Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0002;cc-rep-3
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[2]
[[.,.],.]=>[1,2]=>[1,2]=>[1,1]
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>[2,1]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[3]
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[2,1]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>[2,1,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>[3,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,3,1,2]=>[3,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[4]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[3,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,4,1,3]=>[2,1,1]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,4,3,1]=>[3,1]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>[2,2]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[2,1,1]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>[2,1,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[3,1]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[2,1,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,1]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[2,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[3,1,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,1,4,2,3]=>[3,1,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[4,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,1,2,4]=>[3,1,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,1,4,2]=>[3,2]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,4,2,1,3]=>[4,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,3,4,1,2]=>[3,1,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[5]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,3,4,2,1]=>[4,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[4,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[3,1,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>[2,1,1,1]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,5,1,4,3]=>[3,1,1]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>[3,1,1]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>[4,1]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[3,1,1]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>[2,2,1]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,5,4,2]=>[3,2]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>[2,1,1,1]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[3,1,1]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>[2,2,1]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,3,1,5,2]=>[3,2]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>[2,2,1]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>[2,2,1]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[2,1,1,1]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[2,1,1,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[3,1,1]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,3,1,2,5]=>[3,1,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[4,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[3,1,1]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[2,4,1,3,5]=>[2,1,1,1]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[3,1,1]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[2,2,1]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[2,1,1,1]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[2,1,1,1]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[3,1,1]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[2,1,1,1]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,1,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[2,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[3,1,1,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,1,2,5,3,4]=>[3,1,1,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[4,1,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[3,1,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,1,4,2,3,5]=>[3,1,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,1,4,2,5,3]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,1,5,3,2,4]=>[4,1,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,1,4,5,2,3]=>[3,1,1,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[4,1,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[5,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,1,4,5,3,2]=>[4,1,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[4,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,3,1,2,4,5]=>[3,1,1,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,3,1,2,5,4]=>[3,2,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>[3,2,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,3,1,5,4,2]=>[4,2]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,3,1,4,5,2]=>[3,2,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,2,1,3,5]=>[4,1,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,2,1,5,3]=>[4,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,1,2,5]=>[3,1,1,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,1,5,2]=>[3,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,5,2,3,1,4]=>[4,1,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,5,4,2,1,3]=>[5,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,5,2,1,4]=>[4,1,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,4,2,5,1,3]=>[4,1,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,3,4,5,1,2]=>[3,1,1,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[4,1,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[5,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,5,4,2,3,1]=>[5,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[6]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[5,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,5,2,4,1]=>[4,1,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,5,4,2,1]=>[5,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,4,2,5,3,1]=>[4,2]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,3,4,5,2,1]=>[4,1,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[4,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[5,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,3,4,2,5,1]=>[4,1,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[4,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[3,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>[2,1,1,1,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>[3,1,1,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,6,1,5,3,4]=>[3,1,1,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,6,1,5,4,3]=>[4,1,1]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,6,1,4,5,3]=>[3,1,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>[3,1,1,1]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>[3,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>[4,1,1]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,6,4,5,1,3]=>[3,1,1,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>[4,1,1]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,6,5,4,3,1]=>[5,1]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,6,4,5,3,1]=>[4,1,1]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,6,4,3,5,1]=>[4,1,1]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[3,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>[2,2,1,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,6,2,5,4]=>[3,2,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,6,5,2,4]=>[3,2,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>[4,2]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,6,4,5,2]=>[3,2,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>[2,1,1,1,1]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,3,6,1,5,4]=>[3,1,1,1]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>[3,1,1,1]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>[4,1,1]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[3,1,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>[2,2,1,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,6,5,3]=>[3,2,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,3,1,6,2,5]=>[3,2,1]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,3,1,6,5,2]=>[3,3]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>[2,2,1,1]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,4,1,6,5,3]=>[3,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>[2,2,1,1]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,1,4,6,5,2]=>[3,2,1]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>[2,1,1,1,1]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[3,1,1,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>[2,2,1,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,4,2,6,3]=>[3,2,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,1,2,6,4]=>[3,2,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,4,2,1,6,3]=>[4,2]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,3,4,1,6,2]=>[3,2,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>[2,2,1,1]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>[3,2,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>[2,2,1,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>[2,2,1,1]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,3,1,5,6,2]=>[3,2,1]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>[2,2,1,1]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>[2,2,1,1]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[2,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[2,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>[3,1,1,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,1,4,2,3,6]=>[3,1,1,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>[4,1,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>[3,1,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,1,2,4,6]=>[3,1,1,1]