Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[1,2]=>[1,2]=>[2]
[[.,.],.]=>[1,2]=>[2,1]=>[2,1]=>[1,1]
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>[1,2,3]=>[3]
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>[1,3,2]=>[2,1]
[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>[2,1,3]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>[2,3,1]=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]=>[4]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>[1,2,4,3]=>[3,1]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>[1,3,2,4]=>[2,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>[1,3,4,2]=>[3,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>[1,4,3,2]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>[2,1,3,4]=>[1,3]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>[2,1,4,3]=>[1,2,1]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>[2,3,1,4]=>[2,2]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>[3,2,1,4]=>[1,1,2]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>[2,3,4,1]=>[3,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>[2,4,3,1]=>[2,1,1]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>[3,2,4,1]=>[1,2,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>[3,4,2,1]=>[2,1,1]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[4,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[3,2]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[2,1,2]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[1,3,5,4,2]=>[3,1,1]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[1,4,3,5,2]=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[1,4,5,3,2]=>[3,1,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[2,1,1,1]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[1,3,1]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[1,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[2,3]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[2,2,1]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[1,1,2,1]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[3,2]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[2,4,3,1,5]=>[2,1,2]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[1,2,2]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[2,1,2]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[1,1,1,2]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[4,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[2,3,5,4,1]=>[3,1,1]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[2,4,3,5,1]=>[2,2,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[2,4,5,3,1]=>[3,1,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[2,5,4,3,1]=>[2,1,1,1]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[1,3,1]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[3,2,5,4,1]=>[1,2,1,1]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[2,2,1]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[1,1,2,1]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[3,1,1]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[3,5,4,2,1]=>[2,1,1,1]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[1,2,1,1]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[2,1,1,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[5,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[4,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[4,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[3,1,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>[5,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[1,2,4,6,5,3]=>[4,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[1,2,5,4,6,3]=>[3,2,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[1,2,5,6,4,3]=>[4,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[2,3,1]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[2,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[3,3]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[3,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[2,1,3]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[2,1,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[4,2]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[1,3,5,4,2,6]=>[3,1,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[1,4,3,5,2,6]=>[2,2,2]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[1,4,5,3,2,6]=>[3,1,2]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[2,1,1,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[5,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[1,3,4,6,5,2]=>[4,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[1,3,5,4,6,2]=>[3,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[1,3,5,6,4,2]=>[4,1,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[1,3,6,5,4,2]=>[3,1,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[1,4,3,5,6,2]=>[2,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[1,4,3,6,5,2]=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[1,4,5,3,6,2]=>[3,2,1]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[1,5,4,3,6,2]=>[2,1,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[1,4,5,6,3,2]=>[4,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[1,4,6,5,3,2]=>[3,1,1,1]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[1,5,4,6,3,2]=>[2,2,1,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[1,5,6,4,3,2]=>[3,1,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[1,4,1]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[1,3,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[1,3,2]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[1,2,1,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[1,4,1]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[2,1,4,6,5,3]=>[1,3,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[2,1,5,4,6,3]=>[1,2,2,1]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[2,1,5,6,4,3]=>[1,3,1,1]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[2,4]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[2,3,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[2,2,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[2,3,1]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[2,3,1,6,5,4]=>[2,2,1,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[1,1,4]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[1,1,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[1,1,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[3,2,1,5,6,4]=>[1,1,3,1]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[3,2,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[2,4,3,1,5,6]=>[2,1,3]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[2,4,3,1,6,5]=>[2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[1,2,3]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[3,2,4,1,6,5]=>[1,2,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[2,1,3]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[3,4,2,1,6,5]=>[2,1,2,1]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[4,2]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[2,3,5,4,1,6]=>[3,1,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[2,4,3,5,1,6]=>[2,2,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[2,4,5,3,1,6]=>[3,1,2]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[2,5,4,3,1,6]=>[2,1,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[1,3,2]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[3,2,5,4,1,6]=>[1,2,1,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[1,1,2,2]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[3,1,2]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[3,5,4,2,1,6]=>[2,1,1,2]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[1,2,1,2]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[2,1,1,2]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[5,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[2,3,4,6,5,1]=>[4,1,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[2,3,5,4,6,1]=>[3,2,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[2,3,5,6,4,1]=>[4,1,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[2,3,6,5,4,1]=>[3,1,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[2,4,3,5,6,1]=>[2,3,1]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[2,4,3,6,5,1]=>[2,2,1,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[2,4,5,3,6,1]=>[3,2,1]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[2,5,4,3,6,1]=>[2,1,2,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[2,4,5,6,3,1]=>[4,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[2,4,6,5,3,1]=>[3,1,1,1]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[2,5,4,6,3,1]=>[2,2,1,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[2,5,6,4,3,1]=>[3,1,1,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[1,4,1]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[3,2,4,6,5,1]=>[1,3,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[3,2,5,4,6,1]=>[1,2,2,1]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