Identifier
Mp00017:
Binary trees
—to 312-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]
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>[2,1]
[[.,[.,.]],.]=>[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]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[1,3,4,2]=>[3,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>[2,2]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,3,4,1]=>[3,1]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,3,1]=>[2,1,1]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,4,2,1]=>[2,1,1]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>[1,3]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>[1,2,1]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[4,2,3,1]=>[1,2,1]
[[[.,[.,.]],.],.]=>[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]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[4,1]
[.,[.,[[.,[.,.]],.]]]=>[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]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[4,1]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[3,1,1]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[3,2]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[3,1,1]
[.,[[.,[.,[.,.]]],.]]=>[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]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[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]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[4,1]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[3,1,1]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[3,1,1]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[2,2,1]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[2,1,1,1]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[3,2]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[2,1,2]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,1,1]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[2,1,1,1]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[2,3]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[2,2,1]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[2,2,1]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,2]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[2,1,1,1]
[[.,[.,[.,[.,.]]]],.]=>[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]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[1,3,1]
[[.,[[.,[.,.]],.]],.]=>[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]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[1,3,1]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[1,2,1,1]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[1,2,2]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[1,2,1,1]
[[[.,[.,[.,.]]],.],.]=>[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]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[1,1,2,1]
[[[[.,[.,.]],.],.],.]=>[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]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[5,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[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]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[5,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[4,1,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[4,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[4,1,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[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]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[3,2,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[5,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[4,1,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[4,1,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[3,2,1]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[3,1,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[4,2]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[3,1,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[4,1,1]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[3,1,1,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[3,3]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[3,2,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[3,2,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[3,1,2]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[3,1,1,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[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]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[2,3,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[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]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[2,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[2,2,2]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[2,2,1,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[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]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[2,1,2,1]
[.,[[[[.,[.,.]],.],.],.]]=>[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]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[5,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[4,1,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[4,1,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[3,2,1]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[3,1,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[4,1,1]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[3,1,1,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[3,2,1]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[3,1,1,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[2,3,1]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[2,2,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[2,2,1,1]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[2,1,2,1]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[4,2]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[3,1,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[3,1,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[2,2,2]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[2,1,1,2]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[4,1,1]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[3,1,1,1]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[3,1,1,1]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[2,2,1,1]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[2,1,3]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[3,2,1]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[3,2,1]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[2,1,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[3,1,2]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[2,1,1,2]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[2,4]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[2,3,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[2,3,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[2,2,2]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[2,2,1,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[2,3,1]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[2,2,1,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[2,2,1,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[2,1,3]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[2,1,2,1]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[2,1,2,1]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,1,2]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[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]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[1,4,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[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]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[1,4,1]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[1,3,1,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[1,3,2]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[1,3,1,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[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]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[1,2,2,1]
[[.,[[[.,[.,.]],.],.]],.]=>[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]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,4,1]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[1,3,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[1,3,1,1]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[1,2,2,1]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[1,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[1,3,2]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[1,2,1,2]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[1,3,1,1]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[1,2,1,1,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[1,2,3]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[1,2,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,2,2,1]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[1,2,1,2]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[1,2,1,1,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[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]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[1,1,3,1]
[[[.,[[.,[.,.]],.]],.],.]=>[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]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[1,1,3,1]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[1,1,2,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[1,1,2,2]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[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]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[1,1,1,2,1]
[[[[[.,[.,.]],.],.],.],.]=>[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]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[6,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[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]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[6,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>[5,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[5,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[5,1,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[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]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[6,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>[5,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>[5,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>[4,2,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[5,2]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>[4,1,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[5,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[4,3]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[4,2,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[4,2,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[4,1,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[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]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[3,3,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[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]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[3,2,2]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[3,2,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[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]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[3,1,2,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[6,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>[5,1,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>[5,1,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>[4,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>[5,1,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>[4,2,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>[3,3,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>[3,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>[3,2,1,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>[3,1,2,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[5,2]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>[4,1,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>[4,1,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>[3,2,2]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>[3,1,1,2]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[5,1,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>[3,2,1,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[4,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>[3,1,3]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[4,2,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>[3,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[4,2,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>[3,1,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[4,1,2]