Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00064: Permutations —reverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[1,2]=>[2]
[[.,.],.]=>[1,2]=>[2,1]=>[1,1]
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>[3]
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>[2,1]
[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>[1,2]
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>[3,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>[2,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>[2,2]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>[1,3]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>[1,2,1]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>[1,3]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>[1,1,2]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>[1,3]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>[1,2,1]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>[1,1,2]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>[1,1,2]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[3,2]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[2,3]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[2,1,2]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[2,3]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[2,2,1]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[2,1,2]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[2,1,2]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[2,1,1,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[1,2,2]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[1,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[1,4]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[1,3,1]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[1,1,2,1]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[1,4]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[1,2,2]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[1,1,3]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[1,1,3]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[1,1,1,2]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[1,4]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[1,3,1]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[1,2,2]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[1,2,2]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[1,2,1,1]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[1,1,3]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[1,1,2,1]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[1,1,3]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[1,1,1,2]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[1,1,3]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[1,1,2,1]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[1,1,1,2]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[1,1,1,2]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[4,2]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[4,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[3,3]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[3,1,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[3,3]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[3,2,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[3,1,2]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[3,1,2]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[2,2,2]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[2,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[2,4]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[2,3,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[2,1,3]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[2,1,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[2,4]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[2,2,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[2,1,3]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[2,1,3]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[2,1,1,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[2,4]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[2,3,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[2,2,2]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[2,2,2]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[2,2,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[2,1,3]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[2,1,2,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[2,1,3]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[2,1,1,2]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[2,1,3]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[2,1,2,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[2,1,1,2]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[2,1,1,2]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[1,3,2]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[1,3,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[1,2,3]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[1,2,1,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[1,2,3]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[1,2,2,1]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[1,2,1,2]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[1,2,1,2]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[1,5]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[1,4,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[1,3,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[1,3,2]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[1,3,1,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[1,1,4]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[1,1,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[1,1,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[1,1,2,2]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[1,5]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[1,4,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[1,2,3]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[1,2,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[1,1,4]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[1,1,3,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[1,1,4]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[1,1,3,1]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[1,5]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[1,3,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[1,2,3]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[1,2,3]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[1,2,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[1,1,4]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[1,1,2,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[1,1,4]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[1,1,1,3]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[1,1,4]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[1,1,2,2]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[1,1,1,3]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[1,1,1,3]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,5]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[1,4,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[1,3,2]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[1,3,2]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[1,3,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[1,2,3]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[1,2,2,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[1,2,3]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[1,2,1,2]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[1,2,3]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[1,2,2,1]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[1,2,1,2]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[1,2,1,2]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[1,2,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[1,1,4]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[1,1,3,1]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[1,1,2,2]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[1,1,2,2]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[1,1,2,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[1,1,4]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[1,1,3,1]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[1,1,1,3]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[1,1,1,2,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[1,1,4]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[1,1,2,2]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[1,1,1,3]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[1,1,1,3]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,1,4]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[1,1,3,1]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[1,1,2,2]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[1,1,2,2]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[1,1,2,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[1,1,1,3]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[1,1,1,2,1]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[1,1,1,3]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,1,1,3]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[1,1,1,2,1]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[5,2]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[5,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>[4,3]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>[4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[4,3]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[4,2,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>[4,1,2]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[4,1,2]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>[3,2,2]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>[3,4]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>[3,3,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[3,1,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>[3,1,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>[3,4]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>[3,2,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>[3,1,3]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>[3,1,3]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[3,4]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[3,3,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>[3,2,2]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[3,2,2]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[3,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>[3,1,3