[3,2,5,6,4,1]=>[1,3,1,1]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[3,2,6,5,4,1]=>[1,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[2,3,1]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[3,4,2,6,5,1]=>[2,2,1,1]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[1,1,3,1]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[4,3,2,6,5,1]=>[1,1,2,1,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[3,2,1]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[3,5,4,2,6,1]=>[2,1,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[1,2,2,1]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[2,1,2,1]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[4,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[3,4,6,5,2,1]=>[3,1,1,1]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[3,5,4,6,2,1]=>[2,2,1,1]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[3,5,6,4,2,1]=>[3,1,1,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[1,3,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[4,3,6,5,2,1]=>[1,2,1,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[2,2,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7]=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[6,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[5,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[5,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[6,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,5,7,6,4]=>[5,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>[1,2,3,6,5,7,4]=>[4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[1,2,3,6,7,5,4]=>[5,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[3,3,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[4,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[4,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[3,1,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[3,1,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[5,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>[1,2,4,6,5,3,7]=>[4,1,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>[1,2,5,4,6,3,7]=>[3,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>[1,2,5,6,4,3,7]=>[4,1,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[6,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[1,2,4,5,7,6,3]=>[5,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>[1,2,4,6,5,7,3]=>[4,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[1,2,4,6,7,5,3]=>[5,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>[1,2,5,4,6,7,3]=>[3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>[1,2,5,4,7,6,3]=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>[1,2,5,6,4,7,3]=>[4,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>[1,2,6,5,4,7,3]=>[3,1,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[1,2,5,6,7,4,3]=>[5,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>[1,2,6,5,7,4,3]=>[3,2,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[2,4,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[2,3,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[2,3,2]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[2,2,1,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[2,4,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>[1,3,2,5,7,6,4]=>[2,3,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>[1,3,2,6,5,7,4]=>[2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>[1,3,2,6,7,5,4]=>[2,3,1,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[3,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[3,3,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[3,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[3,3,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>[1,3,4,2,7,6,5]=>[3,2,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[2,1,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[2,1,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>[1,4,3,2,6,7,5]=>[2,1,3,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[4,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[4,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>[1,3,5,4,2,6,7]=>[3,1,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>[1,3,5,4,2,7,6]=>[3,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>[1,4,3,5,2,6,7]=>[2,2,3]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>[1,4,3,5,2,7,6]=>[2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>[1,4,5,3,2,6,7]=>[3,1,3]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>[1,4,5,3,2,7,6]=>[3,1,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[5,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>[1,3,4,6,5,2,7]=>[4,1,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>[1,3,5,4,6,2,7]=>[3,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>[1,3,5,6,4,2,7]=>[4,1,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>[1,3,6,5,4,2,7]=>[3,1,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>[1,4,3,5,6,2,7]=>[2,3,2]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>[1,4,3,6,5,2,7]=>[2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>[1,4,5,3,6,2,7]=>[3,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>[1,5,4,3,6,2,7]=>[2,1,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>[1,4,5,6,3,2,7]=>[4,1,2]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>[1,4,6,5,3,2,7]=>[3,1,1,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>[1,5,4,6,3,2,7]=>[2,2,1,2]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>[1,5,6,4,3,2,7]=>[3,1,1,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[6,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[1,3,4,5,7,6,2]=>[5,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>[1,3,4,6,5,7,2]=>[4,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[1,3,4,6,7,5,2]=>[5,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>[1,3,5,4,6,7,2]=>[3,3,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>[1,3,5,4,7,6,2]=>[3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>[1,3,5,6,4,7,2]=>[4,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>[1,3,6,5,4,7,2]=>[3,1,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[1,3,5,6,7,4,2]=>[5,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>[1,3,6,5,7,4,2]=>[3,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>[1,4,3,5,6,7,2]=>[2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>[1,4,3,5,7,6,2]=>[2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>[1,4,3,6,5,7,2]=>[2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>[1,4,3,6,7,5,2]=>[2,3,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>[1,4,3,7,6,5,2]=>[2,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>[1,4,5,3,6,7,2]=>[3,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>[1,4,5,3,7,6,2]=>[3,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>[1,5,4,3,6,7,2]=>[2,1,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>[1,5,4,3,7,6,2]=>[2,1,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>[1,4,5,6,3,7,2]=>[4,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>[1,4,6,5,3,7,2]=>[3,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>[1,5,4,6,3,7,2]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>[1,5,6,4,3,7,2]=>[3,1,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[1,4,5,6,7,3,2]=>[5,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>[1,4,6,5,7,3,2]=>[3,2,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>[1,5,4,6,7,3,2]=>[2,3,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[1,5,4,7,6,3,2]=>[2,2,1,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[1,5,6,4,7,3,2]=>[3,2,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[1,6,5,7,4,3,2]=>[2,2,1,1,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[1,5,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[1,4,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[1,5,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>[2,1,3,5,7,6,4]=>[1,4,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>[2,1,3,6,5,7,4]=>[1,3,2,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>[2,1,3,6,7,5,4]=>[1,4,1,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[1,2,3,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[1,3,3]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[1,3,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[1,4,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>[2,1,4,6,5,3,7]=>[1,3,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>[2,1,5,4,6,3,7]=>[1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>[2,1,5,6,4,3,7]=>[1,3,1,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[1,5,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>[2,1,4,5,7,6,3]=>[1,4,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>[2,1,4,6,5,7,3]=>[1,3,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>[2,1,4,6,7,5,3]=>[1,4,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>[2,1,4,7,6,5,3]=>[1,3,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