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>[3,1,1,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[3,4]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[3,3,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[3,3,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[3,2,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[3,2,1,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[3,3,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>[3,2,1,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[3,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[3,2,1,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[3,1,3]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[3,1,2,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[3,1,2,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[3,1,1,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[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]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[2,4,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[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]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[2,4,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>[2,3,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[2,3,2]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[2,3,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[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]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[2,2,2,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[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]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>[2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>[2,3,1,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>[2,2,2,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>[2,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[2,3,2]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>[2,2,1,2]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[2,3,1,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>[2,2,1,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[2,2,3]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[2,2,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[2,2,1,2]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[2,2,1,1,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[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]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[2,1,3,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[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]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[2,1,3,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[2,1,2,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[2,1,2,2]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[2,1,2,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[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]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[2,1,1,2,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[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]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[6,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>[5,1,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>[5,1,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>[4,2,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>[5,1,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>[4,2,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>[3,3,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>[3,2,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>[3,2,1,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>[3,1,2,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[5,1,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[3,2,1,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>[4,2,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>[3,1,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>[3,3,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>[3,2,1,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>[3,2,1,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>[3,1,2,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>[2,4,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>[2,3,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>[2,3,1,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>[2,2,2,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>[2,2,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>[2,3,1,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>[2,2,1,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>[2,2,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>[2,2,1,1,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>[2,1,3,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>[2,1,2,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>[2,1,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>[2,1,1,2,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[5,2]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>[4,1,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>[4,1,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>[3,2,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>[3,1,1,2]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>[4,1,2]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>[3,1,1,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>[3,2,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>[3,1,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>[2,3,2]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>[2,2,1,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>[2,2,1,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>[2,1,2,2]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[2,1,1,1,2]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>[3,2,1,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>[3,2,1,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>[2,3,1,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>[2,2,1,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[2,2,1,1,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[2,1,2,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[4,3]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>[3,1,3]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>[3,1,3]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>[2,2,3]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>[2,1,1,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[4,2,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>[3,1,2,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>[3,1,2,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>[2,2,2,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[2,1,1,2,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[4,2,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>[3,1,2,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>[3,1,2,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>[2,2,2,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[2,1,1,2,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[4,1,2]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>[3,1,1,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>[3,1,1,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>[2,2,1,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[2,1,1,1,2]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>[2,2,1,1,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[3,4]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>[2,1,4]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[3,3,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>[2,1,3,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[3,3,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>[2,1,3,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[3,2,2]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>[2,1,2,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[3,2,1,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[2,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[3,3,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>[2,1,3,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>[3,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[2,1,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[3,2,2]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[2,1,2,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[3,2,1,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[2,1,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[3,1,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>[2,1,1,3]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[3,1,2,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[2,1,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[3,1,2,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[2,1,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[3,1,1,2]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[2,1,1,1,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[2,5]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[2,4,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[2,4,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[2,3,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[2,3,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[2,4,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>[2,3,1,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[2,3,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[2,3,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[2,2,3]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[2,2,2,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[2,2,2,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[2,2,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[2,2,1,1,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[2,4,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>[2,3,1,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>[2,3,1,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>[2,2,2,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[2,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[2,3,1,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[2,2,1,1,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[2,2,3]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[2,2,2,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[2,2,1,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[2,1,4]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[2,1,3,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[2,1,3,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[2,1,2,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[2,1,2,1,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[2,1,3,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[2,1,2,1,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[2,1,2,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[2,1,1,3]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[2,1,1,2,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[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]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[1,5,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[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]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[1,5,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>[1,4,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[1,4,2]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[1,4,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[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]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[1,3,2,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[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]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[1,5,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>[1,4,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>[1,4,1,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>[1,3,2,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>[1,3,1,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[1,4,2]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>[1,3,1,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[1,4,1,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>[1,3,1,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[1,3,3]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[1,3,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[1,3,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[1,3,1,2]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[1,3,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[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]