Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0010;cc-rep-0Cc0009;cc-rep-3
[.,.]=>[1]=>[1]=>{{1}}
[.,[.,.]]=>[2,1]=>[2,1]=>{{1,2}}
[[.,.],.]=>[1,2]=>[1,2]=>{{1},{2}}
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>{{1,3},{2}}
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>{{1,2,3}}
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>{{1,2,3}}
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}}
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>{{1,4},{2,3}}
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>{{1,2,3,4}}
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>{{1,4},{2},{3}}
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>{{1,3,4},{2}}
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>{{1,2,3,4}}
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[3,4,2,1]=>{{1,2,3,4}}
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,1,3]=>{{1,2,3,4}}
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,4,1]=>{{1,3,4},{2}}
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,4,1]=>{{1,2,3,4}}
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}}
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>{{1,2,3},{4}}
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,3,1,4]=>{{1,2,3},{4}}
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}}
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>{{1,2,4,5},{3}}
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}}
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>{{1,2,3,4,5}}
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>{{1,3,5},{2,4}}
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,4,1,3]=>{{1,3,4,5},{2}}
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>{{1,4,5},{2,3}}
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>{{1,2,3,4,5}}
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,3,1,4]=>{{1,4,5},{2},{3}}
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>{{1,3,4,5},{2}}
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>{{1,2,3,4,5}}
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[4,5,3,2,1]=>{{1,2,4,5},{3}}
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,5,4,1,2]=>{{1,3,4},{2,5}}
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,5,2,4,1]=>{{1,2,3,5},{4}}
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,5,2,1,4]=>{{1,2,3,4,5}}
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,1,3,4]=>{{1,2,3,4,5}}
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[4,3,5,2,1]=>{{1,2,3,4,5}}
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,5,1,4]=>{{1,3,4,5},{2}}
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,4,2,5,1]=>{{1,2,3,4,5}}
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[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}}
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>{{1,2,3,4},{5}}
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>{{1,3,4},{2},{5}}
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}}
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}}
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,4,1,3,5]=>{{1,2,3,4},{5}}
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}}
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>{{1,2,3,5,6},{4}}
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}}
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>{{1,2,3,4,5,6}}
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>{{1,4,6},{2},{3,5}}
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>{{1,4,5,6},{2,3}}
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>{{1,4,5,6},{2},{3}}
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>{{1,3,4,5,6},{2}}
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}}
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}}
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>{{1,2,3,4,5,6}}
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>{{1,2,3,4,5,6}}
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>{{1,2,4,5,6},{3}}
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>{{1,2,3,4,5,6}}
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>{{1,2,4,6},{3},{5}}
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>{{1,2,4,5,6},{3}}
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>{{1,3,4},{2,5,6}}
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>{{1,2,3,5,6},{4}}
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>{{1,3,4,5,6},{2}}
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>{{1,2,3,4,5,6}}
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>{{1,3,5,6},{2,4}}
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>{{1,4,5,6},{2,3}}
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>{{1,4,5,6},{2},{3}}
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>{{1,3,4,5,6},{2}}
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>{{1,2,3,5,6},{4}}
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[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}}
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>{{1,3,4,5},{2},{6}}
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>{{1,3,4,5},{2},{6}}
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}}
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}}
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}}
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}}
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}}
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}}
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}}
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>{{1,2,6,7},{3},{4,5}}
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>{{1,7},{2,4,5,6},{3}}
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>{{1,4,5,7},{2,3,6}}
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>{{1,2,4,6,7},{3},{5}}
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>{{1,2,3,4,6,7},{5}}
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}}
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}}
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}}
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}}
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}}
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}}
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}}
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>{{1,5,7},{2,3,6},{4}}
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}}
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}}
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}}
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}}
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}}
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>{{1,3,6,7},{2,4,5}}
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>{{1,4,5,7},{2,3,6}}
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>{{1,2,3,4,6,7},{5}}
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>{{1,5,7},{2,3,6},{4}}
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>{{1,2,3,4,5,6,7}}
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>{{1,5,7},{2,3,4,6}}
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>{{1,3,4,5,6,7},{2}}
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>{{1,2,4,6,7},{3},{5}}
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>{{1,7},{2,4,5,6},{3}}
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>{{1,2,4,5,6,7},{3}}
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>{{1,5,7},{2,3},{4,6}}
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>{{1,2,3,4,6,7},{5}}
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>{{1,5,7},{2},{3},{4,6}}
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>{{1,5,6,7},{2,4},{3}}
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>{{1,5,6,7},{2,3},{4}}
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>{{1,5,6,7},{2},{3},{4}}
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}}
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}}
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}}
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}}
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}}
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>{{1,2,3,5,6,7},{4}}
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}}
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}}
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}}
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}}
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}}
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}}