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,1,4,2,6]=>[3,2,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,4,2,1,3,6]=>[4,1,1]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,3,4,1,2,6]=>[3,1,1,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>[4,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[5,1]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,3,4,2,1,6]=>[4,1,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[4,1,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[3,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>[2,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,5,1,4,3,6]=>[3,1,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>[3,1,1,1]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>[4,1,1]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[3,1,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>[2,2,1,1]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,1,5,4,2,6]=>[3,2,1]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>[2,1,1,1,1]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[3,1,1,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>[2,2,1,1]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,3,1,5,2,6]=>[3,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>[2,2,1,1]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>[2,2,1,1]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[2,1,1,1,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[2,1,1,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[3,1,1,1]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,3,1,2,5,6]=>[3,1,1,1]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[4,1,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[3,1,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>[2,1,1,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[3,1,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[2,2,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[2,1,1,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[2,1,1,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[3,1,1,1]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[2,1,1,1,1]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,1,1,1]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[2,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>[3,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,1,2,3,6,4,5]=>[3,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>[4,1,1,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>[3,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,1,2,5,3,4,6]=>[3,1,1,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,1,2,5,3,6,4]=>[3,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,1,2,6,4,3,5]=>[4,1,1,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,1,2,5,6,3,4]=>[3,1,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>[4,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>[5,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,1,2,5,6,4,3]=>[4,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>[4,1,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>[3,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,1,4,2,3,5,6]=>[3,1,1,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,1,4,2,3,6,5]=>[3,2,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,1,4,2,6,3,5]=>[3,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,1,4,2,6,5,3]=>[4,2,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,1,4,2,5,6,3]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,1,5,3,2,4,6]=>[4,1,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,1,5,3,2,6,4]=>[4,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,1,4,5,2,3,6]=>[3,1,1,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,1,4,5,2,6,3]=>[3,2,1,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,1,6,3,4,2,5]=>[4,1,1,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,1,6,5,3,2,4]=>[5,1,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,1,4,6,3,2,5]=>[4,1,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,1,5,3,6,2,4]=>[4,1,1,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,1,4,5,6,2,3]=>[3,1,1,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>[4,1,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>[5,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,1,6,5,3,4,2]=>[5,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>[6,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>[5,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,1,4,6,3,5,2]=>[4,1,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,1,4,6,5,3,2]=>[5,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,1,5,3,6,4,2]=>[4,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,1,4,5,6,3,2]=>[4,1,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>[4,1,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>[5,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,1,4,5,3,6,2]=>[4,1,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,3,1,2,4,5,6]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,3,1,2,4,6,5]=>[3,2,1,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,3,1,2,6,4,5]=>[3,2,1,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,3,1,2,6,5,4]=>[4,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,3,1,2,5,6,4]=>[3,2,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,3,1,5,2,4,6]=>[3,2,1,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,3,1,5,2,6,4]=>[3,2,2]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,3,1,6,4,2,5]=>[4,2,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,3,1,5,6,2,4]=>[3,2,1,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,3,1,6,4,5,2]=>[4,2,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,3,1,6,5,4,2]=>[5,2]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,3,1,5,6,4,2]=>[4,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,3,1,5,4,6,2]=>[4,2,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,3,1,4,5,6,2]=>[3,2,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,4,2,1,3,5,6]=>[4,1,1,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,4,2,1,3,6,5]=>[4,2,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,4,2,1,6,3,5]=>[4,2,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,4,2,1,6,5,3]=>[4,3]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,4,2,1,5,6,3]=>[4,2,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,3,4,1,2,5,6]=>[3,1,1,1,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,3,4,1,2,6,5]=>[3,2,1,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,3,4,1,6,2,5]=>[3,2,1,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,3,4,1,6,5,2]=>[4,2,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,3,4,1,5,6,2]=>[3,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,2,3,1,4,6]=>[4,1,1,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,2,3,1,6,4]=>[4,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,4,2,1,3,6]=>[5,1,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,4,2,1,6,3]=>[5,2]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,3,5,2,1,4,6]=>[4,1,1,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,3,5,2,1,6,4]=>[4,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,2,5,1,3,6]=>[4,1,1,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,2,5,1,6,3]=>[4,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,1,2,6]=>[3,1,1,1,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,1,6,2]=>[3,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,6,2,3,4,1,5]=>[4,1,1,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,6,2,5,3,1,4]=>[5,1,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,6,4,2,3,1,5]=>[5,1,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,6,5,3,2,1,4]=>[6,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,6,4,5,2,1,3]=>[5,1,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,3,6,2,4,1,5]=>[4,1,1,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,3,6,5,2,1,4]=>[5,1,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,2,6,3,1,5]=>[4,2,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,6,2,1,5]=>[4,1,1,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,5,2,3,6,1,4]=>[4,1,1,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,5,4,2,6,1,3]=>[5,1,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,5,2,6,1,4]=>[4,1,1,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,4,2,5,6,1,3]=>[4,1,1,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,3,4,5,6,1,2]=>[3,1,1,1,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>[4,1,1,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>[5,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,6,2,5,3,4,1]=>[5,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>[6,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>[5,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,6,4,2,3,5,1]=>[5,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,6,4,2,5,3,1]=>[5,2]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,6,5,3,2,4,1]=>[6,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,6,4,5,2,3,1]=>[5,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>[6,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[7]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,4,5,3,2,1]=>[6,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[6,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[5,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,3,6,2,4,5,1]=>[4,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,3,6,2,5,4,1]=>[5,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,3,6,5,2,4,1]=>[5,1,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,3,6,5,4,2,1]=>[6,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,3,6,4,5,2,1]=>[5,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,2,6,3,5,