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[1,2,3,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[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]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[1,2,3,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>[1,2,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[1,2,2,2]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[1,2,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[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]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[1,2,1,2,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[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]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,5,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>[1,4,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>[1,4,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>[1,3,2,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>[1,3,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>[1,4,1,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[1,3,1,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>[1,3,2,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>[1,3,1,1,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>[1,2,3,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>[1,2,2,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>[1,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>[1,2,1,2,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[1,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>[1,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>[1,3,1,2]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>[1,2,2,2]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[1,2,1,1,2]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[1,4,1,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>[1,3,1,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>[1,3,1,1,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>[1,2,2,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[1,3,3]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>[1,2,1,3]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[1,3,2,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[1,2,1,2,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[1,3,2,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[1,2,1,2,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[1,3,1,2]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[1,2,1,1,2]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[1,2,4]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[1,2,3,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[1,2,3,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[1,2,2,2]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[1,2,2,1,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[1,2,3,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[1,2,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[1,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[1,2,1,3]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[1,2,1,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[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]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[1,1,4,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[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]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[1,1,4,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>[1,1,3,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[1,1,3,2]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[1,1,3,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[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]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[1,1,2,2,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[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]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[1,1,4,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>[1,1,3,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>[1,1,3,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>[1,1,2,2,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[1,1,3,2]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[1,1,2,1,2]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[1,1,2,3]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[1,1,2,2,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[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]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[1,1,1,3,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[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]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[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]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[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]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>[7,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[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]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[1,2,3,4,6,7,8,5]=>[7,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6]=>[6,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[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]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[1,2,3,4,8,6,7,5]=>[5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[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]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,4]=>[7,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[1,2,3,5,8,6,7,4]=>[5,2,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[1,2,3,6,7,8,4,5]=>[6,2]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[1,2,3,6,8,7,4,5]=>[5,1,2]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[1,2,3,7,8,4,5,6]=>[5,3]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[1,2,3,7,8,4,6,5]=>[5,2,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[1,2,3,7,8,5,6,4]=>[5,2,1]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[1,2,3,7,8,6,4,5]=>[5,1,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[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]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[1,2,3,8,4,6,7,5]=>[4,3,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[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]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[1,2,3,8,5,6,7,4]=>[4,3,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[1,2,3,8,5,7,6,4]=>[4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[1,2,3,8,6,7,4,5]=>[4,2,2]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[1,2,3,8,6,7,5,4]=>[4,2,1,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[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]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[1,2,3,8,7,5,6,4]=>[4,1,2,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[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]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[1,2,4,5,6,7,8,3]=>[7,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[1,2,4,5,8,6,7,3]=>[5,2,1]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[3,6,7,8,5,4,2,1]=>[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[1,2,4,8,5,6,7,3]=>[4,3,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[3,6,5,7,8,4,2,1]=>[1,2,4,8,7,5,6,3]=>[4,1,2,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,2,5,6,7,8,3,4]=>[6,2]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,2,5,6,8,7,3,4]=>[5,1,2]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[1,2,5,7,8,6,3,4]=>[5,1,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[1,2,5,8,6,7,3,4]=>[4,2,2]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[1,2,5,8,7,6,3,4]=>[4,1,1,2]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[3,4,7,8,6,5,2,1]=>[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[3,4,6,8,7,5,2,1]=>[1,2,5,7,8,6,4,3]=>[5,1,1,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[1,2,5,8,6,7,4,3]=>[4,2,1,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,2,6,8,7,3,4,5]=>[4,1,3]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[1,2,6,8,7,3,5,4]=>[4,1,2,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>[1,2,6,8,7,4,5,3]=>[4,1,2,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[1,2,6,7,8,5,3,4]=>[5,1,2]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[1,2,6,8,7,5,3,4]=>[4,1,1,2]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,2,7,8,3,4,5,6]=>[4,4]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[1,2,7,8,3,4,6,5]=>[4,3,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[1,2,7,8,3,5,6,4]=>[4,3,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,2,7,8,3,6,4,5]=>[4,2,2]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[1,2,7,8,3,6,5,4]=>[4,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[3,6,5,4,8,7,2,1]=>[1,2,7,8,4,5,6,3]=>[4,3,1]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[3,5,6,4,8,7,2,1]=>[1,2,7,8,4,6,5,3]=>[4,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4]=>[4,2,2]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[3,4,6,5,8,7,2,1]=>[1,2,7,8,5,6,4,3]=>[4,2,1,1]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,2,7,8,6,3,4,5]=>[4,1,3]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[3,5,4,6,8,7,2,1]=>[1,2,7,8,6,4,5,3]=>[4,1,2,1]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[1,2,7,8,6,5,3,4]=>[4,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[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]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[1,2,8,3,4,6,7,5]=>[3,4,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[1,2,8,3,5,6,7,4]=>[3,4,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[4,6,7,5,3,8,2,1]=>[1,2,8,3,5,7,6,4]=>[3,3,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[1,2,8,3,6,7,4,5]=>[3,3,2]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>[3,2,3]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[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]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[1,2,8,4,5,6,7,3]=>[3,4,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[1,2,8,4,5,7,6,3]=>[3,3,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[1,2,8,4,6,7,5,3]=>[3,3,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[1,2,8,4,7,6,5,3]=>[3,2,1,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[1,2,8,5,6,7,3,4]=>[3,3,2]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[4,3,6,7,5,8,2,1]=>[1,2,8,5,7,6,3,4]=>[3,2,1,2]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[1,2,8,6,7,3,4,5]=>[3,2,3]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[1,2,8,6,7,3,5,4]=>[3,2,2,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[1,2,8,6,7,4,5,3]=>[3,2,2,1]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[1,2,8,6,7,5,3,4]=>[3,2,1,2]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[1,2,8,6,7,5,4,3]=>[3,2,1,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[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]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[4,6,5,3,7,8,2,1]=>[1,2,8,7,3,5,6,4]=>[3,1,3,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>[3,1,2,1,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>[1,2,8,7,4,5,6,3]=>[3,1,3,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[1,2,8,7,5,6,3,4]=>[3,1,2,2]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[1,2,8,7,5,6,4,3]=>[3,1,2,1,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[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]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[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]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[1,3,4,5,6,7,8,2]=>[7,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[1,3,4,5,6,8,7,2]=>[6,1,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[1,3,4,5,8,6,7,2]=>[5,2,1]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[2,5,7,8,6,4,3,1]=>[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[1,3,4,7,8,5,6,2]=>[5,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[1,3,4,7,8,6,5,2]=>[5,1,1,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[1,3,4,8,5,6,7,2]=>[4,3,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[1,3,4,8,6,7,5,2]=>[4,2,1,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[2,4,7,6,8,5,3,1]=>[1,3,5,8,6,7,4,2]=>[4,2,1,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[2,4,5,8,7,6,3,1]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[1,3,7,8,4,5,6,2]=>[4,3,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[1,3,7,8,4,6,5,2]=>[4,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[1,3,7,8,5,6,4,2]=>[4,2,1,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[1,3,8,4,5,6,7,2]=>[3,4,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[2,5,7,6,4,8,3,1]=>[1,3,8,4