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>{{1,2,3,5,6,7},{4}}
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>{{1,6,7},{2,3,4,5}}
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>{{1,2,3,4,5,6,7}}
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>{{1,4,6,7},{2},{3,5}}
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}}
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>{{1,4,5,6,7},{2,3}}
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}}
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>{{1,4,5,6,7},{2},{3}}
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}}
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}}
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}}
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}}
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}}
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}}
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>{{1,3,4,5,6,7},{2}}
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}}
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}}
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}}
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}}
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>{{1,3,5,6},{2,7},{4}}
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>{{1,2,5,7},{3,6},{4}}
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>{{1,4,5},{2,3,6,7}}
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>{{1,2,3,4,6,7},{5}}
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>{{1,2,5,7},{3,4,6}}
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>{{1,2,4,7},{3,5,6}}
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>{{1,2,4,5,7},{3,6}}
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>{{1,3,4,6},{2,5,7}}
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>{{1,4,6},{2,7},{3},{5}}
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>{{1,4,6},{2,5,7},{3}}
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>{{1,2,3,5,7},{4,6}}
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>{{1,2,5,6,7},{3,4}}
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>{{1,2,3,5,6,7},{4}}
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>{{1,2,5,7},{3,4},{6}}
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>{{1,2,5,6,7},{3,4}}
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>{{1,3,4,5},{2,6,7}}
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>{{1,2,4,6,7},{3,5}}
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>{{1,2,4,6,7},{3},{5}}
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>{{1,2,4,5,6,7},{3}}
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>{{1,3,4},{2,5,6,7}}
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>{{1,2,3,5,6,7},{4}}
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>{{1,2,4,5,6},{3,7}}
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>{{1,4,5},{2,3,6,7}}
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>{{1,2,3,4,6,7},{5}}
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>{{1,3,4,5,6,7},{2}}
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}}
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>{{1,4,6},{2,3,5,7}}
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>{{1,3,4,6,7},{2,5}}
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>{{1,4,6},{2,5},{3,7}}
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>{{1,3,5,7},{2,4,6}}
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>{{1,3,4,7},{2,5,6}}
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>{{1,3,5,6,7},{2,4}}
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>{{1,3,7},{2,4},{5},{6}}
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>{{1,3,4,6,7},{2,5}}
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>{{1,2,3,4,5,6,7}}
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>{{1,3,6,7},{2,4},{5}}
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>{{1,3,5,6,7},{2,4}}
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>{{1,5,6},{2,4,7},{3}}
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>{{1,2,4,5,6,7},{3}}
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>{{1,4,5,6,7},{2,3}}
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}}
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>{{1,5,6},{2,3,4,7}}
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>{{1,4,5,6,7},{2},{3}}
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}}
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>{{1,4,7},{2,5},{3},{6}}
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>{{1,4,6,7},{2,5},{3}}
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>{{1,4,7},{2,3,5},{6}}
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>{{1,4,6,7},{2,3,5}}
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>{{1,3,4,5,6,7},{2}}
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}}
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}}
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}}
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>{{1,5,6,7},{2,4},{3}}
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}}
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>{{1,5,6,7},{2,3,4}}
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>{{1,5,6,7},{2,3,4}}
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}}
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>{{1,5,6,7},{2,3},{4}}
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>{{1,5,6,7},{2},{3},{4}}
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>{{1,4,5,7},{2,6},{3}}
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>{{1,2,3,5,6,7},{4}}
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}}
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>{{1,3,5,6,7},{2,4}}
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>{{1,4,5,6,7},{2,3}}
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>{{1,4,5,6,7},{2},{3}}
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}}
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>{{1,3,4,5,6,7},{2}}
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}}
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}}
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}}
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>{{1,2,4,6,7},{3,5}}
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>{{1,2,4,5,6,7},{3}}
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>{{1,2,3,4,6,7},{5}}
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}}
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}}
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}}
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}}
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}}
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[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}}
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}}
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}}
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}}
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}}
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>{{1,4,6},{2},{3,5},{7}}
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>{{1,4,5,6},{2,3},{7}}
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>{{1,4,5,6},{2},{3},{7}}
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}}
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}}
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>{{1,3,4,5,6},{2},{7}}
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}}
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}}
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}}
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}}
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}}
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>{{1,3,4},{2,5,6},{7}}
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>{{1,4,5},{2,3,6},{7}}
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>{{1,3,6},{2,4},{5},{7}}
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>{{1,3,5,6},{2,4},{7}}
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>{{1,4,5,6},{2,3},{7}}
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>{{1,4,5,6},{2},{3},{7}}
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>{{1,3,4,5,6},{2},{7}}
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}}
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
searching the database
Sorry, this map was not found in the database.