,6,8},{7}}=>{{1,3,6,7},{2},{4,5,8}}
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>{{1,3,6,8},{2},{4,5},{7}}=>{{1,3,6,8},{2},{4,5},{7}}
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}=>{{1,3,5,7,8},{2},{4},{6}}
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>{{1,5,6,8},{2,4},{3},{7}}=>{{1,3,4,8},{2},{5,7},{6}}
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>{{1,2,5,6,8},{3,4},{7}}=>{{1,3,4,7,8},{2},{5,6}}
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>{{1,2,4,5,6,8},{3},{7}}=>{{1,3,4,5,7,8},{2},{6}}
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}=>{{1,3,4,5,6,7,8},{2}}
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>{{1,7,8},{2,6},{3,5},{4}}=>{{1,2,8},{3,7},{4,6},{5}}
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>{{1,6},{2,7,8},{3,5},{4}}=>{{1,2,7},{3,8},{4,6},{5}}
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>{{1,6},{2,5},{3,7,8},{4}}=>{{1,2,6},{3,8},{4,7},{5}}
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>{{1,4,7,8},{2,5},{3,6}}=>{{1,2,5,8},{3,6},{4,7}}
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>{{1,6},{2,5,7,8},{3,4}}=>{{1,2,4,7},{3,8},{5,6}}
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>{{1,5,7,8},{2,4},{3,6}}=>{{1,2,4,8},{3,6},{5,7}}
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>{{1,4,5,7,8},{2,3,6}}=>{{1,2,4,5,8},{3,6,7}}
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>{{1,2,5,6},{3,4,7,8}}=>{{1,2,5,6},{3,4,7,8}}
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>{{1,2,5,7,8},{3,4,6}}=>{{1,2,4,7,8},{3,5,6}}
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>{{1,3,6},{2},{4,5,7,8}}=>{{1,2,4,5},{3,6,8},{7}}
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>{{1,4,7,8},{2,3},{5,6}}=>{{1,2,5,8},{3,4},{6,7}}
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>{{1,3},{2,4,6},{5,7,8}}=>{{1,2,4},{3,5,7},{6,8}}
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>{{1,2,4,7,8},{3},{5,6}}=>{{1,2,5,7,8},{3,4},{6}}
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>{{1,3,4,7,8},{2},{5,6}}=>{{1,2,5,6,8},{3,4},{7}}
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}=>{{1,2,5,6,7,8},{3,4}}
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>{{1,5,7,8},{2,4},{3},{6}}=>{{1,2,4,8},{3},{5,7},{6}}
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>{{1,4},{2,3,5,7,8},{6}}=>{{1,2,4,6,7},{3},{5,8}}
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>{{1,2,5,7,8},{3,4},{6}}=>{{1,2,4,7,8},{3},{5,6}}
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}=>{{1,2,4,6,8},{3},{5},{7}}
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}=>{{1,2,4,6,7,8},{3},{5}}
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}=>{{1,2,4,5,6,8},{3},{7}}
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>{{1,2,4,6,7,8},{3},{5}}=>{{1,2,3,5,7,8},{4},{6}}
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}}=>{{1,2,3,4,8},{5,7},{6}}
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>{{1,3,5,6,7,8},{2,4}}=>{{1,2,3,4,6,8},{5,7}}
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}}=>{{1,2,3,4,7,8},{5,6}}
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>{{1,4,5,6,7,8},{2,3}}=>{{1,2,3,4,5,8},{6,7}}
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>{{1,3},{2,4,5,6,7,8}}=>{{1,2,3,4,5,7},{6,8}}
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}=>{{1,2,3,4,5,6,8},{7}}
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}}
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>{{1},{2,8},{3,7},{4,6},{5}}=>{{1,7},{2,6},{3,5},{4},{8}}
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>{{1},{2,7},{3,8},{4,6},{5}}=>{{1,6},{2,7},{3,5},{4},{8}}
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>{{1},{2,6},{3,8},{4,7},{5}}=>{{1,6},{2,5},{3,7},{4},{8}}
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>{{1},{2,7},{3,6},{4,8},{5}}=>{{1,5},{2,7},{3,6},{4},{8}}
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>{{1},{2,6},{3,7},{4,8},{5}}=>{{1,5},{2,6},{3,7},{4},{8}}
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>{{1},{2,5,6},{3,8},{4,7}}=>{{1,6},{2,5},{3,4,7},{8}}
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>{{1},{2,7},{3,6},{4,5,8}}=>{{1,4,5},{2,7},{3,6},{8}}
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>{{1},{2,5,8},{3,6},{4,7}}=>{{1,4,7},{2,5},{3,6},{8}}
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>{{1},{2,4,7},{3,8},{5,6}}=>{{1,6},{2,5,7},{3,4},{8}}
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>{{1},{2,4,8},{3,7},{5,6}}=>{{1,5,7},{2,6},{3,4},{8}}