1]=>[4,2,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,2,6,5,3,1]=>[5,2]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,6,2,5,1]=>[4,1,1,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,6,5,2,1]=>[5,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,5,2,3,6,4,1]=>[4,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,5,4,2,6,3,1]=>[5,2]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,5,2,6,4,1]=>[4,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,4,2,5,6,3,1]=>[4,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,3,4,5,6,2,1]=>[4,1,1,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>[4,1,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>[5,1,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,5,4,2,3,6,1]=>[5,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[6,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[5,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,5,2,4,6,1]=>[4,1,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,5,4,2,6,1]=>[5,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,4,2,5,3,6,1]=>[4,2,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,3,4,5,2,6,1]=>[4,1,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,1,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[5,1,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,3,4,2,5,6,1]=>[4,1,1,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[4,1,1,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[3,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,7,1,3,4,6,5]=>[3,1,1,1,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,7,1,3,6,4,5]=>[3,1,1,1,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,7,1,3,6,5,4]=>[4,1,1,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,7,1,3,5,6,4]=>[3,1,1,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,7,1,5,3,4,6]=>[3,1,1,1,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,7,1,5,3,6,4]=>[3,2,1,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,7,1,6,4,3,5]=>[4,1,1,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,7,1,5,6,3,4]=>[3,1,1,1,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,7,1,6,4,5,3]=>[4,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,7,1,6,5,4,3]=>[5,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,7,1,5,6,4,3]=>[4,1,1,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,7,1,5,4,6,3]=>[4,1,1,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,7,1,4,5,6,3]=>[3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>[3,1,1,1,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,7,4,1,3,6,5]=>[3,2,1,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>[3,2,1,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>[4,2,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,7,4,1,5,6,3]=>[3,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>[4,1,1,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,7,5,3,1,6,4]=>[4,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,7,4,5,1,3,6]=>[3,1,1,1,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,7,4,5,1,6,3]=>[3,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>[4,1,1,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,7,6,5,3,1,4]=>[5,1,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,7,4,6,3,1,5]=>[4,1,1,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,7,5,3,6,1,4]=>[4,1,1,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,7,4,5,6,1,3]=>[3,1,1,1,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>[4,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,7,6,3,5,4,1]=>[5,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,7,6,5,3,4,1]=>[5,1,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,7,6,5,4,3,1]=>[6,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,7,6,4,5,3,1]=>[5,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,7,4,6,3,5,1]=>[4,1,1,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,7,4,6,5,3,1]=>[5,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,7,5,3,6,4,1]=>[4,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,7,4,5,6,3,1]=>[4,1,1,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,7,5,3,4,6,1]=>[4,1,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,7,5,4,3,6,1]=>[5,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,7,4,5,3,6,1]=>[4,1,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,7,4,3,5,6,1]=>[4,1,1,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>[2,2,1,1,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,7,2,4,6,5]=>[3,2,1,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,7,2,6,4,5]=>[3,2,1,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,7,2,6,5,4]=>[4,2,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,7,2,5,6,4]=>[3,2,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,7,5,2,4,6]=>[3,2,1,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,7,5,2,6,4]=>[3,2,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,7,6,4,2,5]=>[4,2,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,7,5,6,2,4]=>[3,2,1,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,7,6,4,5,2]=>[4,2,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,7,6,5,4,2]=>[5,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,7,5,6,4,2]=>[4,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,7,5,4,6,2]=>[4,2,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,7,4,5,6,2]=>[3,2,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>[2,1,1,1,1,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,3,7,1,4,6,5]=>[3,1,1,1,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[2,3,7,1,6,4,5]=>[3,1,1,1,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[2,3,7,1,6,5,4]=>[4,1,1,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[2,3,7,1,5,6,4]=>[3,1,1,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>[3,1,1,1,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>[3,2,1,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>[4,1,1,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>[3,1,1,1,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>[4,1,1,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,3,7,6,5,4,1]=>[5,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>[4,1,1,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>[4,1,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[3,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>[2,2,1,1,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,7,3,6,5]=>[3,2,1,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,7,6,3,5]=>[3,2,1,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,7,6,5,3]=>[4,2,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,7,5,6,3]=>[3,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,3,1,7,2,5,6]=>[3,2,1,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,3,1,7,2,6,5]=>[3,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,3,1,7,6,2,5]=>[3,3,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,3,1,7,6,5,2]=>[4,3]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,3,1,7,5,6,2]=>[3,3,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>[2,2,1,1,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,4,1,7,3,6,5]=>[3,2,1,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[2,4,1,7,6,3,5]=>[3,2,1,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[2,4,1,7,6,5,3]=>[4,2,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[2,4,1,7,5,6,3]=>[3,2,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>[2,2,1,1,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[3,1,4,7,2,6,5]=>[3,2,1,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[3,1,4,7,6,2,5]=>[3,2,1,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[3,1,4,7,6,5,2]=>[4,2,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,4,7,5,6,2]=>[3,2,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>[2,1,1,1,1,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,3,4,7,1,6,5]=>[3,1,1,1,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>[3,1,1,1,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[3,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>[2,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,7,6,4]=>[3,2,1,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,4,2,7,3,6]=>[3,2,1,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,4,2,7,6,3]=>[3,3,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,3,1,2,7,4,6]=>[3,2,1,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,3,1,2,7,6,4]=>[3,3,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,4,2,1,7,3,6]=>[4,2,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,4,2,1,7,6,3]=>[4,3]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,3,4,1,7,2,6]=>[3,2,1,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,3,4,1,7,6,2]=>[3,3,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>[2,2,1,1,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,5,1,3,7,6,4]=>[3,2,1,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>[3,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>[3,3,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>[2,2,2,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[3,1,5,2,7,6,4]=>[3,2,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>[2,2,1,1,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,3,5,1,7,6,4]=>[3,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>[2,2,1,1,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[4,1,2,5,7,6,3]=>[3,2,1,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,3,1,5,7,2,6]=>[3,2,1,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[4,3,1,5,7,6,2]=>[3,3,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>[2,2,1,1,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,4,1,5,7,6,3]=>[3,2,1,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>[2,2,1,1,