>[2,1,5,4,6,7,3]=>[1,2,3,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>[2,1,5,4,7,6,3]=>[1,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>[2,1,5,6,4,7,3]=>[1,3,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>[2,1,6,5,4,7,3]=>[1,2,1,2,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>[2,1,5,6,7,4,3]=>[1,4,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>[2,1,5,7,6,4,3]=>[1,3,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>[2,1,6,5,7,4,3]=>[1,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>[2,1,6,7,5,4,3]=>[1,3,1,1,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[2,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[2,4,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[2,3,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[2,4,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>[2,3,1,4,7,6,5]=>[2,3,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[2,2,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[2,3,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>[2,3,1,6,5,4,7]=>[2,2,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[2,4,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>[2,3,1,5,7,6,4]=>[2,3,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>[2,3,1,6,5,7,4]=>[2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>[2,3,1,6,7,5,4]=>[2,3,1,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>[2,3,1,7,6,5,4]=>[2,2,1,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[1,1,4,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[1,1,3,2]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[1,1,4,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>[3,2,1,5,7,6,4]=>[1,1,3,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[3,2,1,6,5,7,4]=>[1,1,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[3,2,1,6,7,5,4]=>[1,1,3,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[3,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[3,3,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[3,3,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>[2,3,4,1,7,6,5]=>[3,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>[2,4,3,1,5,6,7]=>[2,1,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>[2,4,3,1,5,7,6]=>[2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>[2,4,3,1,6,5,7]=>[2,1,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>[2,4,3,1,6,7,5]=>[2,1,3,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>[2,4,3,1,7,6,5]=>[2,1,2,1,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[1,2,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[1,2,3,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[1,2,3,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>[3,2,4,1,7,6,5]=>[1,2,2,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[2,1,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>[3,4,2,1,5,7,6]=>[2,1,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>[3,4,2,1,6,5,7]=>[2,1,2,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>[3,4,2,1,6,7,5]=>[2,1,3,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>[3,4,2,1,7,6,5]=>[2,1,2,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[4,3,2,1,6,7,5]=>[1,1,1,3,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>[2,3,5,4,1,6,7]=>[3,1,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>[2,3,5,4,1,7,6]=>[3,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>[2,4,3,5,1,6,7]=>[2,2,3]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>[2,4,3,5,1,7,6]=>[2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>[2,4,5,3,1,6,7]=>[3,1,3]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>[2,4,5,3,1,7,6]=>[3,1,2,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>[2,5,4,3,1,6,7]=>[2,1,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>[2,5,4,3,1,7,6]=>[2,1,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[1,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[1,3,2,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[3,2,5,4,1,6,7]=>[1,2,1,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[3,2,5,4,1,7,6]=>[1,2,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[2,2,3]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>[3,4,2,5,1,7,6]=>[2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>[4,3,2,5,1,7,6]=>[1,1,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[3,1,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>[3,4,5,2,1,7,6]=>[3,1,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>[3,5,4,2,1,6,7]=>[2,1,1,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>[3,5,4,2,1,7,6]=>[2,1,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>[4,3,5,2,1,7,6]=>[1,2,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>[4,5,3,2,1,7,6]=>[2,1,1,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[5,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>[2,3,4,6,5,1,7]=>[4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>[2,3,5,4,6,1,7]=>[3,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>[2,3,5,6,4,1,7]=>[4,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>[2,3,6,5,4,1,7]=>[3,1,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>[2,4,3,5,6,1,7]=>[2,3,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>[2,4,3,6,5,1,7]=>[2,2,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>[2,4,5,3,6,1,7]=>[3,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>[2,5,4,3,6,1,7]=>[2,1,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>[2,4,5,6,3,1,7]=>[4,1,2]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>[2,4,6,5,3,1,7]=>[3,1,1,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>[2,5,4,6,3,1,7]=>[2,2,1,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>[2,5,6,4,3,1,7]=>[3,1,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[1,4,2]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>[3,2,4,6,5,1,7]=>[1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[3,2,5,4,6,1,7]=>[1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[3,2,5,6,4,1,7]=>[1,3,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>[3,2,6,5,4,1,7]=>[1,2,1,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>[3,4,2,6,5,1,7]=>[2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[4,3,2,6,5,1,7]=>[1,1,2,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[3,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>[3,5,4,2,6,1,7]=>[2,1,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[4,1,2]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>[3,4,6,5,2,1,7]=>[3,1,1,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>[3,5,4,6,2,1,7]=>[2,2,1,2]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[3,5,6,4,2,1,7]=>[3,1,1,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[4,3,6,5,2,1,7]=>[1,2,1,1,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[6,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[2,3,4,5,7,6,1]=>[5,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>[2,3,4,6,5,7,1]=>[4,2,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[2,3,4,6,7,5,1]=>[5,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[2,3,5,4,6,7,1]=>[3,3,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>[2,3,5,4,7,6,1]=>[3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[2,3,5,6,4,7,1]=>[4,2,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[2,3,6,5,4,7,1]=>[3,1,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[2,3,5,6,7,4,1]=>[5,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>[2,3,6,5,7,4,1]=>[3,2,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>[2,4,3,5,6,7,1]=>[2,4,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>[2,4,3,5,7,6,1]=>[2,3,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>[2,4,3,6,5,7,1]=>[2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>[2,4,3,6,7,5,1]=>[2,3,1,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>[2,4,3,7,6,5,1]=>[2,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>[2,4,5,3,6,7,1]=>[3,3,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>[2,4,5,3,7,6,1]=>[3,2,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>[2,5,4,3,6,7,1]=>[2,1,3,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>[2,5,4,3,7,6,1]=>[2,1,2,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[2,4,5,6,3,7,1]=>[4,2,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[2,4,6,5,3,7,1]=>[3,1,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>[2,5,4,6,3,7,1]=>[2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>[2,5,6,4,3,7,1]=>[3,1,2,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[2,4,5,6,7,3,1]=>[5,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>[2,4,6,5,7,3,1]=>[3,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>[2,5,4,6,7,3,1]=>[2,3,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>[2,5,4,7,6,3,1]=>[2,2,1,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>[2,5,6,4,7,3,1]=>[3,2,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>[2,6,5,7,4,3,1]=>[2,2,1,