,6,7,5,2]=>[3,3,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[1,3,8,5,6,7,4,2]=>[3,3,1,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[1,3,8,5,7,6,4,2]=>[3,2,1,1,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[1,3,8,7,4,5,6,2]=>[3,1,3,1]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[1,3,8,7,4,6,5,2]=>[3,1,2,1,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[1,3,8,7,5,6,4,2]=>[3,1,2,1,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[1,4,5,6,7,8,2,3]=>[6,2]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[1,4,5,7,8,6,2,3]=>[5,1,2]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[3,2,6,7,8,5,4,1]=>[1,4,5,8,7,6,2,3]=>[4,1,1,2]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[1,4,6,7,8,5,2,3]=>[5,1,2]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[1,4,6,8,7,5,2,3]=>[4,1,1,2]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[1,4,7,8,5,6,2,3]=>[4,2,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[1,4,8,5,6,7,2,3]=>[3,3,2]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[1,4,8,5,7,6,2,3]=>[3,2,1,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[1,4,8,7,6,5,2,3]=>[3,1,1,1,2]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[2,3,7,6,8,5,4,1]=>[1,4,5,8,6,7,3,2]=>[4,2,1,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[1,4,7,8,5,6,3,2]=>[4,2,1,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[1,4,8,5,6,7,3,2]=>[3,3,1,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[1,4,8,6,7,5,3,2]=>[3,2,1,1,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,5,6,7,8,2,3,4]=>[5,3]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[1,5,6,8,7,2,3,4]=>[4,1,3]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[1,5,7,8,6,2,3,4]=>[4,1,3]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[4,3,2,7,6,8,5,1]=>[1,5,8,6,7,2,3,4]=>[3,2,3]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,5,8,7,6,2,3,4]=>[3,1,1,3]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[1,5,6,7,8,2,4,3]=>[5,2,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[1,5,7,8,6,2,4,3]=>[4,1,2,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[1,5,8,7,6,2,4,3]=>[3,1,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[1,5,6,7,8,3,4,2]=>[5,2,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[2,4,3,7,8,6,5,1]=>[1,5,6,8,7,3,4,2]=>[4,1,2,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[1,5,7,8,6,3,4,2]=>[4,1,2,1]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[2,4,3,7,6,8,5,1]=>[1,5,8,6,7,3,4,2]=>[3,2,2,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[1,5,8,7,6,3,4,2]=>[3,1,1,2,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,5,6,7,8,4,2,3]=>[5,1,2]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[3,2,4,6,8,7,5,1]=>[1,5,7,8,6,4,2,3]=>[4,1,1,2]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[3,2,4,6,7,8,5,1]=>[1,5,8,7,6,4,2,3]=>[3,1,1,1,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>[1,5,8,6,7,4,3,2]=>[3,2,1,1,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>[4,4]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[1,6,8,7,2,3,4,5]=>[3,1,4]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[1,6,7,8,2,3,5,4]=>[4,3,1]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[1,6,8,7,2,3,5,4]=>[3,1,3,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[1,6,7,8,2,5,3,4]=>[4,2,2]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[3,4,5,2,8,7,6,1]=>[1,6,7,8,2,5,4,3]=>[4,2,1,1]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[1,6,8,7,2,5,4,3]=>[3,1,2,1,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[1,6,7,8,3,4,5,2]=>[4,3,1]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[1,6,8,7,3,4,5,2]=>[3,1,3,1]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[1,6,7,8,3,5,4,2]=>[4,2,1,1]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[1,6,8,7,3,5,4,2]=>[3,1,2,1,1]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[3,2,5,4,7,8,6,1]=>[1,6,8,7,4,5,2,3]=>[3,1,2,2]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[1,6,7,8,4,5,3,2]=>[4,2,1,1]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[1,6,8,7,4,5,3,2]=>[3,1,2,1,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[1,6,7,8,5,2,3,4]=>[4,1,3]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[1,6,8,7,5,2,3,4]=>[3,1,1,3]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[1,6,7,8,5,2,4,3]=>[4,1,2,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[1,6,7,8,5,3,4,2]=>[4,1,2,1]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[2,4,3,5,7,8,6,1]=>[1,6,8,7,5,3,4,2]=>[3,1,1,2,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[3,2,4,5,8,7,6,1]=>[1,6,7,8,5,4,2,3]=>[4,1,1,2]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>[3,5]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[1,7,8,2,3,5,6,4]=>[3,4,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,7,8,2,3,6,4,5]=>[3,3,2]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[1,7,8,2,3,6,5,4]=>[3,3,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[1,7,8,2,4,5,6,3]=>[3,4,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[1,7,8,2,4,6,5,3]=>[3,3,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[1,7,8,2,5,6,3,4]=>[3,3,2]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[3,4,6,5,2,8,7,1]=>[1,7,8,2,5,6,4,3]=>[3,3,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[1,7,8,2,6,3,4,5]=>[3,2,3]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[1,7,8,2,6,3,5,4]=>[3,2,2,1]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[1,7,8,2,6,5,4,3]=>[3,2,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[1,7,8,3,4,5,6,2]=>[3,4,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[1,7,8,3,5,6,4,2]=>[3,3,1,1]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[2,5,4,6,3,8,7,1]=>[1,7,8,3,6,4,5,2]=>[3,2,2,1]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[1,7,8,3,6,5,4,2]=>[3,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[1,7,8,4,5,6,2,3]=>[3,3,2]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[3,2,5,6,4,8,7,1]=>[1,7,8,4,6,5,2,3]=>[3,2,1,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[1,7,8,5,6,3,4,2]=>[3,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[1,7,8,5,6,4,2,3]=>[3,2,1,2]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[1,7,8,5,6,4,3,2]=>[3,2,1,1,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[1,7,8,6,2,3,4,5]=>[3,1,4]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[3,5,4,2,6,8,7,1]=>[1,7,8,6,2,4,5,3]=>[3,1,3,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[1,7,8,6,2,5,4,3]=>[3,1,2,1,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[1,7,8,6,3,4,5,2]=>[3,1,3,1]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>[1,7,8,6,3,5,4,2]=>[3,1,2,1,1]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[3,2,5,4,6,8,7,1]=>[1,7,8,6,4,5,2,3]=>[3,1,2,2]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[2,3,5,4,6,8,7,1]=>[1,7,8,6,4,5,3,2]=>[3,1,2,1,1]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[1,7,8,6,5,2,3,4]=>[3,1,1,3]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[1,7,8,6,5,3,4,2]=>[3,1,1,2,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[2,6]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[1,8,2,3,4,6,7,5]=>[2,5,1]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[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]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[1,8,2,3,5,6,7,4]=>[2,5,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[5,4,7,6,3,2,8,1]=>[1,8,2,3,6,7,4,5]=>[2,4,2]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[1,8,2,3,6,7,5,4]=>[2,4,1,1]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[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]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[1,8,2,3,7,5,6,4]=>[2,3,2,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[1,8,2,4,5,6,7,3]=>[2,5,1]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[3,6,7,5,4,2,8,1]=>[1,8,2,4,5,7,6,3]=>[2,4,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[1,8,2,4,6,7,5,3]=>[2,4,1,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[1,8,2,4,7,5,6,3]=>[2,3,2,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[1,8,2,4,7,6,5,3]=>[2,3,1,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[1,8,2,5,6,7,3,4]=>[2,4,2]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[1,8,2,5,7,6,3,4]=>[2,3,1,2]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[1,8,2,5,6,7,4,3]=>[2,4,1,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[1,8,2,5,7,6,4,3]=>[2,3,1,1,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[1,8,2,6,7,3,4,5]=>[2,3,3]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[4,3,5,7,6,2,8,1]=>[1,8,2,6,7,5,3,4]=>[2,3,1,2]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>[1,8,2,6,7,5,4,3]=>[2,3,1,1,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[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]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[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]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[1,8,2,7,4,5,6,3]=>[2,2,3,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[1,8,2,7,4,6,5,3]=>[2,2,2,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,8,2,7,5,6,3,4]=>[2,2,2,2]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[1,8,2,7,5,6,4,3]=>[2,2,2,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[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]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[1,8,2,7,6,4,5,3]=>[2,2,1,2,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[1,8,3,4,6,7,5,2]=>[2,4,1,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[1,8,3,4,7,6,5,2]=>[2,3,1,1,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[1,8,3,5,7,6,4,2]=>[2,3,1,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[1,8,3,6,7,4,5,2]=>[2,3,2,1]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[1,8,3,6,7,5,4,2]=>[2,3,1,1,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[2,6,5,4,7,3,8,1]=>[1,8,3,7,4,5,6,2]=>[2,2,3,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[1,8,3,7,5,6,4,2]=>[2,2,2,1,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[1,8,3,7,6,4,5,2]=>[2,2,1,2,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[1,8,3,7,6,5,4,2]=>[2,2,1,1,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[3,2,7,6,5,4,8,1]=>[1,8,4,5,6,7,2,3]=>[2,4,2]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,8,4,5,7,6,2,3]=>[2,3,1,2]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[1,8,4,6,7,5,2,3]=>[2,3,1,2]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[1,8,4,7,5,6,2,3]=>[2,2,2,2]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,8,4,7,6,5,2,3]=>[2,2,1,1,2]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[1,8,4,5,6,7,3,2]=>[2,4,1,1]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[2,3,6,7,5,4,8,1]=>[1,8,4,5,7,6,3,2]=>[2,3,1,1,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[1,8,4,6,7,5,3,2]=>[2,3,1,1,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[1,8,4,7,6,5,3,2]=>[2,2,1,1,1,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[1,8,5,6,7,2,3,4]=>[2,3,3]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[1,8,5,7,6,2,3,4]=>[2,2,1,3]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[1,8,5,6,7,2,4,3]=>[2,3,2,1]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[1,8,5,7,6,2,4,3]=>[2,2,1,2,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[1,8,5,6,7,3,4,2]=>[2,3,2,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[1,8,5,6,7,4,2,3]=>[2,3,1,2]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[3,2,4,6,7,5,8,1]=>[1,8,5,7,6,4,2,3]=>[2,2,1,1,2]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[1,8,5,6,7,4,3,2]=>[2,3,1,1,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,8,6,7,2,3,4,5]=>[2,2,4]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[4,5,3,2,7,6,8,1]=>[1,8,6,7,2,3,5,4]=>[2,2,3,1]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[3,5,4,2,7,6,8,1]=>[1,8,6,7,2,4,5,3]=>[2,2,3,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,8,6,7,2,5,3,4]=>[2,2,2,2]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[1,8,6,7,2,5,4,3]=>[2,2,2,1,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[1,8,6,7,3,4,5,2]=>[2,2,3,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,8,6,7,4,5,2,3]=>[2,2,2,2]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[1,8,6,7,4,5,3,2]=>[2,2,2,1,1]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,8,6,7,5,2,3,4]=>[2,2,1,3]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[3,4,2,5,7,6,8,1]=>[1,8,6,7,5,2,4,3]=>[2,2,1,2,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[1,8,6,7,5,3,4,2]=>[2,2,1,2,1]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[1,8,6,7,5,4,3,2]=>[2,2,1,1,1,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>[2,1,5]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[4,6,5,3,2,7,8,1]=>[1,8,7,2,3,5,6,4]=>[2,1,4,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[