]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>[3,1,2,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>[3,1,3]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>[3,1,1,2]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[3,1,3]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[3,1,2,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>[3,1,1,2]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[3,1,1,2]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>[2,3,2]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>[2,3,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>[2,2,3]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>[2,2,1,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>[2,2,3]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>[2,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>[2,2,1,2]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>[2,2,1,2]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>[2,5]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>[2,4,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>[2,3,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>[2,3,2]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>[2,3,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>[2,1,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>[2,1,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>[2,1,2,2]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>[2,5]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>[2,4,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>[2,2,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>[2,2,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>[2,1,4]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>[2,1,3,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>[2,1,4]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>[2,1,3,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>[2,5]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>[2,3,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>[2,2,3]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>[2,2,3]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>[2,2,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>[2,1,4]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>[2,1,2,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>[2,1,4]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>[2,1,1,3]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>[2,1,4]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>[2,1,2,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>[2,1,1,3]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>[2,1,1,3]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[2,5]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[2,4,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>[2,3,2]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[2,3,2]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[2,3,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>[2,2,3]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>[2,2,2,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>[2,2,3]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>[2,2,1,2]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[2,2,3]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[2,2,2,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>[2,2,1,2]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[2,2,1,2]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[2,2,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>[2,1,4]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>[2,1,3,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>[2,1,2,2]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>[2,1,2,2]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>[2,1,2,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>[2,1,4]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>[2,1,3,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>[2,1,1,3]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>[2,1,1,2,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>[2,1,4]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>[2,1,2,2]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>[2,1,1,3]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>[2,1,1,3]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[2,1,1,1,2]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[2,1,4]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[2,1,3,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>[2,1,2,2]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[2,1,2,2]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[2,1,2,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>[2,1,1,3]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[2,1,1,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[2,1,1,3]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[2,1,1,1,2]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[2,1,1,3]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[2,1,1,2,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[2,1,1,1,2]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[2,1,1,1,2]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>[1,4,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>[1,3,3]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>[1,3,3]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>[1,3,2,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>[1,3,1,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>[1,3,1,2]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[1,2,2,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[1,2,4]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>[1,2,3,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[1,2,4]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>[1,2,2,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>[1,2,1,3]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>[1,2,1,3]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[1,2,4]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>[1,2,3,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>[1,2,2,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>[1,2,2,2]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>[1,2,2,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>[1,2,1,3]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>[1,2,1,2,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>[1,2,1,3]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>[1,2,1,1,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>[1,2,1,3]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>[1,2,1,2,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>[1,2,1,1,2]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>[1,2,1,1,2]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[1,6]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>[1,5,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>[1,4,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>[1,4,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>[1,4,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>[1,3,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>[1,3,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>[1,3,3]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>[1,3,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>[1,3,3]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>[1,3,2,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>[1,3,1,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>[1,3,1,2]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>[1,3,1,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>[1,1,3,2]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[1,1,2,3]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[1,1,2,3]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>[1,1,2,2,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[1,1,2,1,2]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[1,1,2,1,2]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[1,6]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>[1,5,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>[1,4,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>[1,4,2]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>[1,4,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>[1,2,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>[1,2,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>[1,2,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>[1,2,2,2]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>[1,2,2,1,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[1,1,5]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>[1,1,4,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>[1,1,3,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>[1,1,3,2]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>[1,1,3,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[1,1,5]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>[1,1,4,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>[1,1,3,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>[1,1,3,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>[1,1,3,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[1,1,1,2,2]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[1,6]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>[1,5,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>[1,3,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>[1,3,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>[1,2,4]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>[1,2,3,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>[1,2,4]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>[1,2,3,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>[1,2,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>[1,2,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[1,1,5]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>[1,1,4,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[1,1,2,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[1,1,2,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[1,1,5]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>[1,1,4,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>[1,1,1,3,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[1,1,5]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>[1,1,4,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>[1,1,2,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>[1,1,2,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>[1,1,1,3,