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[3,1,4,5,7,6,2]=>[3,2,1,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>[2,1,1,1,1,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[3,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>[2,2,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,5,3,7,4]=>[3,2,1,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,4,2,3,7,5]=>[3,2,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,5,3,2,7,4]=>[4,2,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,4,5,2,7,3]=>[3,2,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,3,1,2,4,7,5]=>[3,2,1,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,3,1,5,2,7,4]=>[3,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,2,1,3,7,5]=>[4,2,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,1,2,7,5]=>[3,2,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,5,2,3,1,7,4]=>[4,2,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,5,4,2,1,7,3]=>[5,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,5,2,1,7,4]=>[4,2,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,4,2,5,1,7,3]=>[4,2,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,3,4,5,1,7,2]=>[3,2,1,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>[2,2,1,1,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[2,6,1,5,3,7,4]=>[3,2,1,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>[3,2,1,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>[4,2,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[2,6,4,5,1,7,3]=>[3,2,1,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>[2,2,2,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[3,1,6,5,2,7,4]=>[3,2,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>[2,2,1,1,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>[3,2,1,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>[2,2,2,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[4,3,1,6,2,7,5]=>[3,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>[2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>[2,2,2,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>[2,2,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>[2,2,1,1,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,1,4,2,6,7,3]=>[3,2,1,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,1,2,6,7,4]=>[3,2,1,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,4,2,1,6,7,3]=>[4,2,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,3,4,1,6,7,2]=>[3,2,1,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>[2,2,1,1,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>[3,2,1,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>[2,2,2,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>[2,2,1,1,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>[2,2,1,1,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,3,1,5,6,7,2]=>[3,2,1,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>[2,2,1,1,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>[2,2,1,1,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>[3,1,1,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,1,2,5,3,4,7]=>[3,1,1,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>[4,1,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>[3,1,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,1,4,2,3,5,7]=>[3,1,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,1,4,2,5,3,7]=>[3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,1,5,3,2,4,7]=>[4,1,1,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,1,4,5,2,3,7]=>[3,1,1,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>[4,1,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>[5,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,1,4,5,3,2,7]=>[4,1,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>[4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>[3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,3,1,2,4,5,7]=>[3,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,3,1,2,5,4,7]=>[3,2,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,3,1,5,2,4,7]=>[3,2,1,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,3,1,5,4,2,7]=>[4,2,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,3,1,4,5,2,7]=>[3,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,2,1,3,5,7]=>[4,1,1,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,2,1,5,3,7]=>[4,2,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,1,2,5,7]=>[3,1,1,1,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,1,5,2,7]=>[3,2,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,5,2,3,1,4,7]=>[4,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,5,4,2,1,3,7]=>[5,1,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,5,2,1,4,7]=>[4,1,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,4,2,5,1,3,7]=>[4,1,1,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,3,4,5,1,2,7]=>[3,1,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>[4,1,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>[5,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,5,4,2,3,1,7]=>[5,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[6,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[5,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,5,2,4,1,7]=>[4,1,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,5,4,2,1,7]=>[5,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,4,2,5,3,1,7]=>[4,2,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,3,4,5,2,1,7]=>[4,1,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[5,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,3,4,2,5,1,7]=>[4,1,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[4,1,1,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[3,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>[2,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,6,1,3,5,4,7]=>[3,1,1,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[2,6,1,5,3,4,7]=>[3,1,1,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[2,6,1,5,4,3,7]=>[4,1,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[2,6,1,4,5,3,7]=>[3,1,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>[3,1,1,1,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>[3,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>[4,1,1,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[2,6,4,5,1,3,7]=>[3,1,1,1,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>[4,1,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,6,5,4,3,1,7]=>[5,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[2,6,4,5,3,1,7]=>[4,1,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[2,6,4,3,5,1,7]=>[4,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[3,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>[2,2,1,1,1]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,1,6,2,5,4,7]=>[3,2,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[3,1,6,5,2,4,7]=>[3,2,1,1]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,1,6,5,4,2,7]=>[4,2,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,6,4,5,2,7]=>[3,2,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>[2,1,1,1,1,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,3,6,1,5,4,7]=>[3,1,1,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>[3,1,1,1,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>[4,1,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[3,1,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>[2,2,1,1,1]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[4,1,2,6,5,3,7]=>[3,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[4,3,1,6,2,5,7]=>[3,2,1,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[4,3,1,6,5,2,7]=>[3,3,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>[2,2,1,1,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,4,1,6,5,3,7]=>[3,2,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>[2,2,1,1,1]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,1,4,6,5,2,7]=>[3,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>[2,1,1,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[3,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>[2,2,1,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,1,4,2,6,3,7]=>[3,2,1,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,1,2,6,4,7]=>[3,2,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,4,2,1,6,3,7]=>[4,2,1]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,3,4,1,6,2,7]=>[3,2,1,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>[2,2,1,1,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>[3,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>[2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>[2,2,1,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>[2,2,1,1,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,3,1,5,6,2,7]=>[3,2,1,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>[2,2,1,1,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>[2,2,1,1,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[2,1,1,1,1,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[2,1,1,1,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>[3,1,1,1,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,1,4,2,3,6,7]=>[3,1,1,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>[4,1,1,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>[3,1,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,1,2,4,6,7]=>[3,1,1,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,1,4,2,6,7]=>[3,2,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,4,2,1,3,6,7]=>[4,1,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,3,4,1,2,6,7]=>[3,1,1,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,1,1,1]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[5,1,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,3,4