Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
Cc0010;cc-rep-0
[.,[.,.]]=>[2,1]=>[1]=>[1]
[[.,.],.]=>[1,2]=>[1]=>[1]
[.,[.,[.,.]]]=>[3,2,1]=>[2,1]=>[2,1]
[.,[[.,.],.]]=>[2,3,1]=>[2,1]=>[2,1]
[[.,.],[.,.]]=>[3,1,2]=>[1,2]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[2,1]=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[1,2]=>[1,2]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[3,2,1]=>[2,3,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,2,1]=>[2,3,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[2,3,1]=>[3,2,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,1]=>[2,3,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,1]=>[3,2,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,2]=>[3,1,2]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,1,2]=>[3,1,2]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,1,3]=>[2,1,3]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,3]=>[1,2,3]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1]=>[2,3,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1]=>[3,2,1]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2]=>[3,1,2]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3]=>[2,1,3]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3]=>[1,2,3]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[3,4,2,1]=>[2,4,3,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,2,1]=>[2,4,3,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[4,2,3,1]=>[3,4,2,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[4,2,3,1]=>[3,4,2,1]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[3,2,4,1]=>[4,3,2,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[2,3,4,1]=>[4,2,3,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,1]=>[2,4,3,1]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[4,2,3,1]=>[3,4,2,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,1]=>[4,3,2,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,1]=>[4,2,3,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,3,1,2]=>[3,1,4,2]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,3,1,2]=>[3,1,4,2]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[3,4,1,2]=>[4,1,3,2]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,3,1,2]=>[3,1,4,2]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,4,1,2]=>[4,1,3,2]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,2,1,3]=>[2,4,1,3]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,2,1,3]=>[2,4,1,3]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[4,1,2,3]=>[4,1,2,3]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[2,3,1,4]=>[3,2,1,4]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1]=>[2,3,4,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1]=>[2,4,3,1]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1]=>[3,4,2,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1]=>[4,3,2,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1]=>[4,2,3,1]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[4,3,1,2]=>[3,1,4,2]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2]=>[4,1,3,2]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[4,2,1,3]=>[2,4,1,3]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3]=>[4,1,2,3]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4]=>[2,3,1,4]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4]=>[3,2,1,4]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4]=>[3,1,2,4]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4]=>[2,1,3,4]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4]=>[1,2,3,4]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[4,5,3,2,1]=>[2,3,5,4,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,3,2,1]=>[2,3,5,4,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[5,3,4,2,1]=>[2,4,5,3,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[5,3,4,2,1]=>[2,4,5,3,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[4,3,5,2,1]=>[2,5,4,3,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[3,4,5,2,1]=>[2,5,3,4,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,2,1]=>[2,3,5,4,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[5,3,4,2,1]=>[2,4,5,3,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,2,1]=>[2,5,4,3,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,2,1]=>[2,5,3,4,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[5,4,2,3,1]=>[3,4,2,5,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[5,4,2,3,1]=>[3,4,2,5,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[4,5,2,3,1]=>[3,5,2,4,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[5,4,2,3,1]=>[3,4,2,5,1]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[4,5,2,3,1]=>[3,5,2,4,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[5,3,2,4,1]=>[4,3,5,2,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[5,3,2,4,1]=>[4,3,5,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[5,2,3,4,1]=>[4,5,2,3,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[5,2,3,4,1]=>[4,5,2,3,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[4,3,2,5,1]=>[5,3,4,2,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[3,4,2,5,1]=>[5,4,3,2,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[4,2,3,5,1]=>[5,4,2,3,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[3,2,4,5,1]=>[5,3,2,4,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[2,3,4,5,1]=>[5,2,3,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,1]=>[2,3,5,4,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[5,3,4,2,1]=>[2,4,5,3,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,1]=>[2,5,4,3,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,1]=>[2,5,3,4,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[5,4,2,3,1]=>[3,4,2,5,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[4,5,2,3,1]=>[3,5,2,4,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[5,3,2,4,1]=>[4,3,5,2,1]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[5,2,3,4,1]=>