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[1,5,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>[3,2,4,5,7,6,1]=>[1,4,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>[3,2,4,6,5,7,1]=>[1,3,2,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>[3,2,4,6,7,5,1]=>[1,4,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>[3,2,4,7,6,5,1]=>[1,3,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[3,2,5,4,6,7,1]=>[1,2,3,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[3,2,5,4,7,6,1]=>[1,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[3,2,5,6,4,7,1]=>[1,3,2,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>[3,2,6,5,4,7,1]=>[1,2,1,2,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[3,2,5,6,7,4,1]=>[1,4,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>[3,2,5,7,6,4,1]=>[1,3,1,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>[3,2,6,5,7,4,1]=>[1,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>[3,2,6,7,5,4,1]=>[1,3,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[2,4,1]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>[3,4,2,5,7,6,1]=>[2,3,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>[3,4,2,6,5,7,1]=>[2,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>[3,4,2,6,7,5,1]=>[2,3,1,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>[3,4,2,7,6,5,1]=>[2,2,1,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>[4,3,2,5,7,6,1]=>[1,1,3,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[4,3,2,6,5,7,1]=>[1,1,2,2,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[4,3,2,6,7,5,1]=>[1,1,3,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[3,3,1]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>[3,4,5,2,7,6,1]=>[3,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>[3,5,4,2,6,7,1]=>[2,1,3,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>[3,5,4,2,7,6,1]=>[2,1,2,1,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>[4,3,5,2,7,6,1]=>[1,2,2,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>[4,5,3,2,7,6,1]=>[2,1,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[4,2,1]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>[3,4,6,5,2,7,1]=>[3,1,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>[3,5,4,6,2,7,1]=>[2,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>[3,5,6,4,2,7,1]=>[3,1,2,1]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[4,3,6,5,2,7,1]=>[1,2,1,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>[3,4,6,5,7,2,1]=>[3,2,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>[3,5,4,6,7,2,1]=>[2,3,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>[3,5,4,7,6,2,1]=>[2,2,1,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>[3,5,6,4,7,2,1]=>[3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>[3,6,5,7,4,2,1]=>[2,2,1,1,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>[4,3,5,7,6,2,1]=>[1,3,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[4,3,6,5,7,2,1]=>[1,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[4,3,6,7,5,2,1]=>[1,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>[4,5,3,7,6,2,1]=>[2,2,1,1,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>[4,6,5,7,3,2,1]=>[2,2,1,1,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[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]=>[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]=>[1,2,3,4,5,6,8,7]=>[7,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[6,2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>[7,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[5,3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>[6,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>[7,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,7,6,8,5]=>[5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[4,4]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>[4,3,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>[5,3]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>[5,2,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>[6,2]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>[1,2,3,5,7,6,4,8]=>[5,1,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>[1,2,3,6,5,7,4,8]=>[4,2,2]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>[1,2,3,6,7,5,4,8]=>[5,1,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>[7,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>[1,2,3,5,7,6,8,4]=>[5,2,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>[1,2,3,6,5,7,8,4]=>[4,3,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>[1,2,3,6,5,8,7,4]=>[4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>[1,2,3,6,7,5,8,4]=>[5,2,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>[1,2,3,7,6,8,5,4]=>[4,2,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[3,5]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[3,4,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>[3,4,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>[3,3,2]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>[3,4,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,6,8,7,5]=>[3,3,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>[1,2,4,3,7,6,8,5]=>[3,2,2,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,2,4,3,8,7,5,6]=>[1,2,4,3,7,8,6,5]=>[3,3,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>[1,2,4,5,3,6,7,8]=>[4,4]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>[1,2,4,5,3,6,8,7]=>[4,3,1]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>[4,3,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>[1,2,4,5,3,8,7,6]=>[4,2,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6,8]=>[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>[3,1,3,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>[5,3]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>[5,2,1]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7,8]=>[1,2,4,6,5,3,7,8]=>[4,1,3]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>[1,2,5,6,4,3,7,8]=>[4,1,3]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[1,2,6,5,3,4,8,7]=>[1,2,5,6,4,3,8,7]=>[4,1,2,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[1,2,6,5,4,3,8,7]=>[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>[6,2]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5,8]=>[1,2,4,5,7,6,3,8]=>[5,1,2]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5,8]=>[1,2,4,6,7,5,3,8]=>[5,1,2]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[8,4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4,8]=>[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[8,6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>[3,3,2]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6,8]=>[1,2,5,6,4,7,3,8]=>[4,2,2]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5,8]=>[1,2,5,6,7,4,3,8]=>[5,1,2]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[8,4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4,8]=>[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>[7,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,2,8,3,4,7,5,6]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[1,2,8,3,4,7,6,5]=>[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>[1,2,4,6,5,7,8,3]=>[4,3,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>[1,2,4,6,5,8,7,3]=>[4,2,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>[1,2,4,6,7,5,8,3]=>[5,2,1]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,2,8,3,6,5,4,7]=>[1,2,4,7,6,5,8,3]=>[4,1,2,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,2,8,3,7,4,6,5]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>[3,4,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>[1,2,5,4,6,8,7,3]=>[3,3,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>[1,2,5,6,4,7,8,3]=>[4,3,1]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[6,7,4,3,5,8,2,1]=>[1,2,8,5,3,4,7,6]=>[1,2,5,6,4,8,7,3]=>[4,2,1,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,2,8,6,3,4,5,7]=>[1,2,5,6,7,4,8,3]=>[5,2,1]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[7,4,5,3,6,8,2,1]=>[1,2,8,6,3,5,4,7]=>[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>[1,2,5,6,7,8,4,3]=>[6,1,1]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>[1,2,5,7,6,8,4,3]=>[4,2,1,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[1,2,8,7,4,3,5,6]=>[1,2,6,5,7,8,4,3]=>[3,3,1,1]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[1,2,8,7,5,3,4,6]=>[1,2,6,7,5,8,4,3]=>[4,2,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[2,6]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>[2,5,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>[2,5,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>[1,3,2,4,6,8,7,5]=>[2,4,1,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>[1,3,2,4,7,6,8,5]=>[2,3,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>[2,2,3,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>[1,3,2,6,5,4,7,8]=>[2,2,1,3]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[1,3,2,6,5,4,8,7]=>[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