,2,1,6,7]=>[4,1,1,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[4,1,1,1]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[3,1,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>[2,1,1,1,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,5,1,4,3,6,7]=>[3,1,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>[3,1,1,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>[4,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[3,1,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>[2,2,1,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[3,1,5,4,2,6,7]=>[3,2,1,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>[2,1,1,1,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[3,1,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>[2,2,1,1,1]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,3,1,5,2,6,7]=>[3,2,1,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>[2,2,1,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>[2,2,1,1,1]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[2,1,1,1,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[2,1,1,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[3,1,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,1,1,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,1,1,1]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[3,1,1,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>[2,1,1,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[3,1,1,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[2,2,1,1,1]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[2,1,1,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[2,1,1,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,1,1,1,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[2,1,1,1,1,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,1,2,3,4,7,6,5]=>[4,1,1,1,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,1,2,3,4,6,7,5]=>[3,1,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,1,2,3,7,5,4,6]=>[4,1,1,1,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,1,2,3,7,5,6,4]=>[4,1,1,1,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,1,2,3,7,6,5,4]=>[5,1,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,1,2,3,6,7,5,4]=>[4,1,1,1,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,1,2,3,6,5,7,4]=>[4,1,1,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,1,2,3,5,6,7,4]=>[3,1,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,1,2,5,3,4,6,7]=>[3,1,1,1,1,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,1,2,5,3,7,6,4]=>[4,2,1,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,1,2,5,3,6,7,4]=>[3,2,1,1,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[8,1,2,5,6,3,7,4]=>[3,2,1,1,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,1,2,5,6,7,3,4]=>[3,1,1,1,1,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,1,2,7,4,5,6,3]=>[4,1,1,1,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,1,2,7,4,6,5,3]=>[5,1,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,1,2,7,6,4,5,3]=>[5,1,1,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,1,2,7,6,5,4,3]=>[6,1,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,1,2,5,6,7,4,3]=>[4,1,1,1,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,1,2,6,4,5,7,3]=>[4,1,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,1,2,4,5,6,7,3]=>[3,1,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,1,4,2,3,5,6,7]=>[3,1,1,1,1,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,1,4,2,3,5,7,6]=>[3,2,1,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,1,4,2,3,7,6,5]=>[4,2,1,1]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[8,1,4,2,3,6,7,5]=>[3,2,1,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,1,4,2,6,3,5,7]=>[3,2,1,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,1,4,2,6,3,7,5]=>[3,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[8,1,4,2,7,5,3,6]=>[4,2,1,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,1,4,2,6,7,3,5]=>[3,2,1,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,1,4,2,7,5,6,3]=>[4,2,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[8,1,4,2,6,7,5,3]=>[4,2,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,1,4,2,5,6,7,3]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,1,5,3,2,4,7,6]=>[4,2,1,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,1,5,3,2,6,7,4]=>[4,2,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,1,4,5,2,3,6,7]=>[3,1,1,1,1,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,1,4,5,2,6,7,3]=>[3,2,1,1,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[8,1,6,3,4,2,7,5]=>[4,2,1,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,1,5,3,6,2,4,7]=>[4,1,1,1,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[8,1,5,3,6,2,7,4]=>[4,2,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[8,1,7,3,4,5,2,6]=>[4,1,1,1,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,1,7,6,4,3,2,5]=>[6,1,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[8,1,6,3,4,7,2,5]=>[4,1,1,1,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,1,7,3,4,5,6,2]=>[4,1,1,1,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[8,1,7,3,6,4,5,2]=>[5,1,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,1,7,6,4,3,5,2]=>[6,1,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,1,7,6,4,5,3,2]=>[6,1,1]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[8,1,7,6,5,4,3,2]=>[7,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[8,1,7,5,6,4,3,2]=>[6,1,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[8,1,4,7,3,6,5,2]=>[5,1,1,1]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[8,1,5,4,3,6,7,2]=>[5,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,3,1,2,4,5,6,7]=>[3,1,1,1,1,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[8,3,1,2,6,4,7,5]=>[3,2,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,3,1,2,5,6,7,4]=>[3,2,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,3,1,5,2,4,6,7]=>[3,2,1,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,3,1,5,2,7,4,6]=>[3,2,2,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,3,1,5,2,7,6,4]=>[4,2,2]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,3,1,5,2,6,7,4]=>[3,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[8,3,1,6,4,2,5,7]=>[4,2,1,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[8,3,1,5,6,2,7,4]=>[3,2,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,3,1,7,4,5,2,6]=>[4,2,1,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[8,3,1,7,6,4,2,5]=>[5,2,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,3,1,7,6,4,5,2]=>[5,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,3,1,7,6,5,4,2]=>[6,2]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[8,3,1,7,5,6,4,2]=>[5,2,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[8,3,1,5,4,6,7,2]=>[4,2,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,4,2,1,3,5,6,7]=>[4,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,4,2,1,3,5,7,6]=>[4,2,1,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,4,2,1,3,6,7,5]=>[4,2,1,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[8,4,2,1,6,3,5,7]=>[4,2,1,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,4,2,1,7,5,6,3]=>[4,3,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,4,2,1,7,6,5,3]=>[5,3]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[8,4,2,1,6,7,5,3]=>[4,3,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,4,2,1,5,6,7,3]=>[4,2,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,3,4,1,2,5,6,7]=>[3,1,1,1,1,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,3,4,1,2,6,7,5]=>[3,2,1,1,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,3,4,1,7,5,6,2]=>[4,2,1,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,3,4,1,5,6,7,2]=>[3,2,1,1,1]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[8,5,2,3,1,7,6,4]=>[4,3,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[8,5,2,3,1,6,7,4]=>[4,2,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,5,4,2,1,3,6,7]=>[5,1,1,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,5,4,2,1,7,3,6]=>[5,2,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,5,4,2,1,7,6,3]=>[5,3]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[8,3,5,2,1,4,6,7]=>[4,1,1,1,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,3,5,2,1,7,4,6]=>[4,2,1,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,3,5,2,1,6,7,4]=>[4,2,1,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[8,4,2,5,1,3,6,7]=>[4,1,1,1,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,4,2,5,1,6,7,3]=>[4,2,1,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,3,4,5,1,6,7,2]=>[3,2,1,1,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[8,6,2,3,4,1,7,5]=>[4,2,1,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,6,4,2,3,1,5,7]=>[5,1,1,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[8,6,4,2,3,1,7,5]=>[5,2,1]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[8,6,5,3,2,1,7,4]=>[6,2]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[8,3,6,2,4,1,5,7]=>[4,1,1,1,1]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[8,3,6,5,2,1,7,4]=>[5,2,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[8,5,2,3,6,1,4,7]=>[4,1,1,1,1]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,4,2,6,1,7,3]=>[5,2,1]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,2,5,6,1,7,3]=>[4,2,1,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[8,7,4,2,6,3,1,5]=>[5,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,7,5,3,2,4,1,6]=>[6,1,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,7,4,5,2,3,1,6]=>[5,1,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[8,7,6,3,4,2,1,5]=>[6,1,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,7,6,5,3,2,1,4]=>[7,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,3,7,2,6,4,1,5]=>[5,1,1,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