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[1,6]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>[1,4,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>[1,3,3]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>[1,3,3]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>[1,3,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>[1,2,4]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>[1,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>[1,2,4]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>[1,2,1,3]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>[1,2,4]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>[1,2,1,3]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>[1,2,1,3]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[1,2,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[1,1,5]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>[1,1,3,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[1,1,2,3]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[1,1,2,3]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>[1,1,2,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[1,1,5]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>[1,1,3,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[1,1,1,2,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[1,1,5]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>[1,1,2,3]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[1,1,5]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>[1,1,3,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[1,1,2,1,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[1,1,1,2,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[1,6]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[1,5,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>[1,4,2]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[1,4,2]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[1,4,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[1,3,3]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>[1,3,2,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[1,3,3]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[1,3,1,2]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[1,3,3]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[1,3,2,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>[1,3,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[1,3,1,2]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>[1,2,4]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>[1,2,3,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>[1,2,2,2]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>[1,2,2,2]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>[1,2,2,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>[1,2,4]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>[1,2,3,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>[1,2,1,3]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>[1,2,1,2,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[1,2,4]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[1,2,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>[1,2,1,3]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>[1,2,1,3]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>[1,2,1,1,2]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[1,2,4]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[1,2,3,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>[1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[1,2,2,2]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[1,2,2,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>[1,2,1,3]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>[1,2,1,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>[1,2,1,3]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>[1,2,1,1,2]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[1,2,1,3]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[1,2,1,2,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>[1,2,1,1,2]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[1,2,1,1,2]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[1,1,5]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>[1,1,4,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>[1,1,3,2]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>[1,1,3,2]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>[1,1,3,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[1,1,2,3]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[1,1,2,2,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[1,1,2,3]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>[1,1,2,1,2]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[1,1,2,3]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>[1,1,2,2,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>[1,1,2,1,2]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>[1,1,2,1,2]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[1,1,5]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>[1,1,4,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>[1,1,3,2]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>[1,1,3,2]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>[1,1,3,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>[1,1,1,3,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[1,1,1,2,2]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[1,1,1,2,2]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[1,1,5]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>[1,1,4,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>[1,1,2,3]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>[1,1,2,2,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>[1,1,1,3,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>[1,1,1,3,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[1,1,5]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>[1,1,3,2]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>[1,1,2,3]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>[1,1,2,3]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>[1,1,2,1,2]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[1,1,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[1,1,5]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[1,1,4,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>[1,1,3,2]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[1,1,3,2]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>[1,1,2,3]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>[1,1,2,2,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>[1,1,2,3]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>[1,1,2,1,2]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[1,1,2,3]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[1,1,2,2,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>[1,1,2,1,2]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[1,1,2,1,2]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>[1,1,1,3,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[1,1,1,2,2]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[1,1,1,2,2]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>[1,1,1,3,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>[1,1,1,2,2]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>[1,1,1,2,2]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[1,1,1,2,2]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[7,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>[6,2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[6,2]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>[5,3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>[5,3]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>[5,3]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>[5,2,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>[5,1,2]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>[5,1,2]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[4,4]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>[4,2,2]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>[4,4]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>[4,3,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>[4,4]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>[4,2,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>[4,1,3]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>[4,1,3]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>[4,4]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>[4,3,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>[4,2,2]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>[4,2,2]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>[4,2,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>[4,1,3]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>[4,1,2,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>[4,1,3]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>[4,1,1,2]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>[4,1,3]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>[4,1,2,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>[4,1,1,2]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>[4,1,1,2]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>[3,5]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>[3,4,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>[3,3,2]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>[3,2,3]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>[3,2,2,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>[3,2,1,2]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>[3,5]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>[3,4,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>[3,3,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>[3,3,2]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>[3,3,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>[3,1,2,2]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>[3,5]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>[3,4,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[1,2,6,4,3,5,8,7]=>[3,1,3,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>[3,1,4]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>[3,5]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5,8]=>[3,2,3]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[8,6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6,8]=>[3,1,4]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5,8]=>[3,1,2,2]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6,8]=>[3,1,4]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[8,6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6,8]=>[3,1,1,3]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