>[2,4,2]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>[1,3,2,5,7,6,4,8]=>[2,3,1,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>[1,3,2,6,5,7,4,8]=>[2,2,2,2]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5,8]=>[1,3,2,6,7,5,4,8]=>[2,3,1,2]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4,8]=>[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>[2,5,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>[1,3,2,5,7,6,8,4]=>[2,3,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>[1,3,2,5,7,8,6,4]=>[2,4,1,1]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[1,3,2,8,4,7,6,5]=>[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>[1,3,2,6,5,7,8,4]=>[2,2,3,1]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[1,3,2,8,6,4,5,7]=>[1,3,2,6,7,5,8,4]=>[2,3,2,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>[1,3,2,7,6,5,8,4]=>[2,2,1,2,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>[1,3,2,6,7,8,5,4]=>[2,4,1,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[3,5]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[3,4,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[3,3,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>[3,4,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>[1,3,4,2,5,8,7,6]=>[3,3,1,1]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[3,2,2,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[3,3,2]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5,8]=>[1,3,4,2,7,6,5,8]=>[3,2,1,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>[3,4,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,6,8,7,5]=>[3,3,1,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>[1,3,4,2,7,6,8,5]=>[3,2,2,1]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>[1,3,4,2,7,8,6,5]=>[3,3,1,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[2,1,3,2]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>[2,1,4,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7,8]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[1,4,3,2,6,5,8,7]=>[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>[2,1,3,2]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>[2,1,4,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[1,4,3,2,8,5,7,6]=>[1,4,3,2,6,8,7,5]=>[2,1,3,1,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>[1,4,3,2,7,6,8,5]=>[2,1,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>[4,4]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>[1,3,4,5,2,6,8,7]=>[4,3,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>[4,2,2]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>[4,3,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>[1,3,4,5,2,8,7,6]=>[4,2,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>[1,3,5,4,2,6,7,8]=>[3,1,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>[1,3,5,4,2,6,8,7]=>[3,1,3,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>[3,1,2,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>[3,1,3,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>[1,4,3,5,2,7,6,8]=>[2,2,2,2]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>[1,4,3,5,2,7,8,6]=>[2,2,3,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>[3,1,2,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[1,5,4,3,2,6,8,7]=>[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[1,5,4,3,2,8,6,7]=>[1,5,4,3,2,7,8,6]=>[2,1,1,3,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[1,5,4,3,2,8,7,6]=>[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>[5,2,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7,8]=>[1,3,5,6,4,2,7,8]=>[4,1,3]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[8,7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7,8]=>[1,3,6,5,4,2,7,8]=>[3,1,1,3]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>[1,4,3,6,5,2,7,8]=>[2,2,1,3]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7,8]=>[1,4,5,6,3,2,7,8]=>[4,1,3]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>[1,4,5,6,3,2,8,7]=>[4,1,2,1]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7,8]=>[1,4,6,5,3,2,7,8]=>[3,1,1,3]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7,8]=>[1,5,6,4,3,2,7,8]=>[3,1,1,3]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>[6,2]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>[1,3,5,4,7,6,2,8]=>[3,2,1,2]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>[1,3,6,5,4,7,2,8]=>[3,1,2,2]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>[1,3,5,6,7,4,2,8]=>[5,1,2]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>[1,3,5,7,6,4,2,8]=>[4,1,1,2]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4,8]=>[1,3,6,7,5,4,2,8]=>[4,1,1,2]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>[1,4,3,5,7,6,2,8]=>[2,3,1,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>[1,4,3,6,5,7,2,8]=>[2,2,2,2]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>[3,3,2]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[8,5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5,8]=>[1,4,5,3,7,6,2,8]=>[3,2,1,2]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>[1,5,4,3,6,7,2,8]=>[2,1,3,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6,8]=>[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>[1,4,5,6,7,3,2,8]=>[5,1,2]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4,8]=>[1,4,5,7,6,3,2,8]=>[4,1,1,2]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>[1,4,6,5,7,3,2,8]=>[3,2,1,2]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4,8]=>[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>[7,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>[1,3,4,6,5,7,8,2]=>[4,3,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>[1,3,4,6,7,5,8,2]=>[5,2,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>[1,3,4,7,6,5,8,2]=>[4,1,2,1]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[1,8,2,3,7,4,5,6]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[1,8,2,3,7,4,6,5]=>[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,8,2,3,7,6,4,5]=>[1,3,4,7,8,6,5,2]=>[5,1,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>[1,3,5,4,6,7,8,2]=>[3,4,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>[1,3,5,4,7,6,8,2]=>[3,2,2,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>[1,3,5,4,7,8,6,2]=>[3,3,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>[1,3,5,6,4,7,8,2]=>[4,3,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[6,7,3,4,5,2,8,1]=>[1,8,2,5,4,3,7,6]=>[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>[1,3,5,6,7,4,8,2]=>[5,2,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>[1,3,5,7,6,4,8,2]=>[4,1,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[1,8,2,7,3,4,6,5]=>[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[1,8,2,7,4,3,6,5]=>[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[1,8,3,2,4,6,5,7]=>[1,4,3,5,7,6,8,2]=>[2,3,2,1]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>[1,4,3,5,7,8,6,2]=>[2,4,1,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[1,8,3,2,4,7,6,5]=>[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>[1,4,3,6,5,7,8,2]=>[2,2,3,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>[1,4,3,6,7,5,8,2]=>[2,3,2,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[1,8,3,2,7,4,5,6]=>[1,4,3,6,7,8,5,2]=>[2,4,1,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[1,8,3,2,7,4,6,5]=>[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>[3,4,1]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>[1,4,5,3,6,8,7,2]=>[3,3,1,1]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>[1,5,4,3,6,8,7,2]=>[2,1,3,1,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[1,8,4,3,2,6,5,7]=>[1,5,4,3,7,6,8,2]=>[2,1,2,2,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>[1,4,5,6,7,3,8,2]=>[5,2,1]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[1,8,6,2,5,4,3,7]=>[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[1,8,6,5,2,4,3,7]=>[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,8,6,5,3,2,4,7]=>[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[1,8,7,2,4,3,6,5]=>[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>[1,4,6,7,5,8,3,2]=>[4,2,1,1]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,8,7,2,5,4,3,6]=>[1,4,7,6,5,8,3,2]=>[3,1,2,1,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[1,8,7,6,2,3,5,4]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,8,7,6,2,5,3,4]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[1,4,3]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[1,4,2,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,6,7,8,5]=>[1,6,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>[2,1,3,4,7,6,8,5]=>[1,4,2,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>[2,1,3,5,6,4,7,8]=>[1,4,3]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7,8]=>[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5,8]=>[2,1,3,6,7,5,4,8]=>[1,4,1,2]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4,8]=>[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