[8,6,2,3,4,7,1,5]=>[4,1,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,6,4,2,3,7,1,5]=>[5,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[8,6,4,5,2,7,1,3]=>[5,1,1,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[8,3,6,2,4,7,1,5]=>[4,1,1,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,7,2,4,5,6,3,1]=>[5,1,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,7,4,2,6,3,5,1]=>[5,2,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,7,4,2,6,5,3,1]=>[6,2]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,7,5,3,2,4,6,1]=>[6,1,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,7,6,3,4,2,5,1]=>[6,1,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,7,6,5,3,2,4,1]=>[7,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>[6,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>[7,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[8]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[7,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[6,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[6,2]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,3,7,2,6,4,5,1]=>[5,1,1,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[8,3,7,5,2,4,6,1]=>[5,1,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,3,7,5,6,4,2,1]=>[6,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,3,7,4,5,6,2,1]=>[5,1,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,3,4,7,2,5,6,1]=>[4,1,1,1,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[8,5,2,3,7,4,6,1]=>[4,2,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,3,5,2,7,4,6,1]=>[4,2,1,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,2,5,7,6,3,1]=>[5,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,2,6,3,7,5,1]=>[4,2,2]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,6,4,2,5,3,7,1]=>[5,2,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,3,6,2,4,5,7,1]=>[4,1,1,1,1]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,3,6,4,5,2,7,1]=>[5,1,1,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,5,4,2,3,6,7,1]=>[5,1,1,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[5,1,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[5,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,8,1,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2]=>[2,8,1,3,6,7,4,5]=>[3,1,1,1,1,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,8,1,3,7,6,5,4]=>[5,1,1,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,8,1,3,6,5,7,4]=>[4,1,1,1,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,8,1,3,5,6,7,4]=>[3,1,1,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,8,1,5,3,4,7,6]=>[3,2,1,1,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,8,1,5,6,3,7,4]=>[3,2,1,1,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,8,1,7,6,5,4,3]=>[6,1,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,8,1,6,4,7,5,3]=>[4,2,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,8,1,5,4,6,7,3]=>[4,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,8,4,1,3,5,6,7]=>[3,1,1,1,1,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,8,4,1,3,5,7,6]=>[3,2,1,1,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,8,4,1,6,3,7,5]=>[3,2,2,1]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[2,8,4,1,7,5,3,6]=>[4,2,1,1]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[2,8,4,1,6,7,3,5]=>[3,2,1,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,8,4,1,6,7,5,3]=>[4,2,1,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,8,4,1,6,5,7,3]=>[4,2,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,8,4,1,5,6,7,3]=>[3,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,8,5,3,1,4,6,7]=>[4,1,1,1,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,8,5,3,1,4,7,6]=>[4,2,1,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,8,4,5,1,3,6,7]=>[3,1,1,1,1,1]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,8,4,6,3,1,5,7]=>[4,1,1,1,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,8,5,3,6,1,7,4]=>[4,2,1,1]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[8,5,6,3,4,7,1,2]=>[2,8,4,7,6,3,1,5]=>[5,1,1,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,8,6,3,4,7,1,5]=>[4,1,1,1,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,8,5,3,6,7,1,4]=>[4,1,1,1,1]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,8,4,5,6,7,1,3]=>[3,1,1,1,1,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,8,7,3,4,5,6,1]=>[4,1,1,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,8,7,6,5,4,3,1]=>[7,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,8,7,5,6,4,3,1]=>[6,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,8,7,5,4,6,3,1]=>[6,1,1]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,8,4,7,3,6,5,1]=>[5,1,1,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,8,5,3,6,4,7,1]=>[4,2,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,8,5,3,4,6,7,1]=>[4,1,1,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,8,5,4,3,6,7,1]=>[5,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,8,2,4,5,6,7]=>[2,2,1,1,1,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,8,2,6,4,7,5]=>[3,2,2,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,8,2,7,5,4,6]=>[4,2,1,1]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[3,1,8,2,6,7,4,5]=>[3,2,1,1,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,8,2,7,5,6,4]=>[4,2,1,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,8,2,6,5,7,4]=>[4,2,1,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,8,2,5,6,7,4]=>[3,2,1,1,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,8,5,2,7,4,6]=>[3,2,2,1]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[3,1,8,5,2,7,6,4]=>[4,2,2]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[3,1,8,5,6,2,7,4]=>[3,2,2,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,8,5,7,4,2,6]=>[4,2,1,1]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,8,6,4,7,2,5]=>[4,2,1,1]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[3,1,8,7,6,4,5,2]=>[5,2,1]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,8,7,6,5,4,2]=>[6,2]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,1,8,7,5,6,4,2]=>[5,2,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,1,8,5,7,4,6,2]=>[4,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,8,6,4,7,5,2]=>[4,2,2]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,8,5,4,6,7,2]=>[4,2,1,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,8,4,5,6,7,2]=>[3,2,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[2,3,8,1,4,5,6,7]=>[2,1,1,1,1,1,1]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,3,8,1,4,5,7,6]=>[3,1,1,1,1,1]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,3,8,1,6,4,7,5]=>[3,2,1,1,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[2,3,8,1,6,7,4,5]=>[3,1,1,1,1,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[2,3,8,1,7,6,5,4]=>[5,1,1,1]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[2,3,8,1,6,7,5,4]=>[4,1,1,1,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[2,3,8,1,6,5,7,4]=>[4,1,1,1,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[2,3,8,1,5,6,7,4]=>[3,1,1,1,1,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,3,8,5,1,4,7,6]=>[3,2,1,1,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,3,8,6,4,1,7,5]=>[4,2,1,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[2,3,8,7,6,4,1,5]=>[5,1,1,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[2,3,8,7,4,5,6,1]=>[4,1,1,1,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[2,3,8,7,6,5,4,1]=>[6,1,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[2,3,8,5,7,6,4,1]=>[5,1,1,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>[3,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,8,3,5,6,7]=>[2,2,1,1,1,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,8,6,3,7,5]=>[3,2,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,8,7,5,3,6]=>[4,2,1,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,8,7,5,6,3]=>[4,2,1,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,8,7,6,5,3]=>[5,2,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,8,5,6,7,3]=>[3,2,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,3,1,8,2,5,6,7]=>[3,2,1,1,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[4,3,1,8,2,6,7,5]=>[3,3,1,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,3,1,8,6,2,7,5]=>[3,3,2]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[4,3,1,8,7,5,2,6]=>[4,3,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,3,1,8,7,6,5,2]=>[5,3]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,3,1,8,6,7,5,2]=>[4,3,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,3,1,8,6,5,7,2]=>[4,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,3,1,8,5,6,7,2]=>[3,3,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[2,4,1,8,3,5,6,7]=>[2,2,1,1,1,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[2,4,1,8,3,7,5,6]=>[3,2,1,1,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[2,4,1,8,6,3,5,7]=>[3,2,1,1,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,4,1,8,6,3,7,5]=>[3,2,2,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,4,1,8,7,6,5,3]=>[5,2,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[2,4,1,8,5,6,7,3]=>[3,2,1,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[3,1,4,8,2,5,6,7]=>[2,2,1,1,1,1]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,1,4,8,2,6,7,5]=>[3,2,1,1,1]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[3,1,4,8,6,2,5,7]=>[3,2,1,1,1]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[3,1,4,8,6,2,7,5]=>[3,2,2,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,1,4,8,7,6,5,2]=>[5,2,1]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[3,1,4,8,6,5,7,2]=>[4,2,1,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[3,1,4,8,5,6,7,2]=>[3,2,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[2,3,4,8,1,5,6,7]=>[2