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>{{1},{2,3,5,8},{4,7},{6}}=>{{1,4,6,7},{2,5},{3},{8}}
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>{{1},{2,3,6,8},{4,5,7}}=>{{1,3,6,7},{2,4,5},{8}}
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,5,7},{4,6,8}}=>{{1,3,5},{2,4,6,7},{8}}
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}}=>{{1,5,7},{2,4},{3},{6},{8}}
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>{{1},{2,4,7},{3},{5,8},{6}}=>{{1,4},{2,5,7},{3},{6},{8}}
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,7},{3},{5,6,8}}=>{{1,3,4},{2,5,7},{6},{8}}
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}}=>{{1,5,6,7},{2,4},{3},{8}}
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,7},{5,6,8}}=>{{1,3,4},{2,5,6,7},{8}}
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,7},{6,8}}=>{{1,3},{2,4,5,6,7},{8}}
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>{{1},{2,6,8},{3,5},{4},{7}}=>{{1,3,7},{2},{4,6},{5},{8}}
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>{{1},{2,5},{3,6,8},{4},{7}}=>{{1,3,6},{2},{4,7},{5},{8}}
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}=>{{1,3,5,7},{2},{4},{6},{8}}
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}=>{{1,3,4,5,6,7},{2},{8}}
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}}=>{{1,2,3,4,7},{5,6},{8}}
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>{{1},{2,4},{3,5,6,7,8}}=>{{1,2,3,4,6},{5,7},{8}}
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}=>{{1,2,3,4,5,7},{6},{8}}
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7},{8}}
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}=>{{1,6},{2,5},{3,4},{7,8}}
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,4},{2,5},{3,6},{7,8}}
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>{{1,2},{3,6,7},{4,5,8}}=>{{1,4,5},{2,3,6},{7,8}}
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>{{1,2},{3,7},{4,6,8},{5}}=>{{1,3,5},{2,6},{4},{7,8}}
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>{{1,2},{3,6,8},{4,7},{5}}=>{{1,3,6},{2,5},{4},{7,8}}
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>{{1,2},{3,6,8},{4,5,7}}=>{{1,3,6},{2,4,5},{7,8}}
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>{{1,2},{3,5,7},{4,6,8}}=>{{1,3,5},{2,4,6},{7,8}}
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}}=>{{1,5,6},{2,4},{3},{7,8}}
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>{{1,2},{3,4,7},{5,8},{6}}=>{{1,4},{2,5,6},{3},{7,8}}
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}}=>{{1,4,5,6},{2,3},{7,8}}
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>{{1,2},{3,4,5,7},{6,8}}=>{{1,3},{2,4,5,6},{7,8}}
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}}=>{{1,3,5,6},{2},{4},{7,8}}
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>{{1,2},{3,6},{4,5,7,8}}=>{{1,2,4,5},{3,6},{7,8}}
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>{{1,2},{3,5,7,8},{4},{6}}=>{{1,2,4,6},{3},{5},{7,8}}
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,3,4,5,6},{7,8}}
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>{{1},{2},{3,6},{4,7},{5,8}}=>{{1,4},{2,5},{3,6},{7},{8}}
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,5,7},{4,6,8}}=>{{1,3,5},{2,4,6},{7},{8}}
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>{{1},{2},{3,4,8},{5,7},{6}}=>{{1,5,6},{2,4},{3},{7},{8}}
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>{{1},{2},{3,4,6,8},{5,7}}=>{{1,3,5,6},{2,4},{7},{8}}
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>{{1},{2},{3,6,7,8},{4,5}}=>{{1,2,3,6},{4,5},{7},{8}}
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,5},{4,6,7,8}}=>{{1,2,3,5},{4,6},{7},{8}}
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}=>{{1,2,3,4,6},{5},{7},{8}}
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,2,3,4,5,6},{7},{8}}
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6,8},{7}}
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>{{1,3},{2},{4,7},{5,8},{6}}=>{{1,4},{2,5},{3},{6,8},{7}}
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>{{1,3},{2},{4,6,7},{5,8}}=>{{1,4},{2,3,5},{6,8},{7}}
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>{{1,3},{2},{4,7},{5,6,8}}=>{{1,3,4},{2,5},{6,8},{7}}
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>{{1,3},{2},{4,6,8},{5,7}}=>{{1,3,5},{2,4},{6,8},{7}}
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}}=>{{1,4,5},{2,3},{6,8},{7}}
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>{{1,3},{2},{4,5,7},{6,8}}=>{{1,3},{2,4,5},{6,8},{7}}