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]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[1,8,7,2,4,5,6,3]=>[2,1,4,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[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]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[1,8,7,2,6,4,5,3]=>[2,1,2,2,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[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]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[1,8,7,3,4,5,6,2]=>[2,1,4,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[2,5,6,4,3,7,8,1]=>[1,8,7,3,4,6,5,2]=>[2,1,3,1,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[1,8,7,3,6,4,5,2]=>[2,1,2,2,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[3,2,6,5,4,7,8,1]=>[1,8,7,4,5,6,2,3]=>[2,1,3,2]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[1,8,7,4,6,5,3,2]=>[2,1,2,1,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[1,8,7,5,6,3,4,2]=>[2,1,2,2,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[1,8,7,5,6,4,3,2]=>[2,1,2,1,1,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[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]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[1,8,7,6,2,4,5,3]=>[2,1,1,3,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[1,8,7,6,3,4,5,2]=>[2,1,1,3,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[1,8,7,6,4,5,2,3]=>[2,1,1,2,2]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[1,8,7,6,4,5,3,2]=>[2,1,1,2,1,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[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]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[2,3,4,5,7,8,6,1]=>[6,1,1]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[2,3,4,5,8,6,7,1]=>[5,2,1]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[2,3,4,7,8,5,6,1]=>[5,2,1]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,3,4,8,5,6,7,1]=>[4,3,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[2,3,4,8,5,7,6,1]=>[4,2,1,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[2,3,4,8,6,7,5,1]=>[4,2,1,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,3,4,8,7,5,6,1]=>[4,1,2,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[2,3,5,8,6,7,4,1]=>[4,2,1,1]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>[2,3,7,8,4,5,6,1]=>[4,3,1]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[2,3,7,8,5,6,4,1]=>[4,2,1,1]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[2,3,7,8,6,4,5,1]=>[4,1,2,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,3,8,4,5,6,7,1]=>[3,4,1]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,6,7,5,4,8,3,2]=>[2,3,8,4,5,7,6,1]=>[3,3,1,1]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,5,7,6,4,8,3,2]=>[2,3,8,4,6,7,5,1]=>[3,3,1,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[2,3,8,4,7,5,6,1]=>[3,2,2,1]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,5,6,7,4,8,3,2]=>[2,3,8,4,7,6,5,1]=>[3,2,1,1,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[2,3,8,5,6,7,4,1]=>[3,3,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[2,3,8,5,7,6,4,1]=>[3,2,1,1,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,5,4,7,6,8,3,2]=>[2,3,8,6,7,4,5,1]=>[3,2,2,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,3,8,7,4,5,6,1]=>[3,1,3,1]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,5,6,4,7,8,3,2]=>[2,3,8,7,4,6,5,1]=>[3,1,2,1,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,4,6,5,7,8,3,2]=>[2,3,8,7,5,6,4,1]=>[3,1,2,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[2,3,8,7,6,4,5,1]=>[3,1,1,2,1]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[2,4,5,6,7,8,3,1]=>[6,1,1]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[2,4,5,8,6,7,3,1]=>[4,2,1,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[2,4,7,8,5,6,3,1]=>[4,2,1,1]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[2,4,8,5,6,7,3,1]=>[3,3,1,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[2,4,8,5,7,6,3,1]=>[3,2,1,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[2,4,8,6,7,5,3,1]=>[3,2,1,1,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[2,4,8,7,5,6,3,1]=>[3,1,2,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[2,5,6,7,8,3,4,1]=>[5,2,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[2,5,6,8,7,3,4,1]=>[4,1,2,1]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[2,5,7,8,6,3,4,1]=>[4,1,2,1]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,5,8,6,7,3,4,1]=>[3,2,2,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[2,5,8,6,7,4,3,1]=>[3,2,1,1,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[2,6,7,8,3,4,5,1]=>[4,3,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[2,6,7,8,3,5,4,1]=>[4,2,1,1]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[2,6,7,8,4,5,3,1]=>[4,2,1,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[2,6,8,7,4,5,3,1]=>[3,1,2,1,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,6,7,8,5,3,4,1]=>[4,1,2,1]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[2,7,8,3,4,6,5,1]=>[3,3,1,1]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[2,7,8,3,5,6,4,1]=>[3,3,1,1]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,5,4,6,3,8,7,2]=>[2,7,8,3,6,4,5,1]=>[3,2,2,1]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,4,5,6,3,8,7,2]=>[2,7,8,3,6,5,4,1]=>[3,2,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[2,7,8,4,5,6,3,1]=>[3,3,1,1]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,7,8,5,6,3,4,1]=>[3,2,2,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[2,7,8,6,3,4,5,1]=>[3,1,3,1]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[2,7,8,6,3,5,4,1]=>[3,1,2,1,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,3,5,4,6,8,7,2]=>[2,7,8,6,4,5,3,1]=>[3,1,2,1,1]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[2,8,3,4,5,7,6,1]=>[2,4,1,1]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,5,7,6,4,3,8,2]=>[2,8,3,4,6,7,5,1]=>[2,4,1,1]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[2,8,3,5,6,7,4,1]=>[2,4,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[2,8,3,5,7,6,4,1]=>[2,3,1,1,1]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[2,8,3,6,7,5,4,1]=>[2,3,1,1,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,6,5,4,7,3,8,2]=>[2,8,3,7,4,5,6,1]=>[2,2,3,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[2,8,3,7,4,6,5,1]=>[2,2,2,1,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>[2,8,3,7,5,6,4,1]=>[2,2,2,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[2,8,3,7,6,4,5,1]=>[2,2,1,2,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[2,8,3,7,6,5,4,1]=>[2,2,1,1,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,3,7,6,5,4,8,2]=>[2,8,4,5,6,7,3,1]=>[2,4,1,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[2,8,4,6,7,5,3,1]=>[2,3,1,1,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[2,8,5,6,7,4,3,1]=>[2,3,1,1,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[2,8,6,7,4,5,3,1]=>[2,2,2,1,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[2,8,7,3,4,5,6,1]=>[2,1,4,1]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,5,6,4,3,7,8,2]=>[2,8,7,3,4,6,5,1]=>[2,1,3,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,3,6,5,4,7,8,2]=>[2,8,7,4,5,6,3,1]=>[2,1,3,1,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[2,8,7,5,6,4,3,1]=>[2,1,2,1,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,8,7,6,3,4,5,1]=>[2,1,1,3,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[2,8,7,6,4,5,3,1]=>[2,1,1,2,1,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[2,8,7,6,5,3,4,1]=>[2,1,1,1,2,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[6,2]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[3,4,5,6,8,7,1,2]=>[5,1,2]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[3,4,5,7,8,6,1,2]=>[5,1,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[3,4,5,8,6,7,1,2]=>[4,2,2]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[3,4,5,8,7,6,1,2]=>[4,1,1,2]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[3,4,6,7,8,5,1,2]=>[5,1,2]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[3,4,6,8,7,5,1,2]=>[4,1,1,2]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[3,4,7,8,5,6,1,2]=>[4,2,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[3,4,8,5,6,7,1,2]=>[3,3,2]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[3,4,8,5,7,6,1,2]=>[3,2,1,2]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[3,4,8,6,7,5,1,2]=>[3,2,1,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[3,4,8,7,5,6,1,2]=>[3,1,2,2]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[3,4,8,7,6,5,1,2]=>[3,1,1,1,2]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[3,5,6,7,8,4,1,2]=>[5,1,2]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[3,5,6,8,7,4,1,2]=>[4,1,1,2]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[3,5,7,8,6,4,1,2]=>[4,1,1,2]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[3,5,8,6,7,4,1,2]=>[3,2,1,2]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[3,5,8,7,6,4,1,2]=>[3,1,1,1,2]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[3,6,8,7,4,5,1,2]=>[3,1,2,2]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[3,6,7,8,5,4,1,2]=>[4,1,1,2]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>[3,7,8,4,6,5,1,2]=>[3,2,1,2]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[3,7,8,5,6,4,1,2]=>[3,2,1,2]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[3,7,8,6,4,5,1,2]=>[3,1,2,2]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[3,7,8,6,5,4,1,2]=>[3,1,1,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[3,8,4,5,6,7,1,2]=>[2,4,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[3,8,4,7,5,6,1,2]=>[2,2,2,2]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[3,8,6,7,4,5,1,2]=>[2,2,2,2]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[3,8,7,4,5,6,1,2]=>[2,1,3,2]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,2,6,8,7,5,4,3]=>[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[3,4,5,8,6,7,2,1]=>[4,2,1,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[3,4,8,5,6,7,2,1]=>[3,3,1,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[3,4,8,7,5,6,2,1]=>[3,1,2,1,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[3,5,8,6,7,4,2,1]=>[3,2,1,1,1]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[3,6,7,8,4,5,2,1]=>[4,2,1,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>[3,6,8,7,4,5,2,1]=>[3,1,2,1,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[3,7,8,4,5,6,2,1]=>[3,3,1,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[3,7,8,5,6,4,2,1]=>[3,2,1,1,1]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>[3,7,8,6,4,5,2,1]=>[3,1,2,1,1]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[3,8,4,5,6,7,2,1]=>[2,4,1,1]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,2,6,7,5,4,8,3]=>[3,8,4,5,7,6,2,1]=>[2,3,1,1,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,2,6,5,7,4,8,3]=>[3,8,4,7,5,6,2,1]=>[2,2,2,1,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[3,8,4,7,6,5,2,1]=>[2,2,1,1,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[3,8,5,6,7,4,2,1]=>[2,3,1,1,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[3,8,5,7,6,4,2,1]=>[2,2,1,1,1,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[3,8,7,4,5,6,2,1]=>[2,1,3,1,1]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[3,8,7,4,6,5,2,1]=>[2,1,2,1,1,1]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[3,8,7,5,6,4,2,1]=>[2,1,2,1,1,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,8,7,6,4,5,2,1]=>[2,1,1,2,1,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[4,5,6,7,8,1,2,3]=>[5,3]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[4,5,6,8,7,1,2,3]=>[4,1,3]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[4,5,7,8,6,1,2,3]=>[4,1,3]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[4,5,8,6,7,1,2,3]=>[3,2,3]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[4,5,8,7,6,1,2,3]=>[3,1,1,3]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[4,6,7,8,5,1,2,3]=>[4,1,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[4,6,8,7,5,1,2,3]=>[3,1,1,3]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[4,7,8,5,6,1,2,3]=>[3,2,3]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[4,7,8,6,5,1,2,3]=>[3,1,1,3]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[4,8,5,6,7,1,2,3]=>[2,3,3]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[4,8,5,7,6,1,2,3]=>[2,2,1,3]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[4,8,6,7,5,1,2,3]=>[2,2,1,3]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[4,8,7,5,6,1,2,3]=>[2,1,2,3]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,8,7,6,5,1,2,3]=>[2,1,1,1,3]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[4,5,6,7,8,1,3,2]=>[5,2,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[4,5,8,6,7,1,3,2]=>[3,2,2,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[4,5,8,7,6,1,3,2]=>[3,1,1,2,1]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[4,6,7,8,5,1,3,2]=>[4,1,2,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[4,7,8,5,6,1,3,