,1,1,1,1,1,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,3,4,8,1,5,7,6]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[2,3,4,8,1,7,5,6]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[2,3,4,8,1,7,6,5]=>[4,1,1,1,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[2,3,4,8,1,6,7,5]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[2,3,4,8,6,1,5,7]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,3,4,8,6,1,7,5]=>[3,2,1,1,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[2,3,4,8,7,5,1,6]=>[4,1,1,1,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[2,3,4,8,6,7,1,5]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,8,7,5,6,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[2,3,4,8,7,6,5,1]=>[5,1,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[2,3,4,8,6,7,5,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[2,3,4,8,6,5,7,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[3,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,8,4,7,6]=>[3,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,8,7,6,4]=>[4,2,1,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,8,6,7,4]=>[3,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,4,2,8,3,6,7]=>[3,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,4,2,8,3,7,6]=>[3,3,1,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,4,2,8,6,7,3]=>[3,3,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,3,1,2,8,4,6,7]=>[3,2,1,1,1]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,3,1,2,8,4,7,6]=>[3,3,1,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,3,1,2,8,7,4,6]=>[3,3,1,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,3,1,2,8,6,7,4]=>[3,3,1,1]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,4,2,1,8,7,6,3]=>[4,4]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[2,5,1,3,8,6,7,4]=>[3,2,1,1,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,5,4,1,8,3,7,6]=>[3,3,1,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[2,5,4,1,8,6,7,3]=>[3,3,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[3,1,5,2,8,4,6,7]=>[2,2,2,1,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[3,1,5,2,8,4,7,6]=>[3,2,2,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[3,1,5,2,8,7,4,6]=>[3,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[3,1,5,2,8,7,6,4]=>[4,2,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,1,5,2,8,6,7,4]=>[3,2,2,1]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[2,3,5,1,8,4,7,6]=>[3,2,1,1,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[2,3,5,1,8,7,4,6]=>[3,2,1,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[4,1,2,5,8,3,6,7]=>[2,2,1,1,1,1]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[4,1,2,5,8,3,7,6]=>[3,2,1,1,1]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[4,1,2,5,8,7,3,6]=>[3,2,1,1,1]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[4,3,1,5,8,2,7,6]=>[3,3,1,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[4,3,1,5,8,6,7,2]=>[3,3,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[2,4,1,5,8,3,6,7]=>[2,2,1,1,1,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,4,1,5,8,3,7,6]=>[3,2,1,1,1]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[3,1,4,5,8,7,2,6]=>[3,2,1,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[2,3,4,5,8,1,6,7]=>[2,1,1,1,1,1,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,3,4,5,8,1,7,6]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[2,3,4,5,8,7,1,6]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[2,3,4,5,8,7,6,1]=>[4,1,1,1,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>[3,1,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,8,7,5]=>[3,2,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,5,3,8,4,7]=>[3,2,1,1,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,4,2,3,8,5,7]=>[3,2,1,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[6,1,5,3,2,8,4,7]=>[4,2,1,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,4,5,2,8,7,3]=>[3,3,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[6,3,1,2,4,8,5,7]=>[3,2,1,1,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,4,2,1,3,8,5,7]=>[4,2,1,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,4,2,1,3,8,7,5]=>[4,3,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[6,3,4,1,2,8,7,5]=>[3,3,1,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,5,2,3,1,8,7,4]=>[4,3,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[6,3,5,2,1,8,4,7]=>[4,2,1,1]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6]=>[6,4,2,5,1,8,3,7]=>[4,2,1,1]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[2,6,4,1,3,8,5,7]=>[3,2,1,1,1]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,6,4,1,3,8,7,5]=>[3,3,1,1]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[3,1,6,2,4,8,5,7]=>[2,2,2,1,1]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[3,1,6,2,4,8,7,5]=>[3,2,2,1]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[3,1,6,5,2,8,7,4]=>[3,3,2]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,3,6,1,4,8,7,5]=>[3,2,1,1,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[2,3,6,5,1,8,4,7]=>[3,2,1,1,1]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,3,6,5,1,8,7,4]=>[3,3,1,1]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[4,1,2,6,3,8,5,7]=>[2,2,2,1,1]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[4,1,2,6,3,8,7,5]=>[3,2,2,1]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[2,4,1,6,3,8,5,7]=>[2,2,2,1,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[2,4,1,6,3,8,7,5]=>[3,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[3,1,4,6,2,8,5,7]=>[2,2,2,1,1]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[3,1,4,6,2,8,7,5]=>[3,2,2,1]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[2,3,4,6,1,8,5,7]=>[2,2,1,1,1,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,3,4,6,1,8,7,5]=>[3,2,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[5,1,2,3,6,8,4,7]=>[2,2,1,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[5,1,2,3,6,8,7,4]=>[3,2,1,1,1]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[5,4,2,1,6,8,7,3]=>[4,3,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[2,5,1,3,6,8,4,7]=>[2,2,1,1,1,1]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,5,1,3,6,8,7,4]=>[3,2,1,1,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[4,1,2,5,6,8,3,7]=>[2,2,1,1,1,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[4,1,2,5,6,8,7,3]=>[3,2,1,1,1]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[3,1,4,5,6,8,7,2]=>[3,2,1,1,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[3,1,1,1,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,5,6,3,8,4]=>[3,2,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,4,2,3,5,8,6]=>[3,2,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,1,4,2,6,3,8,5]=>[3,2,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,6,3,4,2,8,5]=>[4,2,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,3,1,2,4,5,8,6]=>[3,2,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,3,1,2,6,4,8,5]=>[3,2,2,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,3,4,1,6,2,8,5]=>[3,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,4,2,5,1,3,8,6]=>[4,2,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,6,2,3,4,1,8,5]=>[4,2,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,6,2,5,3,1,8,4]=>[5,2,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[2,7,4,1,6,3,8,5]=>[3,2,2,1]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[8,6,4,3,5,1,2,7]=>[2,7,5,3,1,4,8,6]=>[4,2,1,1]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[2,7,6,5,3,1,8,4]=>[5,2,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[3,1,7,2,6,4,8,5]=>[3,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[3,1,7,6,4,2,8,5]=>[4,2,2]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[2,3,7,1,4,5,8,6]=>[2,2,1,1,1,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[2,3,7,1,6,4,8,5]=>[3,2,1,1,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[2,3,7,5,6,1,8,4]=>[3,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[4,1,2,7,3,5,8,6]=>[2,2,2,1,1]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[4,1,2,7,6,3,8,5]=>[3,2,2,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[4,3,1,7,2,5,8,6]=>[3,2,2,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[4,3,1,7,6,2,8,5]=>[3,3,2]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[2,4,1,7,3,5,8,6]=>[2,2,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[2,3,4,7,1,5,8,6]=>[2,2,1,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[2,3,4,7,6,1,8,5]=>[3,2,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[5,1,2,3,7,4,8,6]=>[2,2,2,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[5,1,4,2,7,3,8,6]=>[3,2,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[2,5,1,3,7,4,8,6]=>[2,2,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[3,1,5,2,7,4,8,6]=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[2,3,5,1,7,4,8,6]=>[2,2,2,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[4,1,2,5,7,3,8,6]=>[2,2,2,1,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,1,2,3,4,7,8,5]=>[2,2,1,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[6,3,1,2,4,7,8,5]=>[3,2,1,1,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,3,1,5,2,7,8,4]=>[3,2,2,1]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[6,3,4,1,2,7,8,5]=>[3,2,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[2,6,4,1,3,7,8,5]=>[3,2,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[3,1,6,2,4,7,8,5]=>[2,2,2,1,1]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[2,3,6,5,1,7,8,4]=>[3,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[4,1,2,6,3,7,8,5]=>[2,2,2,1,1]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[2,4,1,6,3,7,8,5]=>[2,2,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,1,2,3,6,7,8,4]=>[2,2,1,