5,8]=>[3,1,4]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[8,4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4,8]=>[3,1,2,2]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>[3,1,1,3]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>[3,5]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>[3,4,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>[3,2,3]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>[3,2,3]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>[3,2,3]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>[3,2,1,2]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>[3,2,1,2]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>[3,2,1,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>[3,1,4]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>[3,1,3,1]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>[3,1,2,2]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>[3,1,2,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>[3,1,4]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>[3,1,1,3]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>[3,1,1,3]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[7,4,3,5,6,8,2,1]=>[1,2,8,6,5,3,4,7]=>[3,1,1,3]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[1,2,8,6,5,4,3,7]=>[3,1,1,1,2]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>[3,1,4]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>[3,1,3,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>[3,1,2,2]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>[3,1,2,1,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[1,2,8,7,4,3,5,6]=>[3,1,1,3]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>[3,1,1,2,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>[3,1,1,1,2]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>[3,1,1,3]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>[3,1,1,2,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>[3,1,1,1,2]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,2,8,7,6,5,3,4]=>[3,1,1,1,2]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>[2,6]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>[2,4,2]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6,8]=>[2,3,3]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>[2,3,3]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>[2,3,2,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>[2,3,1,2]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>[2,2,1,3]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>[2,2,4]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>[2,2,2,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>[2,2,1,3]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5,8]=>[2,2,1,3]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>[2,2,4]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[1,3,2,8,4,5,7,6]=>[2,2,3,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>[2,2,2,2]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>[2,2,2,2]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[1,3,2,8,4,7,6,5]=>[2,2,2,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>[2,2,1,3]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>[2,2,1,1,2]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>[2,2,1,3]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>[2,2,1,1,2]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>[2,6]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>[2,5,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>[2,4,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>[2,4,2]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>[2,4,1,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>[2,3,3]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>[2,3,2,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[2,3,3]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5,8]=>[2,3,1,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>[2,3,3]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>[2,3,2,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>[2,3,1,2]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>[2,3,1,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>[2,3,1,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>[2,1,3,2]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>[2,1,3,2]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6,8]=>[2,1,2,3]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>[2,1,2,3]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[1,4,3,2,8,5,7,6]=>[2,1,2,2,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>[2,1,2,1,2]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[1,4,3,2,8,7,5,6]=>[2,1,2,1,2]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>[2,6]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>[2,5,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>[2,4,2]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>[2,4,2]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>[2,4,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>[2,2,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>[2,2,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>[2,2,2,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>[2,2,2,2]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>[2,2,2,1,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>[2,1,5]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>[2,1,4,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>[2,1,3,2]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>[2,1,3,2]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>[2,1,3,1,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>[2,1,5]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>[2,1,4,1]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>[2,1,3,2]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>[2,1,3,2]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>[2,1,3,1,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[1,5,4,3,2,8,6,7]=>[2,1,1,2,2]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>[2,6]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>[2,5,1]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[8,7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7,8]=>[2,3,3]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[7,8,4,5,3,2,6,1]=>[1,6,2,3,5,4,8,7]=>[2,3,2,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7,8]=>[2,2,4]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7,8]=>[2,2,4]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[1,6,2,5,3,4,8,7]=>[2,2,3,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>[2,1,5]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>[2,1,2,3]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>[2,1,5]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>[2,1,4,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>[2,1,1,4]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[1,6,4,3,2,5,8,7]=>[2,1,1,3,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>[2,1,4,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>[2,1,1,4]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7,8]=>[2,1,1,4]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>[2,6]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6,8]=>[2,3,3]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>[2,2,2,2]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>[2,2,4]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>[2,2,1,3]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>[2,2,4]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>[2,2,2,2]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3,8]=>[2,2,1,1,2]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>[2,1,5]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>[2,1,3,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>[2,1,2,3]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>[2,1,1,4]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>[2,1,1,4]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6,8]=>[2,1,1,1,3]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>[2,1,5]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4,8]=>[2,1,3,2]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>[2,1,2,3]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>[2,1,1,4]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>[2,1,1,4]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5,8]=>[2,1,1,1,3]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4,8]=>[2,1,1,4]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4,8]=>[2,1,1,1,3]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3,8]=>[2,1,1,1,3]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[2,6]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>[2,4,2]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>[2,4,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>[2,3,3]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>[2,3,3]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>[2,3,1,2]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[1,8,2,3,7,4,5,6]=>[2,3,3]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[1,8,2,3,7,4,6,5]=>[2,3,2,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>[2,3,1,2]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>[2,2,4]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>[2,2,2,2]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>[2,2,2,2]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>[2,2,4]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[1,8,2,5,3,4,7,6]=>[2,2,3,1]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[1,8,2,5,4,3,6,7]=>[2,2,1,3]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>[2,2,4]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>[2,2,2,2]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[1,8,2,6,5,3,4,7]=>[2,2,1,3]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[1,8,2,6,5,4,3,7]=>[2,2,1,1,2]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>[2,2,4]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[1,8,2,7,3,4,6,5]=>[2,2,3,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>[2,2,2,2]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>[2,2,2,2]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>[2,2,2,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>[2,2,1,3]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[1,8,2,7,4,3,6,5]=>[2,2,1,2,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>[2,2,1,3]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>[2,2,1,1,2]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>[2,2,1,3]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>[2,2,1,2,