2]=>[3,2,2,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[4,8,5,6,7,1,3,2]=>[2,3,2,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[4,8,5,7,6,1,3,2]=>[2,2,1,2,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[4,8,6,7,5,1,3,2]=>[2,2,1,2,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[4,8,7,5,6,1,3,2]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,8,7,6,5,1,3,2]=>[2,1,1,1,2,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[4,5,6,7,8,2,3,1]=>[5,2,1]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[4,5,7,8,6,2,3,1]=>[4,1,2,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[4,5,8,6,7,2,3,1]=>[3,2,2,1]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[4,6,7,8,5,2,3,1]=>[4,1,2,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[4,6,8,7,5,2,3,1]=>[3,1,1,2,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[4,7,8,5,6,2,3,1]=>[3,2,2,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[4,8,5,6,7,2,3,1]=>[2,3,2,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[4,8,6,7,5,2,3,1]=>[2,2,1,2,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[4,8,7,5,6,2,3,1]=>[2,1,2,2,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>[2,1,1,1,2,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2]=>[5,1,2]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>[4,1,1,2]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[4,5,7,8,6,3,1,2]=>[4,1,1,2]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[4,6,7,8,5,3,1,2]=>[4,1,1,2]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[4,6,8,7,5,3,1,2]=>[3,1,1,1,2]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[4,8,5,6,7,3,1,2]=>[2,3,1,2]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[4,8,6,7,5,3,1,2]=>[2,2,1,1,2]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[4,8,7,5,6,3,1,2]=>[2,1,2,1,2]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[4,8,7,6,5,3,1,2]=>[2,1,1,1,1,2]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,5,8,6,7,3,2,1]=>[3,2,1,1,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[4,7,8,5,6,3,2,1]=>[3,2,1,1,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,8,5,6,7,3,2,1]=>[2,3,1,1,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[4,8,5,7,6,3,2,1]=>[2,2,1,1,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[4,8,6,7,5,3,2,1]=>[2,2,1,1,1,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[4,8,7,5,6,3,2,1]=>[2,1,2,1,1,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[5,6,8,7,1,2,3,4]=>[3,1,4]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[5,7,8,6,1,2,3,4]=>[3,1,4]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[5,8,6,7,1,2,3,4]=>[2,2,4]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,8,7,6,1,2,3,4]=>[2,1,1,4]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[5,6,7,8,1,2,4,3]=>[4,3,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[5,7,8,6,1,2,4,3]=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[5,8,6,7,1,2,4,3]=>[2,2,3,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,8,7,6,1,2,4,3]=>[2,1,1,3,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[5,6,7,8,1,3,4,2]=>[4,3,1]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[5,6,8,7,1,3,4,2]=>[3,1,3,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[5,7,8,6,1,3,4,2]=>[3,1,3,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>[2,2,3,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[5,8,7,6,1,3,4,2]=>[2,1,1,3,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[5,6,7,8,1,4,2,3]=>[4,2,2]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[5,6,8,7,1,4,2,3]=>[3,1,2,2]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>[3,1,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[5,8,6,7,1,4,2,3]=>[2,2,2,2]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,8,7,6,1,4,2,3]=>[2,1,1,2,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[5,6,7,8,1,4,3,2]=>[4,2,1,1]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[5,6,8,7,1,4,3,2]=>[3,1,2,1,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[5,7,8,6,1,4,3,2]=>[3,1,2,1,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[5,8,6,7,1,4,3,2]=>[2,2,2,1,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[2,1,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1]=>[4,3,1]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[5,7,8,6,2,3,4,1]=>[3,1,3,1]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[5,8,6,7,2,3,4,1]=>[2,2,3,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[5,8,7,6,2,3,4,1]=>[2,1,1,3,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,6,7,8,2,4,3,1]=>[4,2,1,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[5,6,8,7,2,4,3,1]=>[3,1,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[5,7,8,6,2,4,3,1]=>[3,1,2,1,1]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[5,8,6,7,2,4,3,1]=>[2,2,2,1,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,6,8,7,3,4,1,2]=>[3,1,2,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,7,8,6,3,4,1,2]=>[3,1,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,8,6,7,3,4,1,2]=>[2,2,2,2]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[5,7,8,6,3,4,2,1]=>[3,1,2,1,1]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[5,8,6,7,3,4,2,1]=>[2,2,2,1,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3]=>[4,1,3]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,6,8,7,4,1,2,3]=>[3,1,1,3]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[5,7,8,6,4,1,2,3]=>[3,1,1,3]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[5,8,6,7,4,1,2,3]=>[2,2,1,3]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[5,8,7,6,4,1,2,3]=>[2,1,1,1,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[5,6,7,8,4,1,3,2]=>[4,1,2,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[5,7,8,6,4,1,3,2]=>[3,1,1,2,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,8,6,7,4,1,3,2]=>[2,2,1,2,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>[2,1,1,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1]=>[4,1,2,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,3,2,4,7,8,6,5]=>[5,6,8,7,4,2,3,1]=>[3,1,1,2,1]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[5,7,8,6,4,2,3,1]=>[3,1,1,2,1]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[5,8,6,7,4,2,3,1]=>[2,2,1,2,1]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2]=>[4,1,1,2]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[5,6,8,7,4,3,1,2]=>[3,1,1,1,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[5,8,6,7,4,3,1,2]=>[2,2,1,1,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[5,8,6,7,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5]=>[3,5]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,8,7,1,2,3,4,5]=>[2,1,5]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[6,7,8,1,2,3,5,4]=>[3,4,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[4,5,3,2,1,7,8,6]=>[6,8,7,1,2,3,5,4]=>[2,1,4,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[6,7,8,1,2,4,5,3]=>[3,4,1]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[6,7,8,1,2,5,3,4]=>[3,3,2]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[4,3,5,2,1,7,8,6]=>[6,8,7,1,2,5,3,4]=>[2,1,3,2]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[6,7,8,1,2,5,4,3]=>[3,3,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[6,7,8,1,3,4,5,2]=>[3,4,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,8,7,1,3,4,5,2]=>[2,1,4,1]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[6,7,8,1,3,5,4,2]=>[3,3,1,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[6,8,7,1,3,5,4,2]=>[2,1,3,1,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[6,7,8,1,4,5,2,3]=>[3,3,2]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,8,7,1,4,5,2,3]=>[2,1,3,2]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[6,7,8,1,4,5,3,2]=>[3,3,1,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[6,8,7,1,4,5,3,2]=>[2,1,3,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[6,7,8,1,5,2,3,4]=>[3,2,3]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,8,7,1,5,2,3,4]=>[2,1,2,3]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[6,7,8,1,5,2,4,3]=>[3,2,2,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[6,8,7,1,5,2,4,3]=>[2,1,2,2,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[6,7,8,1,5,3,4,2]=>[3,2,2,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[6,8,7,1,5,3,4,2]=>[2,1,2,2,1]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>[2,1,2,1,1,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1]=>[3,4,1]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[6,8,7,2,3,4,5,1]=>[2,1,4,1]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[6,7,8,2,3,5,4,1]=>[3,3,1,1]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[6,8,7,2,4,5,3,1]=>[2,1,3,1,1]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>[2,1,2,1,1,1]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[2,1,4,5,3,7,8,6]=>[6,8,7,3,5,4,1,2]=>[2,1,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>[2,1,3,1,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[6,7,8,3,5,4,2,1]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[2,3,1,5,4,8,7,6]=>[6,7,8,4,5,1,3,2]=>[3,2,2,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[6,7,8,4,5,3,1,2]=>[3,2,1,2]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>[6,8,7,4,5,3,1,2]=>[2,1,2,1,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[6,8,7,4,5,3,2,1]=>[2,1,2,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4]=>[3,1,4]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[6,8,7,5,1,2,3,4]=>[2,1,1,4]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[6,7,8,5,1,2,4,3]=>[3,1,3,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[3,4,2,1,5,7,8,6]=>[6,8,7,5,1,2,4,3]=>[2,1,1,3,1]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[6,8,7,5,1,3,4,2]=>[2,1,1,3,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[6,7,8,5,1,4,2,3]=>[3,1,2,2]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[6,8,7,5,1,4,2,3]=>[2,1,1,2,2]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,7,8,5,1,4,3,2]=>[3,1,2,1,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1]=>[3,1,3,1]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[6,7,8,5,3,4,1,2]=>[3,1,2,2]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[6,8,7,5,4,1,2,3]=>[2,1,1,1,3]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[2,1,1,1,2,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[6,7,8,5,4,3,1,2]=>[3,1,1,1,2]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[6,8,7,5,4,3,1,2]=>[2,1,1,1,1,2]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[2,6]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,8,1,2,3,4,6,5]=>[2,5,1]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[7,8,1,2,3,5,6,4]=>[2,5,1]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,8,1,2,3,6,4,5]=>[2,4,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,8,1,2,3,6,5,4]=>[2,4,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,8,1,2,4,5,6,3]=>[2,5,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,8,1,2,4,6,5,3]=>[2,4,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,8,1,2,5,6,3,4]=>[2,4,2]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[7,8,1,2,5,6,4,3]=>[2,4,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[7,8,1,2,6,3,4,5]=>[2,3,3]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,8,1,2,6,3,5,4]=>[2,3,2,1]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,8,1,2,6,5,3,4]=>[2,3,1,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,8,1,2,6,5,4,3]=>[2,3,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,8,1,3,4,5,6,2]=>[2,5,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[7,8,1,3,4,6,5,2]=>[2,4,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[7,8,1,3,5,6,4,2]=>[2,4,1,1]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[2,4,5,6,3,1,8,7]=>[7,8,1,3,6,5,4,2]=>[2,3,1,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,8,1,4,5,6,3,2]=>[2,4,1,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[7,8,1,4,6,5,3,2]=>[2,3,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[7,8,1,5,6,2,4,3]=>[2,3,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,8,1,5,6,3,4,2]=>[2,3,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[3,2,4,6,5,1,8,7]=>[7,8,1,5,6,4,2,3]=>[2,3,1,2]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[2,3,4,6,5,1,8,7]=>[7,8,1,5,6,4,3,2]=>[2,3,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,8,1,6,2,3,4,5]=>[2,2,4]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,8,1,6,2,3,5,4]=>[2,2,3,1]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[7,8,1,6,2,4,5,3]=>[2,2,3,1]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,8,1,6,2,5,3,4]=>[2,2,2,2]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[7,8,1,6,3,5,4,2]=>[2,2,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,8,1,6,4,5,2,3]=>[2,2,2,2]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[2,3,5,4,6,1,8,7]=>[7,8,1,6,4,5,3,2]=>[2,2,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[7,8,1,6,5,2