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}}=>{{1,3,5},{2},{4},{6,8},{7}}
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>{{1,3},{2},{4,5,6,8},{7}}=>{{1,3,4,5},{2},{6,8},{7}}
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}}=>{{1,2,5},{3,4},{6,8},{7}}
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>{{1,3},{2},{4,6},{5,7,8}}=>{{1,2,4},{3,5},{6,8},{7}}
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}}=>{{1,2,4,5},{3},{6,8},{7}}
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}}=>{{1,2,3,5},{4},{6,8},{7}}
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}}=>{{1,2,3,4,5},{6,8},{7}}
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6,7,8}}
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6,7},{8}}
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6},{7,8}}
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}}=>{{1,5},{2,4},{3},{6},{7},{8}}
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,7},{5,8},{6}}=>{{1,4},{2,5},{3},{6},{7},{8}}
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,6,7},{5,8}}=>{{1,4},{2,3,5},{6},{7},{8}}
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,7},{5,6,8}}=>{{1,3,4},{2,5},{6},{7},{8}}
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>{{1},{2},{3},{4,6,8},{5,7}}=>{{1,3,5},{2,4},{6},{7},{8}}
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}}=>{{1,4,5},{2,3},{6},{7},{8}}
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,7},{6,8}}=>{{1,3},{2,4,5},{6},{7},{8}}
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}=>{{1,3,5},{2},{4},{6},{7},{8}}
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}=>{{1,3,4,5},{2},{6},{7},{8}}
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}}=>{{1,2,5},{3,4},{6},{7},{8}}
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,6},{5,7,8}}=>{{1,2,4},{3,5},{6},{7},{8}}
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}=>{{1,2,4,5},{3},{6},{7},{8}}
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}=>{{1,2,3,5},{4},{6},{7},{8}}
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,2,3,4,5},{6},{7},{8}}
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}=>{{1,4},{2,3},{5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>{{1,4},{2,3},{5,7},{6,8}}=>{{1,3},{2,4},{5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}}=>{{1,3,4},{2},{5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}=>{{1,2,4},{3},{5,8},{6,7}}
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}=>{{1,2,3,4},{5,8},{6,7}}
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,7},{6,8}}
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,3},{2,4},{5,7},{6,8}}
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>{{1,3},{2,4},{5,6,8},{7}}=>{{1,3,4},{2},{5,7},{6,8}}
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>{{1,3},{2,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,7},{6,8}}
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}=>{{1,2,3,4},{5,7},{6,8}}
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}=>{{1,4},{2,3},{5,7,8},{6}}
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>{{1,2,4},{3},{5,7},{6,8}}=>{{1,3},{2,4},{5,7,8},{6}}
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}=>{{1,3,4},{2},{5,7,8},{6}}
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}=>{{1,2,4},{3},{5,7,8},{6}}
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}=>{{1,2,3,4},{5,7,8},{6}}
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,8},{7}}
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>{{1,3,4},{2},{5,7},{6,8}}=>{{1,3},{2,4},{5,6,8},{7}}
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>{{1,3,4},{2},{5,6,8},{7}}=>{{1,3,4},{2},{5,6,8},{7}}
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}=>{{1,2,4},{3},{5,6,8},{7}}
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}=>{{1,2,3,4},{5,6,8},{7}}
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,7,8}}
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>{{1,2,3,4},{5,7},{6,8}}=>{{1,3},{2,4},{5,6,7,8}}
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}=>{{1,3,4},{2},{5,6,7,8}}
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6,7,8}}
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7,8}}
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}=>{{1,4},{2,3},{5,7},{6},{8}}
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}}=>{{1,2,4},{3},{5,7},{6},{8}}
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}=>{{1,2,3,4},{5,7},{6},{8}}