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>[2,2,1,1,2]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>[2,1,5]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[1,8,3,2,4,6,5,7]=>[2,1,3,2]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>[2,1,3,2]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>[2,1,2,3]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>[2,1,2,2,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>[2,1,2,3]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[1,8,3,2,7,4,6,5]=>[2,1,2,2,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>[2,1,2,1,2]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>[2,1,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>[2,1,5]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>[2,1,4,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>[2,1,3,2]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>[2,1,3,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>[2,1,1,4]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>[2,1,1,3,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[1,8,4,3,2,6,5,7]=>[2,1,1,2,2]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>[2,1,1,2,1,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[1,8,5,2,3,4,6,7]=>[2,1,5]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>[2,1,1,4]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>[2,1,1,3,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>[2,1,1,3,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>[2,1,1,1,3]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>[2,1,1,1,2,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>[2,1,5]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>[2,1,1,4]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>[2,1,1,4]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[1,8,6,4,3,2,5,7]=>[2,1,1,1,3]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[1,8,6,5,2,3,4,7]=>[2,1,1,4]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[1,8,6,5,2,4,3,7]=>[2,1,1,2,2]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,8,6,5,3,2,4,7]=>[2,1,1,1,3]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>[2,1,5]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>[2,1,3,2]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>[2,1,3,1,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[1,8,7,2,4,3,5,6]=>[2,1,2,3]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[1,8,7,2,4,3,6,5]=>[2,1,2,2,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>[2,1,2,3]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,8,7,2,5,4,3,6]=>[2,1,2,1,2]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>[2,1,2,3]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>[2,1,2,2,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[1,8,7,2,6,4,3,5]=>[2,1,2,1,2]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>[2,1,2,1,2]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>[2,1,2,1,1,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>[2,1,1,4]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>[2,1,1,3,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>[2,1,1,2,2]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>[2,1,1,2,2]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[1,8,7,3,2,6,5,4]=>[2,1,1,2,1,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>[2,1,1,4]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>[2,1,1,1,3]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[1,8,7,4,3,2,6,5]=>[2,1,1,1,2,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>[2,1,1,4]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>[2,1,1,1,3]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[6,3,2,4,5,7,8,1]=>[1,8,7,5,4,2,3,6]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>[2,1,1,1,1,2]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>[2,1,1,4]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[1,8,7,6,2,3,5,4]=>[2,1,1,3,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>[2,1,1,2,2]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>[2,1,1,1,3]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>[2,1,1,1,2,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>[2,1,1,1,3]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>[2,1,1,1,1,2]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>[2,1,1,1,3]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>[2,1,1,1,2,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>[2,1,1,1,1,2]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>[1,4,3]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>[1,4,2,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>[1,4,3]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>[1,4,2,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>[1,4,1,2]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>[1,4,1,2]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>[1,3,4]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>[1,3,4]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>[1,3,3,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>[1,3,2,2]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>[1,3,2,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>[1,3,1,2,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>[1,3,1,3]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>[1,3,1,2,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>[1,3,1,1,2]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>[1,3,1,1,2]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>[1,2,2,3]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>[1,2,2,1,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>[1,2,2,1,2]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>[1,2,5]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>[1,2,4,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>[1,2,4,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>[1,2,2,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>[1,2,1,3,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7,8]=>[1,2,1,4]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>[1,2,1,3,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>[1,2,1,4]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[8,4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4,8]=>[1,2,1,2,2]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>[1,2,1,1,3]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>[1,2,5]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[2,1,8,3,4,5,7,6]=>[1,2,4,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>[1,2,3,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>[1,2,2,2,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>[1,2,2,3]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>[1,2,2,3]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>[1,2,2,2,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>[1,2,2,1,2]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>[1,2,2,1,2]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>[1,2,2,1,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[2,1,8,4,3,5,6,7]=>[1,2,1,4]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>[1,2,1,3,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>[1,2,1,2,2]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>[1,2,1,2,2]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>[1,2,1,1,3]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>[1,2,1,1,2,1]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[2,1,8,6,3,4,5,7]=>[1,2,1,4]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>[1,2,1,1,3]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>[1,2,1,4]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>[1,2,1,3,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>[1,2,1,2,2]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[2,1,8,7,3,6,4,5]=>[1,2,1,2,2]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[2,1,8,7,3,6,5,4]=>[1,2,1,2,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>[1,2,1,1,3]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>[1,2,1,1,2,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>[1,2,1,1,3]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>[1,2,1,1,1,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>[1,2,1,1,3]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>[1,2,1,1,2,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>[1,2,1,1,1,2]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>[1,2,1,1,1,2]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>[1,7]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[1,5,2]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>[1,4,2,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>[1,4,3]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>[1,4,3]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>[1,4,2,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>[1,4,1,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>[1,4,1,2]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>[1,4,1,1,1]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>[1,3,3,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>[1,3,2,2]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>[1,3,3,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7,8]=>[1,3,1,3]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>[1,3,4]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>[1,3,1,3]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>[1,3,1,3]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4,8]=>[1,3,1,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>[1,3,4]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>[1,3,3,1]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[3,1,2,8,4,6,5,7]=>[1,3,2,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>[1,3,2,2]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,1,2,8,4,7,6,5]=>[1,3,2,1,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,1,2,8,5,4,6,7]=>[1,3,1,3]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>[1,3,1,2,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>[1,3,1,3]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>[1,3,1,1,2]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>[1,3,1,3]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>[1,3,1,2,1]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>[1,3,1,1,2]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>[1,3,1,1,2]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>[1,3,1,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>[1,1,4,2]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>[1,1,3,3]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>[1,1,3,1,2]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>[1,1,3,1,2]