>[2,1,3,5,6,7,8,4]=>[1,6,1]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>[2,1,3,5,6,8,7,4]=>[1,5,1,1]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[2,1,3,8,4,6,5,7]=>[2,1,3,5,7,6,8,4]=>[1,4,2,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>[2,1,3,5,7,8,6,4]=>[1,5,1,1]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>[2,1,3,6,5,7,8,4]=>[1,3,3,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>[2,1,3,6,7,5,8,4]=>[1,4,2,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>[2,1,3,6,7,8,5,4]=>[1,5,1,1]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,6,7,8,5]=>[1,2,4,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>[1,3,4]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>[2,1,4,5,3,6,8,7]=>[1,3,3,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[2,1,5,4,3,8,6,7]=>[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7,8]=>[2,1,4,5,6,3,7,8]=>[1,4,3]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>[2,1,4,5,6,3,8,7]=>[1,4,2,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7,8]=>[2,1,4,6,5,3,7,8]=>[1,3,1,3]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7,8]=>[2,1,5,6,4,3,7,8]=>[1,3,1,3]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>[2,1,4,6,7,5,3,8]=>[1,4,1,2]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[8,6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6,8]=>[2,1,5,4,6,7,3,8]=>[1,2,3,2]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>[2,1,5,6,7,4,3,8]=>[1,4,1,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>[1,6,1]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[2,1,8,3,4,5,7,6]=>[2,1,4,5,6,8,7,3]=>[1,5,1,1]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[2,1,8,3,4,7,5,6]=>[2,1,4,5,7,8,6,3]=>[1,5,1,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>[2,1,4,6,7,5,8,3]=>[1,4,2,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>[2,1,4,6,7,8,5,3]=>[1,5,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>[2,1,4,8,7,6,5,3]=>[1,3,1,1,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[2,1,8,4,3,5,6,7]=>[2,1,5,4,6,7,8,3]=>[1,2,4,1]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[2,1,8,6,3,4,5,7]=>[2,1,5,6,7,4,8,3]=>[1,4,2,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>[2,1,5,6,7,8,4,3]=>[1,5,1,1]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[2,1,8,7,3,6,4,5]=>[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[2,1,8,7,3,6,5,4]=>[2,1,5,8,7,6,4,3]=>[1,3,1,1,1,1]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>[2,1,6,8,7,5,4,3]=>[1,3,1,1,1,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>[2,1,7,8,6,5,4,3]=>[1,3,1,1,1,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[2,6]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[2,5,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[3,1,2,4,5,8,7,6]=>[2,3,1,4,5,8,7,6]=>[2,4,1,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>[2,3,1,4,6,7,5,8]=>[2,4,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>[2,3,1,4,6,7,8,5]=>[2,5,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>[2,3,1,4,6,8,7,5]=>[2,4,1,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>[2,3,1,4,7,6,8,5]=>[2,3,2,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>[2,3,1,4,7,8,6,5]=>[2,4,1,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[2,2,4]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[2,2,2,2]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7,8]=>[2,3,1,5,6,4,7,8]=>[2,3,3]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[3,1,2,6,5,4,8,7]=>[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>[2,3,1,6,5,7,4,8]=>[2,2,2,2]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>[2,3,1,6,7,5,4,8]=>[2,3,1,2]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>[2,3,1,5,6,7,8,4]=>[2,5,1]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>[2,3,1,5,6,8,7,4]=>[2,4,1,1]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[3,1,2,8,4,6,5,7]=>[2,3,1,5,7,6,8,4]=>[2,3,2,1]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>[2,3,1,5,7,8,6,4]=>[2,4,1,1]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,1,2,8,4,7,6,5]=>[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,1,2,8,5,4,6,7]=>[2,3,1,6,5,7,8,4]=>[2,2,3,1]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>[2,3,1,6,7,5,8,4]=>[2,3,2,1]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>[2,3,1,6,7,8,5,4]=>[2,4,1,1]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>[3,2,1,4,5,7,8,6]=>[1,1,5,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7,8]=>[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[3,2,1,4,6,5,8,7]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6,8]=>[3,2,1,4,6,7,5,8]=>[1,1,4,2]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>[3,2,1,4,6,7,8,5]=>[1,1,5,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>[3,2,1,4,6,8,7,5]=>[1,1,4,1,1]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>[3,2,1,4,7,6,8,5]=>[1,1,3,2,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>[3,2,1,4,7,8,6,5]=>[1,1,4,1,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[3,2,1,5,4,6,8,7]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,1,2,3]=>[3,2,1,5,4,8,6,7]=>[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[3,2,1,5,4,8,7,6]=>[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>[3,2,1,5,6,4,7,8]=>[1,1,3,3]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[3,2,1,6,4,5,8,7]=>[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>[3,2,1,5,6,7,4,8]=>[1,1,4,2]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>[3,2,1,5,6,7,8,4]=>[1,1,5,1]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>[3,2,1,5,6,8,7,4]=>[1,1,4,1,1]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>[3,2,1,5,7,8,6,4]=>[1,1,4,1,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>[3,2,1,5,8,7,6,4]=>[1,1,3,1,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>[3,2,1,6,5,7,8,4]=>[1,1,2,3,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>[3,2,1,6,7,8,5,4]=>[1,1,4,1,1]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>[3,2,1,6,8,7,5,4]=>[1,1,3,1,1,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>[3,2,1,7,8,6,5,4]=>[1,1,3,1,1,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[3,5]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[3,4,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[3,3,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>[2,3,4,1,5,7,8,6]=>[3,4,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>[2,3,4,1,5,8,7,6]=>[3,3,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[3,2,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[3,2,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>[2,3,4,1,6,7,5,8]=>[3,3,2]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>[2,3,4,1,7,6,5,8]=>[3,2,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[3,4,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>[2,3,4,1,6,8,7,5]=>[3,3,1,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>[2,3,4,1,7,6,8,5]=>[3,2,2,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>[2,3,4,1,7,8,6,5]=>[3,3,1,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[2,1,5]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[4,1,3,2,5,6,8,7]=>[2,4,3,1,5,6,8,7]=>[2,1,4,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[4,1,3,2,5,8,6,7]=>[2,4,3,1,5,7,8,6]=>[2,1,4,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>[2,4,3,1,6,7,8,5]=>[2,1,4,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[1,2,4,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>[3,2,4,1,5,7,8,6]=>[1,2,4,1]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>[3,2,4,1,5,8,7,6]=>[1,2,3,1,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>[3,2,4,1,6,7,5,8]=>[1,2,3,2]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>[3,2,4,1,6,7,8,5]=>[1,2,4,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>[3,4,2,1,5,8,7,6]=>[2,1,3,1,1]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>[3,4,2,1,6,7,8,5]=>[2,1,4,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>[3,4,2,1,7,6,8,5]=>[2,1,2,2,1]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>[4,3,2,1,5,7,8,6]=>[1,1,1,4,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>[4,3,2,1,6,7,8,5]=>[1,1,1,4,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>[4,3,2,1,6,8,7,5]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>[4,3,2,1,7,8,6,5]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>[2,3,4,5,1,6,8,7]=>[4,3,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6,8]=>[2,3,4,5,1,7,6,8]=>[4,2,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>[2,3,4,5,1,7,8,6]=>[4,3,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>[2,3,4,5,1,8,7,6]=>[4,2,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[3,1,4]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>[2,3,5,4,1,7,6,8]=>[3,1,2,2]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[7,6,8,3,4,2,1,5]=>[5,1,2,4,3,8,6,7]=>[2,3,5,4,1,7,8,6]=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