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6,7},{8}}
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6,7},{8}}
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6,7},{8}}
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6},{7,8}}
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,3},{2,4},{5,6},{7,8}}
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}=>{{1,3,4},{2},{5,6},{7,8}}
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>{{1,2},{3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6},{7,8}}
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6},{7,8}}
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}}=>{{1,4},{2,3},{5,6},{7},{8}}
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}=>{{1,2,4},{3},{5,6},{7},{8}}
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}=>{{1,2,3,4},{5,6},{7},{8}}
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,8},{7}}
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>{{1,3},{2},{4},{5,7},{6,8}}=>{{1,3},{2,4},{5},{6,8},{7}}
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>{{1,3},{2},{4},{5,7,8},{6}}=>{{1,2,4},{3},{5},{6,8},{7}}
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6,8},{7}}
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>{{1,2,3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,7,8}}
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}}=>{{1,2,4},{3},{5},{6,7,8}}
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6,7,8}}
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6,7},{8}}
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>{{1},{2,3},{4},{5,7,8},{6}}=>{{1,2,4},{3},{5},{6,7},{8}}
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6,7},{8}}
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6},{7,8}}
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>{{1,2},{3},{4},{5,7},{6,8}}=>{{1,3},{2,4},{5},{6},{7,8}}
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>{{1,2},{3},{4},{5,7,8},{6}}=>{{1,2,4},{3},{5},{6},{7,8}}
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6},{7,8}}
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}}=>{{1,4},{2,3},{5},{6},{7},{8}}
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,7},{6,8}}=>{{1,3},{2,4},{5},{6},{7},{8}}
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}=>{{1,2,4},{3},{5},{6},{7},{8}}
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,2,3,4},{5},{6},{7},{8}}
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}}=>{{1,3},{2},{4,8},{5,7},{6}}
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>{{1,5},{2,4},{3},{6,7,8}}=>{{1,2,3},{4,8},{5,7},{6}}
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>{{1,4},{2,5},{3},{6,8},{7}}=>{{1,3},{2},{4,7},{5,8},{6}}
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>{{1,3,4},{2,5},{6,8},{7}}=>{{1,3},{2},{4,7},{5,6,8}}
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>{{1,4},{2,3,5},{6,8},{7}}=>{{1,3},{2},{4,6,7},{5,8}}
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}=>{{1,3},{2},{4,6,8},{5,7}}
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}=>{{1,3},{2},{4,7,8},{5,6}}
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>{{1,2,4},{3,5},{6,8},{7}}=>{{1,3},{2},{4,6},{5,7,8}}
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>{{1,3,5},{2},{4},{6,8},{7}}=>{{1,3},{2},{4,6,8},{5},{7}}
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}=>{{1,3},{2},{4,6,7,8},{5}}
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}}=>{{1,3},{2},{4,5,8},{6,7}}
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>{{1,3},{2,4,5},{6,8},{7}}=>{{1,3},{2},{4,5,7},{6,8}}
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}=>{{1,3},{2},{4,5,7,8},{6}}
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>{{1,3,4,5},{2},{6,8},{7}}=>{{1,3},{2},{4,5,6,8},{7}}
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}=>{{1,3},{2},{4,5,6,7,8}}
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}}=>{{1,3},{2},{4},{5,8},{6,7}}
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}}=>{{1,2,3},{4},{5,8},{6,7}}
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}}=>{{1,3},{2},{4},{5,6,8},{7}}
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>{{1,3,4},{2},{5},{6,7,8}}=>{{1,2,3},{4},{5,6,8},{7}}
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}=>{{1,3},{2},{4},{5,6,7,8}}
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}=>{{1,2,3},{4},{5,6,7,8}}
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}}=>{{1,3},{2},{4},{5},{6,8},{7}}