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,1,2,3]=>[3,2,1,5,4,8,6,7]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>[1,1,2,4]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>[1,1,2,1,3]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>[1,1,2,2,2]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>[1,1,2,1,3]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>[1,1,2,1,3]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>[1,1,2,4]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>[1,1,2,3,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>[1,1,2,2,2]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>[1,1,2,2,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>[1,1,2,1,3]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>[1,1,2,1,2,1]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>[1,1,2,1,3]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>[1,1,2,1,1,2]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>[1,1,2,1,3]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>[1,1,2,1,2,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>[1,1,2,1,1,2]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>[1,7]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>[1,6,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>[1,5,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>[1,5,2]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>[1,5,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>[1,4,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>[1,4,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>[1,4,3]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>[1,4,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[1,4,3]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>[1,4,2,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>[1,4,1,2]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>[1,4,1,2]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>[1,4,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>[1,2,5]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[4,1,3,2,5,6,8,7]=>[1,2,4,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>[1,2,3,2]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[4,1,3,2,5,8,6,7]=>[1,2,3,2]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>[1,2,2,2,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>[1,2,2,3]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>[1,2,2,2,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[1,2,2,1,2]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>[1,2,2,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>[1,1,6]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>[1,1,5,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>[1,1,4,2]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>[1,1,4,2]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>[1,1,4,1,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>[1,1,3,3]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>[1,1,3,2,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>[1,1,3,3]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>[1,1,3,3]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[1,1,3,2,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>[1,1,3,1,2]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>[1,1,3,1,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>[1,1,6]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>[1,1,5,1]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>[1,1,4,2]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>[1,1,4,1,1]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>[1,1,3,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>[1,1,3,2,1]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6,8]=>[1,1,3,3]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>[1,1,3,3]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>[1,1,3,2,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>[1,1,3,1,2]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[1,1,3,1,2]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>[1,1,3,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>[1,1,1,2,3]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>[1,7]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>[1,6,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6,8]=>[1,5,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>[1,5,2]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>[1,5,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>[1,3,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>[1,3,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>[1,3,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[7,6,8,3,4,2,1,5]=>[5,1,2,4,3,8,6,7]=>[1,3,2,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>[1,3,2,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>[1,2,5]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>[1,2,4,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>[1,2,3,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>[1,2,3,2]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>[1,2,3,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>[1,2,5]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>[1,2,3,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>[1,2,3,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>[1,2,1,4]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[5,1,4,3,2,8,6,7]=>[1,2,1,2,2]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>[1,2,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>[1,1,6]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[5,2,1,3,4,8,6,7]=>[1,1,4,2]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>[1,1,4,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>[1,1,2,4]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>[1,1,2,3,1]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>[1,1,2,2,2]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>[1,1,2,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>[1,1,6]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>[1,1,5,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>[1,1,4,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>[1,1,4,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>[1,1,4,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>[1,1,1,4,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>[1,1,1,3,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>[1,1,1,3,2]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>[1,1,1,3,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>[1,1,6]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>[1,1,4,2]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>[1,1,2,4]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[5,4,1,3,2,6,8,7]=>[1,1,2,3,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6,8]=>[1,1,2,2,2]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>[1,1,2,2,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>[1,1,1,5]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6,8]=>[1,1,1,3,2]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[5,4,2,1,3,8,6,7]=>[1,1,1,3,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>[1,1,1,3,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>[1,1,1,3,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[5,4,3,1,2,8,6,7]=>[1,1,1,3,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>[1,7]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>[1,6,1]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>[1,4,3]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>[1,3,4]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>[1,3,3,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>[1,2,2,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>[1,2,5]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>[1,2,4,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>[1,2,4,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7,8]=>[1,2,2,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>[1,2,2,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>[1,2,1,3,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>[1,2,1,1,2,1]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>[1,1,2,4]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>[1,1,2,3,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>[1,1,2,1,3]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>[1,1,6]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>[1,1,5,1]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>[1,1,3,2,1]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>[1,1,1,5]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>[1,1,1,4,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>[1,1,1,2,3]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>[1,1,1,2,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>[1,1,6]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[6,4,1,2,3,5,8,7]=>[1,1,5,1]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>[1,1,2,4]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>[1,1,1,4,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>[1,1,1,5]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>[1,1,1,4,1]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>[1,1,1,1,3,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7,8]=>[1,1,6]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>[1,1,5,1]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7,8]=>[1,1,3,3]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>[1,1,3,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7,8]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>[1,1,2,3,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,5,1,4,3,2,8,7]=>[1,1,2,1,2,1]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>[1,1,1,4,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>[1,1,1,2,2,1]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>[1,1,1,4,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>[1,1,1,1,3,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>[1,1,1,5]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>[1,1,1,1,3,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>[1,7]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>[1,4,3]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>[1,4,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>[1,3,4]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5,8]=>[1,3,2,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>[1,3,4]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>[1,3,2,2]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>[1,3,1,3]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>[1,2,5]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5,8]=>[1