,3,4]=>[2,2,1,3]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[7,8,1,6,5,2,4,3]=>[2,2,1,2,1]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[3,2,4,5,6,1,8,7]=>[7,8,1,6,5,4,2,3]=>[2,2,1,1,2]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>[7,8,2,4,5,6,3,1]=>[2,4,1,1]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,3,4,6,5,2,8,7]=>[7,8,2,5,6,4,3,1]=>[2,3,1,1,1]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,4,5,3,6,2,8,7]=>[7,8,2,6,3,5,4,1]=>[2,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,4,3,5,6,2,8,7]=>[7,8,2,6,5,3,4,1]=>[2,2,1,2,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[7,8,3,4,6,5,1,2]=>[2,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[7,8,3,5,6,4,1,2]=>[2,3,1,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[7,8,3,6,4,5,1,2]=>[2,2,2,2]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,2,5,6,4,3,8,7]=>[7,8,3,4,6,5,2,1]=>[2,3,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[7,8,4,5,6,1,2,3]=>[2,3,3]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[7,8,4,6,5,1,2,3]=>[2,2,1,3]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[7,8,4,5,6,1,3,2]=>[2,3,2,1]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]=>[7,8,4,5,6,2,3,1]=>[2,3,2,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[7,8,4,5,6,3,1,2]=>[2,3,1,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[7,8,4,6,5,3,2,1]=>[2,2,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[2,2,4]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[7,8,5,6,1,2,4,3]=>[2,2,3,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[7,8,5,6,1,3,4,2]=>[2,2,3,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[7,8,5,6,1,4,2,3]=>[2,2,2,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[7,8,5,6,2,3,4,1]=>[2,2,3,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[7,8,5,6,4,1,2,3]=>[2,2,1,3]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5]=>[2,1,5]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[7,8,6,1,2,3,5,4]=>[2,1,4,1]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[7,8,6,1,2,4,5,3]=>[2,1,4,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[7,8,6,1,2,5,3,4]=>[2,1,3,2]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[7,8,6,1,3,4,5,2]=>[2,1,4,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[7,8,6,1,3,5,4,2]=>[2,1,3,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[7,8,6,1,4,5,2,3]=>[2,1,3,2]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[7,8,6,1,4,5,3,2]=>[2,1,3,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[7,8,6,1,5,2,3,4]=>[2,1,2,3]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>[7,8,6,1,5,3,4,2]=>[2,1,2,2,1]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>[2,1,2,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1]=>[2,1,4,1]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[7,8,6,2,3,5,4,1]=>[2,1,3,1,1]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>[7,8,6,2,5,4,3,1]=>[2,1,2,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2]=>[2,1,3,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1]=>[2,1,3,1,1]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[7,8,6,3,5,4,2,1]=>[2,1,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[7,8,6,4,5,1,2,3]=>[2,1,2,3]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[7,8,6,5,1,3,4,2]=>[2,1,1,3,1]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[7,8,6,5,1,4,2,3]=>[2,1,1,2,2]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>[2,1,1,2,1,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>[2,1,1,2,1,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[7,8,6,5,4,1,2,3]=>[2,1,1,1,3]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[7,8,6,5,4,1,3,2]=>[2,1,1,1,2,1]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[1,7]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[8,1,2,3,4,6,7,5]=>[1,6,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[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]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>[1,6,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[8,1,2,3,5,7,6,4]=>[1,5,1,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[8,1,2,3,6,7,4,5]=>[1,5,2]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[8,1,2,3,6,7,5,4]=>[1,5,1,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[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]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[8,1,2,3,7,5,6,4]=>[1,4,2,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[8,1,2,4,5,6,7,3]=>[1,6,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[8,1,2,4,6,7,5,3]=>[1,5,1,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[8,1,2,4,7,6,5,3]=>[1,4,1,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[8,1,2,5,6,7,3,4]=>[1,5,2]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>[1,5,1,1]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>[8,1,2,6,7,3,4,5]=>[1,4,3]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[8,1,2,6,7,3,5,4]=>[1,4,2,1]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[8,1,2,6,7,4,5,3]=>[1,4,2,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[8,1,2,6,7,5,3,4]=>[1,4,1,2]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[3,4,5,7,6,2,1,8]=>[8,1,2,6,7,5,4,3]=>[1,4,1,1,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[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]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[8,1,2,7,3,5,6,4]=>[1,3,3,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[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]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[8,1,2,7,4,5,6,3]=>[1,3,3,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[8,1,2,7,4,6,5,3]=>[1,3,2,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[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]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[8,1,3,5,6,7,4,2]=>[1,5,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[8,1,3,5,7,6,4,2]=>[1,4,1,1,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[8,1,3,6,7,4,5,2]=>[1,4,2,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[8,1,3,6,7,5,4,2]=>[1,4,1,1,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[2,6,5,4,7,3,1,8]=>[8,1,3,7,4,5,6,2]=>[1,3,3,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[8,1,3,7,4,6,5,2]=>[1,3,2,1,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[2,4,6,5,7,3,1,8]=>[8,1,3,7,5,6,4,2]=>[1,3,2,1,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[8,1,3,7,6,4,5,2]=>[1,3,1,2,1]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[8,1,3,7,6,5,4,2]=>[1,3,1,1,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[8,1,4,5,6,7,2,3]=>[1,5,2]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[8,1,4,5,7,6,2,3]=>[1,4,1,2]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[8,1,4,6,7,5,2,3]=>[1,4,1,2]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[8,1,4,7,6,5,2,3]=>[1,3,1,1,2]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[8,1,4,5,6,7,3,2]=>[1,5,1,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[8,1,4,5,7,6,3,2]=>[1,4,1,1,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>[8,1,4,6,7,5,3,2]=>[1,4,1,1,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[8,1,4,7,5,6,3,2]=>[1,3,2,1,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[8,1,4,7,6,5,3,2]=>[1,3,1,1,1,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[8,1,5,6,7,2,3,4]=>[1,4,3]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[4,3,2,6,7,5,1,8]=>[8,1,5,7,6,2,3,4]=>[1,3,1,3]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[8,1,5,6,7,2,4,3]=>[1,4,2,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[3,2,4,7,6,5,1,8]=>[8,1,5,6,7,4,2,3]=>[1,4,1,2]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[8,1,5,7,6,4,2,3]=>[1,3,1,1,2]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[8,1,5,6,7,4,3,2]=>[1,4,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[8,1,6,7,2,3,4,5]=>[1,3,4]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[8,1,6,7,2,3,5,4]=>[1,3,3,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[8,1,6,7,2,4,5,3]=>[1,3,3,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[8,1,6,7,2,5,3,4]=>[1,3,2,2]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>[8,1,6,7,2,5,4,3]=>[1,3,2,1,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[8,1,6,7,4,5,2,3]=>[1,3,2,2]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[8,1,6,7,5,2,3,4]=>[1,3,1,3]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[2,4,3,5,7,6,1,8]=>[8,1,6,7,5,3,4,2]=>[1,3,1,2,1]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[8,1,6,7,5,4,3,2]=>[1,3,1,1,1,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>[1,2,5]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[4,6,5,3,2,7,1,8]=>[8,1,7,2,3,5,6,4]=>[1,2,4,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[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]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[8,1,7,2,4,5,6,3]=>[1,2,4,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[8,1,7,2,4,6,5,3]=>[1,2,3,1,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[8,1,7,2,5,6,3,4]=>[1,2,3,2]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[8,1,7,2,5,6,4,3]=>[1,2,3,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[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]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[8,1,7,2,6,4,5,3]=>[1,2,2,2,1]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[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]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[8,1,7,3,6,4,5,2]=>[1,2,2,2,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[2,4,5,6,3,7,1,8]=>[8,1,7,3,6,5,4,2]=>[1,2,2,1,1,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[8,1,7,4,5,6,2,3]=>[1,2,3,2]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[2,3,6,5,4,7,1,8]=>[8,1,7,4,5,6,3,2]=>[1,2,3,1,1]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[8,1,7,4,6,5,3,2]=>[1,2,2,1,1,1]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[4,3,2,6,5,7,1,8]=>[8,1,7,5,6,2,3,4]=>[1,2,2,3]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[8,1,7,5,6,3,4,2]=>[1,2,2,2,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[8,1,7,5,6,4,2,3]=>[1,2,2,1,2]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[8,1,7,5,6,4,3,2]=>[1,2,2,1,1,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[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]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[8,1,7,6,2,4,5,3]=>[1,2,1,3,1]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>[1,2,1,2,1,1]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[2,4,5,3,6,7,1,8]=>[8,1,7,6,3,5,4,2]=>[1,2,1,2,1,1]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[3,2,5,4,6,7,1,8]=>[8,1,7,6,4,5,2,3]=>[1,2,1,2,2]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[8,1,7,6,4,5,3,2]=>[1,2,1,2,1,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[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]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[8,2,3,4,7,5,6,1]=>[1,4,2,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[8,2,3,4,7,6,5,1]=>[1,4,1,1,1]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,4,6,7,5,3,2,8]=>[8,2,3,5,7,6,4,1]=>[1,4,1,1,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[8,2,3,6,7,5,4,1]=>[1,4,1,1,1]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,6,5,4,7,3,2,8]=>[8,2,3,7,4,5,6,1]=>[1,3,3,1]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[8,2,3,7,5,6,4,1]=>[1,3,2,1,1]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,5,4,6,7,3,2,8]=>[8,2,3,7,6,4,5,1]=>[1,3,1,2,1]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[8,2,3,7,6,5,4,1]=>[1,3,1,1,1,1]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[8,2,4,5,6,7,3,1]=>[1,5,1,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[8,2,4,6,7,5,3,1]=>[1,4,1,1,1]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,3,6,5,7,4,2,8]=>[8,2,4,7,5,6,3,1]=>[1,3,2,1,1]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[8,2,4,7,6,5,3,1]=>[1,3,1,1,1,1]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,3,4,7,6,5,2,8]=>[8,2,5,6,7,4,3,1]=>[1,4,1,1,1]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[8,2,5,7,6,4,3,1]=>[1,3,1,1,1,1]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[8,2,6,7,3,5,4,1]=>[1,3,2,1,1]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[8,2,6,7,4,5,3,1]=>[1,3,2,1,1]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[8,2,6,7,5,3,4,1]=>[1,3,1,2,1]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[8,2,6,7,5,4,3,1]=>[1,3,1,1,1,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,6,5,4,3,7,2,8]=>[8,2,7,3,4,5,6,1]=>[1,2,4,1]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[8,2,7,3,6,4,5,1]=>[1,2,2,2,1]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[8,2,7,4,5,6,3,1]=>[1,2,3,1,1]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[8,2,7,4,6,5,3,1]=>[1,2,2,1,