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}=>{{1,2,3},{4},{5},{6,7,8}}
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}=>{{1,3},{2},{4},{5},{6},{7},{8}}
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,2,3},{4},{5},{6},{7},{8}}
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}=>{{1,2},{3,8},{4,7},{5,6}}
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>{{1,5},{2,6},{3,4},{7,8}}=>{{1,2},{3,7},{4,8},{5,6}}
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,2},{3,6},{4,7},{5,8}}
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>{{1,3,5},{2,6},{4},{7,8}}=>{{1,2},{3,7},{4,6,8},{5}}
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>{{1,4,5},{2,3,6},{7,8}}=>{{1,2},{3,6,7},{4,5,8}}
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>{{1,5},{2,4,6},{3},{7,8}}=>{{1,2},{3,5,7},{4,8},{6}}
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>{{1,4,6},{2,5},{3},{7,8}}=>{{1,2},{3,5,8},{4,7},{6}}
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>{{1,4,6},{2,3,5},{7,8}}=>{{1,2},{3,5,8},{4,6,7}}
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}}=>{{1,2},{3,6,7,8},{4,5}}
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}}=>{{1,2},{3,5,7,8},{4},{6}}
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>{{1,5,6},{2,4},{3},{7,8}}=>{{1,2},{3,4,8},{5,7},{6}}
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>{{1,4},{2,5,6},{3},{7,8}}=>{{1,2},{3,4,7},{5,8},{6}}
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>{{1,4},{2,3,5,6},{7,8}}=>{{1,2},{3,4,6,7},{5,8}}
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>{{1,3,5,6},{2},{4},{7,8}}=>{{1,2},{3,4,6,8},{5},{7}}
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>{{1,4,5,6},{2,3},{7,8}}=>{{1,2},{3,4,5,8},{6,7}}
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6,7,8}}
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>{{1},{2,5},{3,6},{4},{7,8}}=>{{1,2},{3,6},{4,7},{5},{8}}
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}}
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,5},{4,6},{7,8}}
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}}=>{{1,2},{3,5,6},{4},{7,8}}
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>{{1,2},{3,5,6},{4},{7,8}}=>{{1,2},{3,4,6},{5},{7,8}}
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2},{3,4,5,6},{7,8}}
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}=>{{1,2},{3,4},{5,8},{6,7}}
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,7},{6,8}}
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}=>{{1,2},{3,4},{5,7,8},{6}}
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}=>{{1,2},{3,4},{5,6,8},{7}}
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6,7,8}}
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}}
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}}=>{{1,2},{3},{4,8},{5,7},{6}}
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}}=>{{1,2},{3},{4},{5,8},{6,7}}
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>{{1,3,4},{2},{5},{6},{7,8}}=>{{1,2},{3},{4},{5,6,8},{7}}
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}}=>{{1,2},{3},{4},{5,6,7,8}}
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}}=>{{1,2},{3},{4},{5},{6},{7,8}}
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,2},{3},{4},{5},{6},{7},{8}}
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}}=>{{1},{2,8},{3,7},{4,6},{5}}
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>{{1,6},{2,7},{3,5},{4},{8}}=>{{1},{2,7},{3,8},{4,6},{5}}
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>{{1,5},{2,7},{3,6},{4},{8}}=>{{1},{2,7},{3,6},{4,8},{5}}
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>{{1,6},{2,5},{3,7},{4},{8}}=>{{1},{2,6},{3,8},{4,7},{5}}
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>{{1,5},{2,6},{3,7},{4},{8}}=>{{1},{2,6},{3,7},{4,8},{5}}
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>{{1,4,5},{2,7},{3,6},{8}}=>{{1},{2,7},{3,6},{4,5,8}}
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>{{1,6},{2,5},{3,4,7},{8}}=>{{1},{2,5,6},{3,8},{4,7}}
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>{{1,4,7},{2,5},{3,6},{8}}=>{{1},{2,5,8},{3,6},{4,7}}
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>{{1,3,7},{2,4,6},{5},{8}}=>{{1},{2,6,8},{3,5,7},{4}}
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>{{1,3,7},{2},{4,6},{5},{8}}=>{{1},{2,6,8},{3,5},{4},{7}}
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>{{1,3,6},{2},{4,7},{5},{8}}=>{{1},{2,5},{3,6,8},{4},{7}}
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{8}}=>{{1},{2,4,8},{3},{5,7},{6}}