,2,3,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>[1,2,2,3]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4,8]=>[1,2,2,1,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>[1,2,1,4]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>[1,2,1,4]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>[1,2,1,4]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>[1,2,5]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4,8]=>[1,2,3,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>[1,2,2,3]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3,8]=>[1,2,2,1,2]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4,8]=>[1,2,1,2,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>[1,2,1,4]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5,8]=>[1,2,1,1,3]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4,8]=>[1,2,1,4]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>[1,2,1,1,3]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5,8]=>[1,1,3,3]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>[1,1,2,2,2]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>[1,1,2,1,3]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>[1,1,2,2,2]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>[1,1,2,1,3]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>[1,1,6]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>[1,1,4,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>[1,1,3,3]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>[1,1,3,3]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>[1,1,1,3,2]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>[1,1,1,2,3]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4,8]=>[1,1,1,2,1,2]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>[1,1,2,4]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>[1,1,2,2,2]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>[1,1,1,5]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>[1,1,1,3,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>[1,1,1,1,2,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>[1,1,6]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>[1,1,3,3]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>[1,1,2,4]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6,8]=>[1,1,2,1,3]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6,8]=>[1,1,1,5]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6,8]=>[1,1,1,2,3]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6,8]=>[1,1,1,5]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>[1,1,1,2,3]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>[1,1,6]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[8,5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5,8]=>[1,1,3,3]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>[1,1,3,1,2]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4,8]=>[1,1,2,2,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>[1,1,2,4]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>[1,1,2,1,3]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[8,4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4,8]=>[1,1,2,4]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[8,4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4,8]=>[1,1,1,2,3]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3,8]=>[1,1,1,2,1,2]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5,8]=>[1,1,1,5]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5,8]=>[1,1,1,5]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[8,5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5,8]=>[1,1,1,2,3]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>[1,1,1,3,2]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>[1,1,1,2,3]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4,8]=>[1,1,1,1,4]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>[1,1,1,1,2,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[1,7]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>[1,5,2]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>[1,5,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>[1,4,3]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>[1,4,2,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[8,1,2,3,6,4,5,7]=>[1,4,3]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>[1,4,1,2]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>[1,4,3]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[8,1,2,3,7,4,6,5]=>[1,4,2,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>[1,4,1,2]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>[1,3,4]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>[1,3,3,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>[1,3,2,2]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[8,1,2,4,3,7,5,6]=>[1,3,2,2]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>[1,3,2,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>[1,3,4]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>[1,3,1,3]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[6,7,3,4,5,2,1,8]=>[8,1,2,5,4,3,7,6]=>[1,3,1,2,1]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[8,1,2,6,3,4,5,7]=>[1,3,4]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[8,1,2,6,3,5,4,7]=>[1,3,2,2]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>[1,3,4]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>[1,3,3,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[8,1,2,7,3,5,4,6]=>[1,3,2,2]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>[1,3,2,2]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>[1,3,2,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>[1,3,1,2,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[8,1,2,7,5,3,4,6]=>[1,3,1,3]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>[1,3,1,1,2]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>[1,3,1,3]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>[1,3,1,2,1]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[5,3,4,6,7,2,1,8]=>[8,1,2,7,6,4,3,5]=>[1,3,1,1,2]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>[1,2,5]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>[1,2,3,2]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>[1,2,3,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>[1,2,2,3]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>[1,2,2,2,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>[1,2,2,1,2]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[8,1,3,2,7,4,5,6]=>[1,2,2,3]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>[1,2,2,2,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>[1,2,2,1,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[8,1,3,2,7,6,4,5]=>[1,2,2,1,2]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>[1,2,5]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>[1,2,4,1]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[8,1,4,2,3,7,5,6]=>[1,2,3,2]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>[1,2,3,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>[1,2,1,4]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>[1,2,1,3,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>[1,2,1,2,2]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>[1,2,1,2,2]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>[1,2,1,2,1,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[8,1,5,2,3,4,6,7]=>[1,2,5]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[8,1,5,2,3,4,7,6]=>[1,2,4,1]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[7,6,3,4,2,5,1,8]=>[8,1,5,2,4,3,6,7]=>[1,2,2,3]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>[1,2,1,4]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>[1,2,1,3,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>[1,2,1,4]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[8,1,5,4,2,3,7,6]=>[1,2,1,3,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>[1,2,1,1,3]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>[1,2,5]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[8,1,6,2,3,5,4,7]=>[1,2,3,2]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>[1,2,2,3]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>[1,2,2,3]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>[1,2,1,4]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>[1,2,1,2,2]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>[1,2,1,4]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[8,1,6,5,2,3,4,7]=>[1,2,1,4]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[7,3,4,2,5,6,1,8]=>[8,1,6,5,2,4,3,7]=>[1,2,1,2,2]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[8,1,6,5,3,2,4,7]=>[1,2,1,1,3]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>[1,2,5]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>[1,2,3,2]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>[1,2,3,1,1]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[6,5,3,4,2,7,1,8]=>[8,1,7,2,4,3,5,6]=>[1,2,2,3]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>[1,2,2,2,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>[1,2,2,3]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>[1,2,2,1,2]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>[1,2,2,3]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>[1,2,2,2,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>[1,2,2,1,2]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[8,1,7,2,6,5,3,4]=>[1,2,2,1,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>[1,2,2,1,1,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>[1,2,1,2,1,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>[1,2,1,4]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>[1,2,1,3,1]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[8,1,7,4,3,2,5,6]=>[1,2,1,1,3]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>[1,2,1,1,2,1]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[6,4,3,2,5,7,1,8]=>[8,1,7,5,2,3,4,6]=>[1,2,1,4]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>[1,2,1,2,2]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>[1,2,1,1,3]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>[1,2,1,1,3]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>[1,2,1,4]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[8,1,7,6,2,3,5,4]=>[1,2,1,3,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>[1,2,1,2,2]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>[1,2,1,2,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>[1,2,1,1,3]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[8,1,7,6,3,2,5,4]=>[1,2,1,1,2,1]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>[1,2,1,1,1,2]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>[1,2,1,1,3]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>[1,2,1,1,2,1]