[2,2,4]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>[2,4,3,5,1,7,6,8]=>[2,2,2,2]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>[2,4,3,5,1,7,8,6]=>[2,2,3,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>[2,4,3,5,1,8,7,6]=>[2,2,2,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>[2,4,5,3,1,6,7,8]=>[3,1,4]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[7,8,6,3,2,4,1,5]=>[5,1,4,2,3,6,8,7]=>[2,4,5,3,1,6,8,7]=>[3,1,3,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6,8]=>[2,4,5,3,1,7,6,8]=>[3,1,2,2]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>[2,4,5,3,1,7,8,6]=>[3,1,3,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,1,4,3,2,6,8,7]=>[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[5,1,4,3,2,8,6,7]=>[2,5,4,3,1,7,8,6]=>[2,1,1,3,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[5,2,1,3,4,8,6,7]=>[3,2,4,5,1,7,8,6]=>[1,3,3,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>[3,2,4,5,1,8,7,6]=>[1,3,2,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>[3,2,5,4,1,6,7,8]=>[1,2,1,4]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>[3,4,2,5,1,6,8,7]=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>[3,4,2,5,1,7,6,8]=>[2,2,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>[3,4,2,5,1,7,8,6]=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[5,4,1,2,3,6,8,7]=>[3,4,5,2,1,6,8,7]=>[3,1,3,1]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6,8]=>[3,4,5,2,1,7,6,8]=>[3,1,2,2]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>[3,4,5,2,1,7,8,6]=>[3,1,3,1]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[5,4,1,3,2,6,8,7]=>[3,5,4,2,1,6,8,7]=>[2,1,1,3,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6,8]=>[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6,8]=>[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[5,4,2,1,3,8,6,7]=>[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[5,4,3,1,2,6,8,7]=>[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[5,4,3,1,2,8,6,7]=>[4,5,3,2,1,7,8,6]=>[2,1,1,3,1]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>[5,4,3,2,1,7,8,6]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[5,3]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>[2,3,4,5,6,1,8,7]=>[5,2,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>[2,3,5,4,6,1,7,8]=>[3,2,3]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[6,1,2,5,3,4,8,7]=>[2,3,5,6,4,1,8,7]=>[4,1,2,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>[2,4,5,3,6,1,8,7]=>[3,2,2,1]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7,8]=>[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[6,1,4,3,2,5,8,7]=>[2,5,4,3,6,1,8,7]=>[2,1,2,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7,8]=>[2,4,5,6,3,1,7,8]=>[4,1,3]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7,8]=>[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>[2,5,6,4,3,1,8,7]=>[3,1,1,2,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[6,2,1,5,3,4,8,7]=>[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>[3,4,2,5,6,1,8,7]=>[2,3,2,1]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7,8]=>[3,4,2,6,5,1,7,8]=>[2,2,1,3]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>[4,3,2,5,6,1,8,7]=>[1,1,3,2,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>[4,3,2,6,5,1,7,8]=>[1,1,2,1,3]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>[3,2,3]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[6,4,1,2,3,5,8,7]=>[3,4,5,2,6,1,8,7]=>[3,2,2,1]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>[3,5,4,2,6,1,7,8]=>[2,1,2,3]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,1,3,2,5,8,7]=>[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>[3,4,5,6,2,1,8,7]=>[4,1,2,1]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[6,5,1,3,2,4,8,7]=>[3,5,4,6,2,1,8,7]=>[2,2,1,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7,8]=>[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7,8]=>[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,5,1,4,3,2,8,7]=>[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7,8]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7,8]=>[4,3,6,5,2,1,7,8]=>[1,2,1,1,3]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7,8]=>[4,5,3,6,2,1,7,8]=>[2,2,1,3]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>[5,4,3,6,2,1,8,7]=>[1,1,2,1,2,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[6,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>[2,3,5,4,6,7,1,8]=>[3,3,2]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6,8]=>[2,3,5,6,4,7,1,8]=>[4,2,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>[2,3,5,6,7,4,1,8]=>[5,1,2]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>[2,3,6,5,7,4,1,8]=>[3,2,1,2]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>[2,3,6,7,5,4,1,8]=>[4,1,1,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5,8]=>[2,4,3,5,7,6,1,8]=>[2,3,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>[2,4,3,6,5,7,1,8]=>[2,2,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[8,6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6,8]=>[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>[2,4,5,6,7,3,1,8]=>[5,1,2]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4,8]=>[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3,8]=>[2,4,7,6,5,3,1,8]=>[3,1,1,1,2]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4,8]=>[2,5,4,7,6,3,1,8]=>[2,2,1,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>[2,5,6,4,7,3,1,8]=>[3,2,1,2]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4,8]=>[2,5,6,7,4,3,1,8]=>[4,1,1,2]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>[2,6,5,7,4,3,1,8]=>[2,2,1,1,2]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5,8]=>[3,2,4,6,7,5,1,8]=>[1,4,1,2]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3,8]=>[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>[3,4,2,6,5,7,1,8]=>[2,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>[3,4,2,6,7,5,1,8]=>[2,3,1,2]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4,8]=>[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>[3,3,2]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5,8]=>[3,4,5,2,7,6,1,8]=>[3,2,1,2]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6,8]=>[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6,8]=>[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>[3,4,7,6,5,2,1,8]=>[3,1,1,1,2]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4,8]=>[3,5,4,7,6,2,1,8]=>[2,2,1,1,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>[3,5,6,4,7,2,1,8]=>[3,2,1,2]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[8,4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4,8]=>[3,5,6,7,4,2,1,8]=>[4,1,1,2]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[8,4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4,8]=>[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3,8]=>[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5,8]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[8,5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5,8]=>[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>[4,5,7,6,3,2,1,8]=>[3,1,1,1,2]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>[4,6,7,5,3,2,1,8]=>[3,1,1,1,2]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4,8]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[8,1,2,3,4,6,5,7]=>[2,3,4,5,7,6,8,1]=>[5,2,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>[2,3,4,5,7,8,6,1]=>[6,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>[2,3,4,6,5,7,8,1]=>[4,3,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>[2,3,4,6,5,8,7,1]=>[4,2,1,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[8,1,2,3,7,4,6,5]=>[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[8,1,2,3,7,6,4,5]=>[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>[2,3,5,4,6,7,8,1]=>[3,4,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>[2,3,5,4,7,6,8,1]=>[3,2,2,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>[2,3,5,4,8,7,6,1]=>[3,2,1,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>[2,3,5,6,4,7,8,1]=>[4,3,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[8,1,2,6,3,5,4,7]=>[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[8,1,2,7,3,5,4,6]=>[2,3,5,7,6,8,4,1]=>[4,2,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>[2,3,6,5,8,7,4,1]=>[3,2,1,1,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[8,1,2,7,5,3,4,6]=>[2,3,6,7,5,8,4,1]=>[4,2,1,1]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[5,3,4,6,7,2,1,8]=>[8,1,2,7,6,4,3,5]=>[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[2,5,1]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>[2,4,3,5,6,8,7,1]=>[2,4,1,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>[2,4,3,5,7,6,8,1]=>[2,3,2,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>[2,4,3,5,8,7,6,1]=>[2,3,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>[2,4,3,6,5,7,8,1]=>[2,2,3,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>[2,4,3,7,6,5,