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>{{1,4},{2,5,7},{3},{6},{8}}=>{{1},{2,4,7},{3},{5,8},{6}}
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>{{1,3,4},{2,5,7},{6},{8}}=>{{1},{2,4,7},{3},{5,6,8}}
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}=>{{1},{2,4,6,8},{3},{5},{7}}
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}=>{{1},{2,4,5,6,7,8},{3}}
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>{{1,4,6,7},{2,5},{3},{8}}=>{{1},{2,3,5,8},{4,7},{6}}
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}}=>{{1},{2,3,4,8},{5,7},{6}}
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>{{1,3,4},{2,5,6,7},{8}}=>{{1},{2,3,4,7},{5,6,8}}
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}=>{{1},{2,3,4,5,6,8},{7}}
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}=>{{1},{2,3,4,5,6,7,8}}
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,6},{5,7},{8}}=>{{1},{2,4},{3,5,6,7},{8}}
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}=>{{1},{2,4,5,6,7},{3},{8}}
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>{{1,2,3},{4,5,6,7},{8}}=>{{1},{2,3,4,5},{6,7,8}}
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}}=>{{1},{2,4},{3},{5,8},{6,7}}
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}}=>{{1},{2,3,4},{5,8},{6,7}}
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>{{1,3,4},{2},{5,7},{6},{8}}=>{{1},{2,4},{3},{5,6,8},{7}}
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>{{1,3,4},{2},{5,6,7},{8}}=>{{1},{2,3,4},{5,6,8},{7}}
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}}=>{{1},{2,4},{3},{5,6,7,8}}
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}=>{{1},{2,3,4},{5,6,7,8}}
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}=>{{1},{2,4},{3},{5,7},{6},{8}}
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}=>{{1},{2,3,4},{5,6,7},{8}}
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}}=>{{1},{2,4},{3},{5},{6,8},{7}}
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>{{1,5},{2,4},{3},{6,7},{8}}=>{{1},{2,3},{4,8},{5,7},{6}}
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,8},{7}}
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7,8}}
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6,7},{8}}
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1},{2,3},{4,5},{6},{7},{8}}
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}}=>{{1},{2,3},{4},{5,8},{6,7}}
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>{{1,3,4},{2},{5},{6,7},{8}}=>{{1},{2,3},{4},{5,6,8},{7}}
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5,6,7,8}}
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6,7},{8}}
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1},{2,3},{4},{5},{6},{7},{8}}
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}}=>{{1},{2},{3,8},{4,7},{5,6}}
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}=>{{1},{2},{3,5,6,7,8},{4}}
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}}=>{{1},{2},{3,4,8},{5,7},{6}}
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>{{1,4},{2,5,6},{3},{7},{8}}=>{{1},{2},{3,4,7},{5,8},{6}}
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}=>{{1},{2},{3,4,5,6,7,8}}
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}=>{{1},{2},{3,5,6},{4},{7},{8}}
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,8},{6,7}}
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>{{1,3,4},{2},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,6,8},{7}}
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,6,7,8}}
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1},{2},{3,4},{5,6},{7},{8}}
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}}=>{{1},{2},{3},{4,8},{5,7},{6}}
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>{{1,3,5},{2},{4},{6},{7},{8}}=>{{1},{2},{3},{4,6,8},{5},{7}}
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5,6,7,8}}
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6,7},{8}}
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1},{2},{3},{4,5},{6},{7},{8}}
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,8},{6,7}}
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,6,8},{7}}
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5,6,7,8}}
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6,8},{7}}
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1},{2},{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}}=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>{{1,9},{2,8},{3,7},{4,6},{5}}=>{{1,9},{2,8},{3,7},{4,6},{5}}