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[8,2,7,5,6,3,4,1]=>[1,2,2,2,1]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>[8,2,7,5,6,4,3,1]=>[1,2,2,1,1,1]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[8,2,7,6,3,4,5,1]=>[1,2,1,3,1]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,3,5,4,6,7,2,8]=>[8,2,7,6,4,5,3,1]=>[1,2,1,2,1,1]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,4,3,5,6,7,2,8]=>[8,2,7,6,5,3,4,1]=>[1,2,1,1,2,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[8,3,4,5,6,7,1,2]=>[1,5,2]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>[8,3,4,5,7,6,1,2]=>[1,4,1,2]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[2,1,5,7,6,4,3,8]=>[8,3,4,6,7,5,1,2]=>[1,4,1,2]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[2,1,6,5,4,7,3,8]=>[8,3,7,4,5,6,1,2]=>[1,2,3,2]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[8,3,7,6,4,5,1,2]=>[1,2,1,2,2]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[2,1,4,5,6,7,3,8]=>[8,3,7,6,5,4,1,2]=>[1,2,1,1,1,2]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[8,3,4,7,6,5,2,1]=>[1,3,1,1,1,1]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[8,3,5,7,6,4,2,1]=>[1,3,1,1,1,1]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,2,6,5,4,7,3,8]=>[8,3,7,4,5,6,2,1]=>[1,2,3,1,1]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[8,3,7,5,6,4,2,1]=>[1,2,2,1,1,1]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[8,3,7,6,4,5,2,1]=>[1,2,1,2,1,1]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[8,4,7,6,5,1,2,3]=>[1,2,1,1,3]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8]=>[8,4,5,6,7,1,3,2]=>[1,4,2,1]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[8,4,5,7,6,1,3,2]=>[1,3,1,2,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[2,3,1,5,7,6,4,8]=>[8,4,6,7,5,1,3,2]=>[1,3,1,2,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>[1,2,1,1,2,1]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[8,4,5,7,6,2,3,1]=>[1,3,1,2,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[8,4,6,7,5,2,3,1]=>[1,3,1,2,1]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[8,4,7,5,6,2,3,1]=>[1,2,2,2,1]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>[1,2,1,1,2,1]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[2,1,3,5,7,6,4,8]=>[8,4,6,7,5,3,1,2]=>[1,3,1,1,2]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[2,1,3,6,5,7,4,8]=>[8,4,7,5,6,3,1,2]=>[1,2,2,1,2]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>[1,2,1,1,1,2]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[8,4,5,7,6,3,2,1]=>[1,3,1,1,1,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[8,4,6,7,5,3,2,1]=>[1,3,1,1,1,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[8,4,7,5,6,3,2,1]=>[1,2,2,1,1,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4]=>[1,3,4]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[8,5,7,6,1,2,3,4]=>[1,2,1,4]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[3,4,2,1,7,6,5,8]=>[8,5,6,7,1,2,4,3]=>[1,3,3,1]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[3,4,2,1,6,7,5,8]=>[8,5,7,6,1,2,4,3]=>[1,2,1,3,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[2,4,3,1,7,6,5,8]=>[8,5,6,7,1,3,4,2]=>[1,3,3,1]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[2,4,3,1,6,7,5,8]=>[8,5,7,6,1,3,4,2]=>[1,2,1,3,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[8,5,6,7,1,4,2,3]=>[1,3,2,2]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[8,5,7,6,1,4,2,3]=>[1,2,1,2,2]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[8,5,6,7,1,4,3,2]=>[1,3,2,1,1]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[8,5,7,6,2,3,4,1]=>[1,2,1,3,1]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[8,5,6,7,2,4,3,1]=>[1,3,2,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]=>[8,5,6,7,3,4,1,2]=>[1,3,2,2]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[8,5,7,6,3,4,1,2]=>[1,2,1,2,2]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3]=>[1,3,1,3]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[8,5,7,6,4,1,2,3]=>[1,2,1,1,3]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[8,5,7,6,4,1,3,2]=>[1,2,1,1,2,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[8,5,6,7,4,2,3,1]=>[1,3,1,2,1]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,3,2,4,6,7,5,8]=>[8,5,7,6,4,2,3,1]=>[1,2,1,1,2,1]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[2,1,3,4,6,7,5,8]=>[8,5,7,6,4,3,1,2]=>[1,2,1,1,1,2]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1]=>[1,3,1,1,1,1]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5]=>[1,2,5]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[8,6,7,1,2,3,5,4]=>[1,2,4,1]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[8,6,7,1,2,5,3,4]=>[1,2,3,2]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[8,6,7,1,2,5,4,3]=>[1,2,3,1,1]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[8,6,7,1,3,5,4,2]=>[1,2,3,1,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[8,6,7,1,4,5,2,3]=>[1,2,3,2]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[8,6,7,1,4,5,3,2]=>[1,2,3,1,1]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[8,6,7,1,5,2,3,4]=>[1,2,2,3]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[8,6,7,1,5,2,4,3]=>[1,2,2,2,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>[1,2,2,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1]=>[1,2,4,1]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[8,6,7,2,3,5,4,1]=>[1,2,3,1,1]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[8,6,7,2,4,5,3,1]=>[1,2,3,1,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[8,6,7,2,5,3,4,1]=>[1,2,2,2,1]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[8,6,7,2,5,4,3,1]=>[1,2,2,1,1,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1]=>[1,2,3,1,1]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>[8,6,7,3,5,4,2,1]=>[1,2,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3]=>[1,2,2,3]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[8,6,7,4,5,1,3,2]=>[1,2,2,2,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4]=>[1,2,1,4]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[8,6,7,5,1,4,2,3]=>[1,2,1,2,2]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>[1,2,1,2,1,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1]=>[1,2,1,3,1]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[8,6,7,5,4,1,3,2]=>[1,2,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[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]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[4,6,5,3,2,1,7,8]=>[8,7,1,2,3,5,6,4]=>[1,1,5,1]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>[1,1,4,2]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[8,7,1,2,4,5,6,3]=>[1,1,5,1]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>[8,7,1,2,5,6,3,4]=>[1,1,4,2]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[3,4,6,5,2,1,7,8]=>[8,7,1,2,5,6,4,3]=>[1,1,4,1,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>[1,1,3,3]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[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]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[8,7,1,3,5,6,4,2]=>[1,1,4,1,1]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[8,7,1,3,6,4,5,2]=>[1,1,3,2,1]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[8,7,1,3,6,5,4,2]=>[1,1,3,1,1,1]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[3,2,6,5,4,1,7,8]=>[8,7,1,4,5,6,2,3]=>[1,1,4,2]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[3,2,5,6,4,1,7,8]=>[8,7,1,4,6,5,2,3]=>[1,1,3,1,2]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>[8,7,1,4,5,6,3,2]=>[1,1,4,1,1]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[2,3,5,6,4,1,7,8]=>[8,7,1,4,6,5,3,2]=>[1,1,3,1,1,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[8,7,1,5,6,2,3,4]=>[1,1,3,3]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[8,7,1,5,6,2,4,3]=>[1,1,3,2,1]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[8,7,1,5,6,4,3,2]=>[1,1,3,1,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[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]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[8,7,1,6,2,4,5,3]=>[1,1,2,3,1]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[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]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[2,5,4,3,6,1,7,8]=>[8,7,1,6,3,4,5,2]=>[1,1,2,3,1]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[2,4,5,3,6,1,7,8]=>[8,7,1,6,3,5,4,2]=>[1,1,2,2,1,1]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[8,7,1,6,4,5,3,2]=>[1,1,2,2,1,1]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[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]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[8,7,2,4,5,6,3,1]=>[1,1,4,1,1]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,3,4,6,5,2,7,8]=>[8,7,2,5,6,4,3,1]=>[1,1,3,1,1,1]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>[8,7,2,6,3,5,4,1]=>[1,1,2,2,1,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[8,7,2,6,4,5,3,1]=>[1,1,2,2,1,1]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,4,3,5,6,2,7,8]=>[8,7,2,6,5,3,4,1]=>[1,1,2,1,2,1]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[8,7,2,6,5,4,3,1]=>[1,1,2,1,1,1,1]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[2,1,6,5,4,3,7,8]=>[8,7,3,4,5,6,1,2]=>[1,1,4,2]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[8,7,3,5,6,4,1,2]=>[1,1,3,1,2]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[2,1,4,5,6,3,7,8]=>[8,7,3,6,5,4,1,2]=>[1,1,2,1,1,2]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[1,1,4,1,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[8,7,3,4,6,5,2,1]=>[1,1,3,1,1,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[8,7,3,5,6,4,2,1]=>[1,1,3,1,1,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,2,5,4,6,3,7,8]=>[8,7,3,6,4,5,2,1]=>[1,1,2,2,1,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[1,1,2,1,1,1,1]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[8,7,4,5,6,1,2,3]=>[1,1,3,3]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[8,7,4,6,5,1,2,3]=>[1,1,2,1,3]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[8,7,4,5,6,1,3,2]=>[1,1,3,2,1]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[8,7,4,6,5,1,3,2]=>[1,1,2,1,2,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[8,7,4,5,6,2,3,1]=>[1,1,3,2,1]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[8,7,4,6,5,2,3,1]=>[1,1,2,1,2,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[2,4,3,1,6,5,7,8]=>[8,7,5,6,1,3,4,2]=>[1,1,2,3,1]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[8,7,5,6,1,4,2,3]=>[1,1,2,2,2]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1]=>[1,1,2,3,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[2,3,1,4,6,5,7,8]=>[8,7,5,6,4,1,3,2]=>[1,1,2,1,2,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[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]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[8,7,6,1,2,4,5,3]=>[1,1,1,4,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[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]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[8,7,6,1,3,4,5,2]=>[1,1,1,4,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[8,7,6,1,3,5,4,2]=>[1,1,1,3,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[8,7,6,1,4,5,2,3]=>[1,1,1,3,2]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[8,7,6,1,4,5,3,2]=>[1,1,1,3,1,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[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]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[8,7,6,1,5,3,4,2]=>[1,1,1,2,2,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[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]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1]=>[1,1,1,4,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[8,7,6,2,4,5,3,1]=>[1,1,1,3,1,1]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[8,7,6,2,5,3,4,1]=>[1,1,1,2,2,1]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>[1,1,1,2,1,1,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>[1,1,1,2,1,2]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1]=>[1,1,1,3,1,1]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>[1,1,1,2,1,1,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[8,7,6,4,5,1,2,3]=>[1,1,1,2,3]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[8,7,6,4,5,1,3,2]=>[1,1,1,2,2,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[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]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[8,7,6,5,1,3,4,2]=>[1,1,1,1,3,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[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]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[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]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[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 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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.