8,1]=>[2,2,1,2,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[8,1,3,2,7,4,5,6]=>[2,4,3,6,7,8,5,1]=>[2,4,1,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>[2,4,5,3,6,7,8,1]=>[3,4,1]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>[2,5,4,3,6,8,7,1]=>[2,1,3,1,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>[2,5,4,3,7,6,8,1]=>[2,1,2,2,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>[2,5,4,3,7,8,6,1]=>[2,1,3,1,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>[2,5,4,6,3,7,8,1]=>[2,2,3,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>[2,4,5,6,7,3,8,1]=>[5,2,1]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[8,1,6,2,3,5,4,7]=>[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>[2,4,6,7,5,3,8,1]=>[4,1,2,1]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>[2,5,4,6,7,3,8,1]=>[2,3,2,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[7,3,4,2,5,6,1,8]=>[8,1,6,5,2,4,3,7]=>[2,5,7,6,4,3,8,1]=>[3,1,1,2,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>[2,4,5,6,7,8,3,1]=>[6,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[8,1,7,2,6,5,3,4]=>[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[8,1,7,4,3,2,5,6]=>[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[8,1,7,6,2,3,5,4]=>[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[4,3,5,2,6,7,1,8]=>[8,1,7,6,2,5,3,4]=>[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[8,1,7,6,3,2,5,4]=>[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[8,1,7,6,4,2,3,5]=>[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>[2,7,6,5,8,4,3,1]=>[2,1,2,1,1,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[1,6,1]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>[3,2,4,5,7,6,8,1]=>[1,4,2,1]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>[3,2,4,7,6,5,8,1]=>[1,3,1,2,1]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,3,1,2,8]=>[8,2,1,3,7,4,5,6]=>[3,2,4,6,7,8,5,1]=>[1,5,1,1]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[8,2,1,4,3,5,6,7]=>[3,2,5,4,6,7,8,1]=>[1,2,4,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>[3,2,5,6,7,4,8,1]=>[1,4,2,1]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>[3,2,6,5,7,4,8,1]=>[1,2,2,2,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>[3,2,5,6,7,8,4,1]=>[1,5,1,1]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[8,2,1,7,3,4,6,5]=>[3,2,5,6,8,7,4,1]=>[1,4,1,1,1]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[4,5,6,3,7,1,2,8]=>[8,2,1,7,3,6,5,4]=>[3,2,5,8,7,6,4,1]=>[1,3,1,1,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>[3,2,6,8,7,5,4,1]=>[1,3,1,1,1,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[2,5,1]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>[3,4,2,5,6,8,7,1]=>[2,4,1,1]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>[3,4,2,5,7,8,6,1]=>[2,4,1,1]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>[3,4,2,6,5,7,8,1]=>[2,2,3,1]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>[3,4,2,7,6,5,8,1]=>[2,2,1,2,1]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>[3,4,2,6,7,8,5,1]=>[2,4,1,1]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,2,1,3,8]=>[8,3,1,2,7,5,4,6]=>[3,4,2,7,6,8,5,1]=>[2,2,2,1,1]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>[3,4,2,7,8,6,5,1]=>[2,3,1,1,1]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>[4,3,2,5,6,8,7,1]=>[1,1,4,1,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>[4,3,2,5,7,6,8,1]=>[1,1,3,2,1]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>[4,3,2,5,8,7,6,1]=>[1,1,3,1,1,1]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>[4,3,2,6,7,5,8,1]=>[1,1,3,2,1]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>[4,3,2,7,6,5,8,1]=>[1,1,2,1,2,1]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>[4,3,2,6,7,8,5,1]=>[1,1,4,1,1]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>[4,3,2,6,8,7,5,1]=>[1,1,3,1,1,1]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>[3,4,1]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[6,7,5,3,2,1,4,8]=>[8,4,1,2,3,5,7,6]=>[3,4,5,2,6,8,7,1]=>[3,3,1,1]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[8,4,1,2,3,6,5,7]=>[3,4,5,2,7,6,8,1]=>[3,2,2,1]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>[3,4,5,2,7,8,6,1]=>[3,3,1,1]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[8,4,1,2,3,7,6,5]=>[3,4,5,2,8,7,6,1]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>[3,5,4,2,6,7,8,1]=>[2,1,4,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[1,2,4,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[8,4,3,1,2,5,6,7]=>[4,5,3,2,6,7,8,1]=>[2,1,4,1]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>[4,5,3,2,7,6,8,1]=>[2,1,2,2,1]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>[5,4,3,2,6,8,7,1]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>[5,4,3,2,7,8,6,1]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>[3,5,4,6,2,7,8,1]=>[2,2,3,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[8,5,1,4,3,2,6,7]=>[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[8,5,1,4,3,2,7,6]=>[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[8,5,4,1,3,2,7,6]=>[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[8,5,4,2,1,3,7,6]=>[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>[3,4,6,5,7,2,8,1]=>[3,2,2,1]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>[3,4,6,7,5,2,8,1]=>[4,1,2,1]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>[3,4,7,6,5,2,8,1]=>[3,1,1,2,1]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[7,4,5,2,3,1,6,8]=>[8,6,1,3,2,5,4,7]=>[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>[3,5,6,7,4,2,8,1]=>[4,1,2,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>[5,4,3,7,6,2,8,1]=>[1,1,2,1,2,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[8,6,5,2,1,4,3,7]=>[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[7,4,2,1,3,5,6,8]=>[8,6,5,3,1,2,4,7]=>[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[8,7,1,2,3,6,5,4]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[5,3,4,6,2,1,7,8]=>[8,7,1,2,6,4,3,5]=>[3,4,7,6,8,5,2,1]=>[3,2,1,1,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>[3,5,4,7,6,8,2,1]=>[2,2,2,1,1]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[6,3,4,2,5,1,7,8]=>[8,7,1,5,2,4,3,6]=>[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[8,7,1,5,3,2,4,6]=>[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>[3,6,7,5,4,8,2,1]=>[3,1,2,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[8,7,1,6,3,2,4,5]=>[3,6,5,7,8,4,2,1]=>[2,3,1,1,1]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[4,5,2,3,6,1,7,8]=>[8,7,1,6,3,2,5,4]=>[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>[3,6,7,5,8,4,2,1]=>[3,2,1,1,1]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>[4,3,5,7,6,8,2,1]=>[1,3,2,1,1]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[4,5,3,6,1,2,7,8]=>[8,7,2,1,6,3,5,4]=>[4,3,6,8,7,5,2,1]=>[1,3,1,1,1,1]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[8,7,2,1,6,4,3,5]=>[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[4,3,5,6,1,2,7,8]=>[8,7,2,1,6,5,3,4]=>[4,3,7,8,6,5,2,1]=>[1,3,1,1,1,1]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[8,7,3,1,2,4,5,6]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[8,7,3,1,2,5,4,6]=>[4,5,3,7,6,8,2,1]=>[2,2,2,1,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>[5,4,3,6,8,7,2,1]=>[1,1,3,1,1,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>[5,4,3,7,8,6,2,1]=>[1,1,3,1,1,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[8,7,4,1,3,2,5,6]=>[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[8,7,4,1,3,2,6,5]=>[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[8,7,4,3,1,2,6,5]=>[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>[4,5,7,6,3,8,2,1]=>[3,1,2,1,1]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[8,7,5,2,1,4,3,6]=>[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>[5,7,6,4,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[8,7,5,4,2,1,3,6]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>[4,5,7,6,8,3,2,1]=>[3,2,1,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>[4,6,5,8,7,3,2,1]=>[2,2,1,1,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[4,5,3,1,2,6,7,8]=>[8,7,6,2,1,3,5,4]=>[5,4,6,8,7,3,2,1]=>[1,3,1,1,1,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>[5,4,7,6,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[8,7,6,2,1,5,3,4]=>[5,4,7,8,6,3,2,1]=>[1,3,1,1,1,1]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[8,7,6,2,1,5,4,3]=>[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[8,7,6,3,1,2,5,4]=>[5,6,4,8,7,3,2,1]=>[2,2,1,1,1,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>[5,7,6,4,8,3,2,1]=>[2,1,2,1,1,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>[5,7,6,8,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
inverse
Description
Sends a permutation to its inverse.
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 $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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