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>{{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]=>{{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]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>{{1,6},{2,7},{3,8},{4,9},{5,10}}
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8},{9}}
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>{{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]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>{{1,8,9},{2,7},{3,6},{4,5}}=>{{1,2,9},{3,8},{4,7},{5,6}}
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>{{1,8},{2,7},{3,6},{4,5},{9}}=>{{1},{2,9},{3,8},{4,7},{5,6}}
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>{{1,9,10},{2,8},{3,7},{4,6},{5}}=>{{1,2,10},{3,9},{4,8},{5,7},{6}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>{{1,9},{2,8},{3,7},{4,6},{5},{10}}=>{{1},{2,10},{3,9},{4,8},{5,7},{6}}
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}}=>{{1,2,3,4,5,6,7,9},{8}}
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}}=>{{1,2,3,4,5,6,7,8,10},{9}}
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}=>{{1,2,3,4,5,6,7,8,9,10,11}}
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}=>{{1,2,3},{4},{5},{6},{7},{8},{9}}
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}=>{{1,2,3,4},{5},{6},{7},{8},{9}}
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1,2,3,4,5},{6},{7},{8},{9}}
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1,2,3,4,5,6},{7},{8},{9}}
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7},{8},{9}}
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}=>{{1,2,4},{3},{5},{6},{7},{8},{9}}
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>{{1},{2},{3},{4},{5,7,8,9},{6}}=>{{1,2,3,5},{4},{6},{7},{8},{9}}
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>{{1},{2},{3},{4,6,7,8,9},{5}}=>{{1,2,3,4,6},{5},{7},{8},{9}}
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1,2,3,4,5,6},{7},{8},{9},{10}}
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>{{1},{2},{3,5,6,7,8,9},{4}}=>{{1,2,3,4,5,7},{6},{8},{9}}
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7},{8},{9},{10}}
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>{{1},{2,4,5,6,7,8,9},{3}}=>{{1,2,3,4,5,6,8},{7},{9}}
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8},{9},{10}}
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8,9},{10}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>{{1},{2,9},{3,8},{4,7},{5,6}}=>{{1,8},{2,7},{3,6},{4,5},{9}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>{{1},{2,10},{3,9},{4,8},{5,7},{6}}=>{{1,9},{2,8},{3,7},{4,6},{5},{10}}
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11}}=>{{1},{2,11},{3,10},{4,9},{5,8},{6,7}}
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>{{1},{2,11},{3,10},{4,9},{5,8},{6,7}}=>{{1,10},{2,9},{3,8},{4,7},{5,6},{11}}
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>{{1,7},{2,6},{3,5},{4},{8},{9}}=>{{1},{2},{3,9},{4,8},{5,7},{6}}
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>{{1,6},{2,5},{3,4},{7},{8},{9}}=>{{1},{2},{3},{4,9},{5,8},{6,7}}
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>{{1,5},{2,4},{3},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5,9},{6,8},{7}}
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6,9},{7,8}}
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>{{1,8},{2,7},{3,6},{4,5},{9},{10}}=>{{1},{2},{3,10},{4,9},{5,8},{6,7}}
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>{{1,7},{2,6},{3,5},{4},{8},{9},{10}}=>{{1},{2},{3},{4,10},{5,9},{6,8},{7}}
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5,10},{6,9},{7,8}}
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>{{1,5},{2,4},{3},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6,10},{7,9},{8}}
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>{{1,4},{2,3},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7,10},{8,9}}
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}=>{{1},{2,3,4,5,6,7,8,9}}
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1},{2},{3,4,5,6,7,8,9}}
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}=>{{1},{2,3,4,5,6,7,8,9,10}}
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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 $i\leq\pi(i)$.
Map
complement
Description
The complement of a set partition obtained by replacing $i$ with $n+1-i$.
searching the database
Sorry, this map was not found in the database.