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[5,1,4,2,6,7,8,3]=>[3,2,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[5,3,1,2,6,7,8,4]=>[3,2,1,1,1]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[5,4,2,1,6,7,8,3]=>[4,2,1,1]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,3,4,1,6,7,8,2]=>[3,2,1,1,1]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[2,5,1,3,6,7,8,4]=>[2,2,1,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[2,5,4,1,6,7,8,3]=>[3,2,1,1,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[3,1,5,2,6,7,8,4]=>[2,2,2,1,1]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[2,3,5,1,6,7,8,4]=>[2,2,1,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,1,2,5,6,7,8,3]=>[2,2,1,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,3,1,5,6,7,8,2]=>[3,2,1,1,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[2,4,1,5,6,7,8,3]=>[2,2,1,1,1,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,1,2,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,1,2,3,6,5,4,8]=>[4,1,1,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,1,2,3,5,6,4,8]=>[3,1,1,1,1,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,1,2,6,4,5,3,8]=>[4,1,1,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>[5,1,1,1]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,1,2,5,4,6,3,8]=>[4,1,1,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,1,4,2,6,3,5,8]=>[3,2,1,1,1]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[7,1,4,2,6,5,3,8]=>[4,2,1,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[7,1,4,2,5,6,3,8]=>[3,2,1,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[7,1,5,3,2,4,6,8]=>[4,1,1,1,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,1,4,5,2,3,6,8]=>[3,1,1,1,1,1]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,1,6,5,3,2,4,8]=>[5,1,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[7,1,4,6,5,3,2,8]=>[5,1,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,3,1,2,4,5,6,8]=>[3,1,1,1,1,1]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,3,1,2,4,6,5,8]=>[3,2,1,1,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,3,1,2,6,4,5,8]=>[3,2,1,1,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[7,3,1,2,5,6,4,8]=>[3,2,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,3,1,5,2,4,6,8]=>[3,2,1,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,3,1,5,2,6,4,8]=>[3,2,2,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,3,1,5,6,2,4,8]=>[3,2,1,1,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,3,1,6,5,4,2,8]=>[5,2,1]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,4,2,1,5,6,3,8]=>[4,2,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,3,4,1,2,5,6,8]=>[3,1,1,1,1,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,3,4,1,2,6,5,8]=>[3,2,1,1,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,3,4,1,6,2,5,8]=>[3,2,1,1,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,3,4,1,6,5,2,8]=>[4,2,1,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,3,4,1,5,6,2,8]=>[3,2,1,1,1]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[7,5,2,3,1,6,4,8]=>[4,2,1,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,3,5,2,1,4,6,8]=>[4,1,1,1,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[7,4,2,5,1,3,6,8]=>[4,1,1,1,1]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[7,4,2,5,1,6,3,8]=>[4,2,1,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[7,6,2,3,4,1,5,8]=>[4,1,1,1,1]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[7,6,2,5,3,1,4,8]=>[5,1,1,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,6,4,2,3,1,5,8]=>[5,1,1,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,3,6,5,2,1,4,8]=>[5,1,1,1]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[7,3,5,2,6,1,4,8]=>[4,1,1,1,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,6,2,3,4,5,1,8]=>[4,1,1,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>[6,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,6,4,2,5,3,1,8]=>[5,2,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,6,4,5,2,3,1,8]=>[5,1,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>[6,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[7,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,3,5,2,6,4,1,8]=>[4,2,1,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[7,4,2,5,6,3,1,8]=>[4,2,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>[4,1,1,1,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[2,7,1,3,5,6,4,8]=>[3,1,1,1,1,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[2,7,1,5,6,3,4,8]=>[3,1,1,1,1,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[2,7,6,3,4,5,1,8]=>[4,1,1,1,1]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[2,7,6,3,5,4,1,8]=>[5,1,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[2,7,5,3,6,4,1,8]=>[4,2,1,1]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[3,1,7,2,5,6,4,8]=>[3,2,1,1,1]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,2,1,3,8]=>[3,1,7,6,5,4,2,8]=>[5,2,1]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[2,3,7,1,6,5,4,8]=>[4,1,1,1,1]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[2,3,7,1,5,6,4,8]=>[3,1,1,1,1,1]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[2,3,7,6,5,4,1,8]=>[5,1,1,1]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[2,3,7,5,6,4,1,8]=>[4,1,1,1,1]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[2,3,7,5,4,6,1,8]=>[4,1,1,1,1]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[4,1,2,7,5,6,3,8]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[4,3,1,7,6,2,5,8]=>[3,3,1,1]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[2,4,1,7,5,6,3,8]=>[3,2,1,1,1]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[3,1,4,7,5,6,2,8]=>[3,2,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[2,3,4,7,1,5,6,8]=>[2,1,1,1,1,1,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[2,3,4,7,1,6,5,8]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[2,3,4,7,6,1,5,8]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[2,3,4,7,6,5,1,8]=>[4,1,1,1,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[2,3,4,7,5,6,1,8]=>[3,1,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[5,1,2,3,7,6,4,8]=>[3,2,1,1,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[5,3,1,2,7,4,6,8]=>[3,2,1,1,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[5,3,4,1,7,2,6,8]=>[3,2,1,1,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[3,1,5,2,7,4,6,8]=>[2,2,2,1,1]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[4,1,2,5,7,3,6,8]=>[2,2,1,1,1,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[4,1,2,5,7,6,3,8]=>[3,2,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[6,3,1,2,4,7,5,8]=>[3,2,1,1,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[6,3,5,2,1,7,4,8]=>[4,2,1,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[2,3,6,1,4,7,5,8]=>[2,2,1,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[4,1,2,6,3,7,5,8]=>[2,2,2,1,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[4,3,1,6,2,7,5,8]=>[3,2,2,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[2,4,1,6,3,7,5,8]=>[2,2,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,1,2,3,6,7,4,8]=>[2,2,1,1,1,1]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[5,4,2,1,6,7,3,8]=>[4,2,1,1]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[2,5,4,1,6,7,3,8]=>[3,2,1,1,1]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[6,1,4,2,5,3,7,8]=>[3,2,1,1,1]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[6,3,1,5,4,2,7,8]=>[4,2,1,1]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,2,1,5,3,7,8]=>[4,2,1,1]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[6,3,4,1,5,2,7,8]=>[3,2,1,1,1]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[6,4,2,5,1,3,7,8]=>[4,1,1,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[4,1,1,1,1]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[2,6,1,3,5,4,7,8]=>[3,1,1,1,1,1]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[2,6,1,5,4,3,7,8]=>[4,1,1,1,1]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[2,6,4,1,5,3,7,8]=>[3,2,1,1,1]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[2,6,5,3,4,1,7,8]=>[4,1,1,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[3,1,6,2,5,4,7,8]=>[3,2,1,1,1]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[3,1,6,5,2,4,7,8]=>[3,2,1,1,1]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[3,1,6,5,4,2,7,8]=>[4,2,1,1]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[4,1,2,6,5,3,7,8]=>[3,2,1,1,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[4,3,1,6,2,5,7,8]=>[3,2,1,1,1]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[4,3,1,6,5,2,7,8]=>[3,3,1,1]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[5,4,2,1,6,3,7,8]=>[4,2,1,1]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[2,4,1,5,6,3,7,8]=>[2,2,1,1,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[3,1,1,1,1,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>[3,1,1,1,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[4,1,1,1,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,1,3,4,2,6,7,8]=>[3,1,1,1,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[3,1,1,1,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>[3,2,1,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[4,1,1,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>[3,1,1,1,1,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,1,1,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,1,1,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,1,1,1,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,1,1,1,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[2,5,3,4,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,1,1,1,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[2,2,1,1,1,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
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