[4,5,2,3,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,1]=>[5,3,4,2,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,1]=>[5,4,3,2,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[4,2,3,5,1]=>[5,4,2,3,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,1]=>[5,3,2,4,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,1]=>[5,2,3,4,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[4,5,3,1,2]=>[3,1,5,4,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[4,5,3,1,2]=>[3,1,5,4,2]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,3,4,1,2]=>[4,1,5,3,2]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,3,4,1,2]=>[4,1,5,3,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[4,3,5,1,2]=>[5,1,4,3,2]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,4,5,1,2]=>[5,1,3,4,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,4,3,1,2]=>[3,1,4,5,2]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[4,5,3,1,2]=>[3,1,5,4,2]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,3,4,1,2]=>[4,1,5,3,2]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[4,3,5,1,2]=>[5,1,4,3,2]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[3,4,5,1,2]=>[5,1,3,4,2]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[4,5,2,1,3]=>[2,5,1,4,3]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,2,1,3]=>[2,4,1,5,3]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[4,5,2,1,3]=>[2,5,1,4,3]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[5,4,1,2,3]=>[4,1,2,5,3]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[5,4,1,2,3]=>[4,1,2,5,3]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,1,2,3]=>[5,1,2,4,3]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[5,4,1,2,3]=>[4,1,2,5,3]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,1,2,3]=>[5,1,2,4,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,3,2,1,4]=>[2,3,5,1,4]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,3,2,1,4]=>[2,3,5,1,4]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,2,3,1,4]=>[3,5,2,1,4]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,2,3,1,4]=>[3,5,2,1,4]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[5,3,1,2,4]=>[3,1,5,2,4]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[3,4,2,1,5]=>[2,4,3,1,5]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[4,2,3,1,5]=>[3,4,2,1,5]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[3,2,4,1,5]=>[4,3,2,1,5]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[2,3,4,1,5]=>[4,2,3,1,5]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,3,1,2,5]=>[3,1,4,2,5]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,4,1,2,5]=>[4,1,3,2,5]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,2,1,3,5]=>[2,4,1,3,5]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,3,5]=>[4,1,2,3,5]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1]=>[2,3,4,5,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1]=>[2,3,5,4,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,3,4,2,1]=>[2,4,5,3,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1]=>[2,5,4,3,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1]=>[2,5,3,4,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,4,2,3,1]=>[3,4,2,5,1]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[4,5,2,3,1]=>[3,5,2,4,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1]=>[4,3,5,2,1]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1]=>[4,5,2,3,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1]=>[5,3,4,2,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1]=>[5,4,3,2,1]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[4,2,3,5,1]=>[5,4,2,3,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1]=>[5,3,2,4,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1]=>[5,2,3,4,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[5,4,3,1,2]=>[3,1,4,5,2]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2]=>[3,1,5,4,2]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[5,3,4,1,2]=>[4,1,5,3,2]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,3,5,1,2]=>[5,1,4,3,2]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,4,5,1,2]=>[5,1,3,4,2]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[5,4,2,1,3]=>[2,4,1,5,3]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,5,2,1,3]=>[2,5,1,4,3]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[5,4,1,2,3]=>[4,1,2,5,3]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[4,5,1,2,3]=>[5,1,2,4,3]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[5,3,2,1,4]=>[2,3,5,1,4]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[5,2,3,1,4]=>[3,5,2,1,4]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[5,3,1,2,4]=>[3,1,5,2,4]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[5,2,1,3,4]=>[2,5,1,3,4]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4]=>[5,1,2,3,4]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5]=>[2,3,4,1,5]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5]=>[2,4,3,1,5]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5]=>[3,4,2,1,5]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5]=>[4,3,2,1,5]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5]=>[4,2,3,1,5]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,3,1,2,5]=>[3,1,4,2,5]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5]=>[4,1,3,2,5]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,2,1,3,5]=>[2,4,1,3,5]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5]=>[4,1,2,3,5]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5]=>[2,3,1,4,5]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5]=>[3,2,1,4,5]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5]=>[3,1,2,4,5]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5]=>[2,1,3,4,5]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5]=>[1,2,3,4,5]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
searching the database
Sorry, this map was not found in the database.