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>[1,2,1,1,1,2]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>[1,1,5,1]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[8,2,1,3,4,7,5,6]=>[1,1,4,2]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>[1,1,3,1,2]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,3,1,2,8]=>[8,2,1,3,7,4,5,6]=>[1,1,3,3]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[8,2,1,3,7,6,4,5]=>[1,1,3,1,2]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[8,2,1,4,3,5,6,7]=>[1,1,2,4]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>[1,1,2,2,2]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[6,7,4,3,5,1,2,8]=>[8,2,1,5,3,4,7,6]=>[1,1,2,3,1]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>[1,1,2,1,2,1]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>[1,1,2,4]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>[1,1,2,1,3]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[8,2,1,6,5,3,4,7]=>[1,1,2,1,3]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[7,3,4,5,6,1,2,8]=>[8,2,1,6,5,4,3,7]=>[1,1,2,1,1,2]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>[1,1,2,4]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>[1,1,2,1,3]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>[1,1,2,1,1,2]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>[1,1,2,1,3]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>[1,1,2,1,2,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>[1,1,6]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>[1,1,5,1]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>[1,1,4,2]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>[1,1,4,2]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>[1,1,4,1,1]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>[1,1,3,3]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>[1,1,3,3]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>[1,1,3,1,2]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>[1,1,3,3]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>[1,1,3,1,2]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>[1,1,3,1,1,1]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>[1,1,1,4,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>[1,1,1,3,2]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[8,3,2,1,4,7,5,6]=>[1,1,1,3,2]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>[1,1,1,3,1,1]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>[1,1,1,2,3]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>[1,1,1,2,2,1]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>[1,1,1,2,3]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>[1,1,1,2,1,2]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>[1,1,1,2,3]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>[1,1,1,2,2,1]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>[1,1,1,2,1,2]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>[1,1,6]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[8,4,1,2,3,6,5,7]=>[1,1,4,2]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>[1,1,4,2]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[8,4,1,2,3,7,6,5]=>[1,1,4,1,1]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>[1,1,2,4]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>[1,1,2,3,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>[1,1,2,2,2]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[8,4,1,3,2,7,6,5]=>[1,1,2,2,1,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>[1,1,1,4,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>[1,1,1,3,2]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>[1,1,1,3,1,1]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[8,4,3,1,2,5,6,7]=>[1,1,1,5]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>[1,1,1,3,2]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>[1,1,6]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[8,5,1,2,3,4,7,6]=>[1,1,5,1]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>[1,1,3,3]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[8,5,1,2,4,3,7,6]=>[1,1,3,2,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>[1,1,2,4]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>[1,1,2,3,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>[1,1,2,4]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>[1,1,2,3,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[8,5,1,4,3,2,6,7]=>[1,1,2,1,3]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[8,5,1,4,3,2,7,6]=>[1,1,2,1,2,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>[1,1,1,5]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>[1,1,1,2,2,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>[1,1,1,5]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>[1,1,1,4,1]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,3,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[8,5,4,1,3,2,6,7]=>[1,1,1,2,3]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[8,5,4,1,3,2,7,6]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[6,7,2,1,3,4,5,8]=>[8,5,4,3,1,2,7,6]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>[1,1,6]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>[1,1,3,3]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>[1,1,3,3]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>[1,1,3,1,2]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>[1,1,2,4]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>[1,1,2,4]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>[1,1,2,1,3]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>[1,1,2,4]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>[1,1,2,2,2]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>[1,1,2,1,1,2]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>[1,1,1,2,3]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>[1,1,1,2,3]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>[1,1,1,2,1,2]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>[1,1,1,3,2]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>[1,1,1,2,3]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>[1,1,1,3,2]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[8,6,5,2,1,4,3,7]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[7,4,2,1,3,5,6,8]=>[8,6,5,3,1,2,4,7]=>[1,1,1,1,4]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>[1,1,6]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>[1,1,5,1]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[8,7,1,2,3,5,4,6]=>[1,1,4,2]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>[1,1,3,3]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>[1,1,3,2,1]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>[1,1,3,3]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[5,3,4,6,2,1,7,8]=>[8,7,1,2,6,4,3,5]=>[1,1,3,1,2]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>[1,1,3,1,2]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>[1,1,3,1,1,1]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>[1,1,2,3,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>[1,1,2,2,2]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>[1,1,2,2,2]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[8,7,1,4,2,3,6,5]=>[1,1,2,3,1]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[8,7,1,4,3,2,5,6]=>[1,1,2,1,3]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[8,7,1,4,3,2,6,5]=>[1,1,2,1,2,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[8,7,1,5,2,3,4,6]=>[1,1,2,4]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>[1,1,2,1,3]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>[1,1,2,4]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>[1,1,2,3,1]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[5,3,4,2,6,1,7,8]=>[8,7,1,6,2,4,3,5]=>[1,1,2,2,2]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>[1,1,2,2,2]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>[1,1,2,2,1,1]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[4,5,2,3,6,1,7,8]=>[8,7,1,6,3,2,5,4]=>[1,1,2,1,2,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>[1,1,2,1,3]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>[1,1,2,1,1,2]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>[1,1,2,1,3]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>[1,1,1,4,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>[1,1,1,3,2]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>[1,1,1,3,2]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>[1,1,1,2,3]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>[1,1,1,2,2,1]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>[1,1,1,2,1,2]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>[1,1,1,2,3]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[4,5,3,6,1,2,7,8]=>[8,7,2,1,6,3,5,4]=>[1,1,1,2,2,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[8,7,2,1,6,4,3,5]=>[1,1,1,2,1,2]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>[1,1,1,4,1]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>[1,1,1,1,3,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>[1,1,1,1,2,2]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>[1,1,1,5]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>[1,1,1,4,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[8,7,4,1,3,2,5,6]=>[1,1,1,2,3]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[8,7,4,1,3,2,6,5]=>[1,1,1,2,2,1]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>[1,1,1,1,3,1]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[6,5,2,1,3,4,7,8]=>[8,7,4,3,1,2,5,6]=>[1,1,1,1,4]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[8,7,4,3,1,2,6,5]=>[1,1,1,1,3,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>[1,1,1,3,2]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[8,7,5,2,1,4,3,6]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[8,7,5,4,2,1,3,6]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>[1,1,1,3,2]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>[1,1,1,3,2]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>[1,1,1,2,3]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>[1,1,1,2,2,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>[1,1,1,2,3]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>[1,1,1,2,3]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>[1,1,1,2,1,2]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>[1,1,1,2,1,2]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[4,5,3,1,2,6,7,8]=>[8,7,6,2,1,3,5,4]=>[1,1,1,1,3,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>[1,1,1,1,2,2]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[8,7,6,2,1,5,3,4]=>[1,1,1,1,2,2]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[8,7,6,3,1,2,5,4]=>[1,1,1,1,3,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
searching the database
Sorry, this map was not found in the database.