Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[1,2]=>[2]
[[.,.],.]=>[1,2]=>[1,2]=>[2,1]=>[1,1]
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>[3]
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>[2,1]
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>[2,1,3]=>[1,2]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,3,1]=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>[1,1,1]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>[1,2,4,3]=>[3,1]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>[1,3,2,4]=>[2,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>[1,3,4,2]=>[3,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[1,4,3,2]=>[2,1,1]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[3,4,2,1]=>[2,1,3,4]=>[1,3]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,1,3]=>[3,1,4,2]=>[1,2,1]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,4,1]=>[2,3,1,4]=>[2,2]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,4,1]=>[3,2,1,4]=>[1,1,2]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>[3,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[2,4,3,1]=>[2,1,1]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,3,1,4]=>[3,2,4,1]=>[1,2,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>[2,1,1]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[4,1]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[3,2]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[4,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[2,3]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[3,2]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[2,1,2]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[4,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[3,1,1]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[3,1,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[2,1,1,1]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[1,4]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[3,1,2,5,4]=>[1,3,1]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[3,1,4,5,2]=>[1,3,1]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[1,2,1,1]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[2,3]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[2,2,1]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,2,1]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[3,2]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[2,1,2]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[1,2,2]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[2,1,2]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[1,1,1,2]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[4,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[3,1,1]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[2,2,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[3,1,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[2,1,1,1]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[1,3,1]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,2,1,1]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[2,2,1]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,2,1]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[3,1,1]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[2,1,1,1]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,2,1,1]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[2,1,1,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[5,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[4,2]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[5,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[4,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[3,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[3,2,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[4,2]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[3,1,2]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[5,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[4,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[3,2,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[4,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[3,1,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[2,4]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>[2,3,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[2,2,2]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>[2,3,1]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[2,2,1,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[3,3]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[3,2,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[2,1,3]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[2,1,2,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[4,2]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[3,1,2]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[2,2,2]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[3,1,2]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[2,1,1,2]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[5,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[4,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[3,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[4,1,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[3,1,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[2,3,1]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[2,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[3,2,1]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[2,1,2,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[4,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[3,1,1,1]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[2,2,1,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[3,1,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[1,5]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[1,4,1]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>[1,3,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[1,4,1]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>[1,3,1,1]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>[1,2,3]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[1,2,2,1]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>[1,3,2]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>[1,2,1,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>[1,4,1]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>[1,3,1,1]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>[1,2,2,1]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>[1,3,1,1]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,2,1,1,1]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[2,4]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>[2,3,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>[2,2,2]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>[2,3,1]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[2,2,1,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[1,1,4]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>[1,1,3,1]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>[1,1,2,2]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>[1,1,3,1]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[3,3]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[3,2,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[2,1,3]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>[2,1,2,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[1,2,3]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[1,2,2,1]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[2,1,3]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[2,1,2,1]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[4,2]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[3,1,2]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[2,2,2]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[3,1,2]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[2,1,1,2]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[1,3,2]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>[1,2,1,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[2,2,2]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[1,1,2,2]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[3,1,2]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[2,1,1,2]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[1,2,1,2]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[2,1,1,2]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[5,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[4,1,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[3,2,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[4,1,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[3,1,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[2,3,1]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[2,2,1,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[3,2,1]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[2,1,2,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[4,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[3,1,1,1]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[2,2,1,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[3,1,1,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[1,4,1]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[1,3,1,1]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>[1,2,2,1]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[1,3,1,1]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[2,3,1]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[2,2,1,1]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[1,1,3,1]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,2,1,1]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[3,2,1]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[2,1,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[1,2,2,1]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[2,1,2,1]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[4,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[3,1,1,1]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[2,2,1,1]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[3,1,1,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,3,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,2,1,1,1]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[2,2,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[6,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[5,2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[6,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[5,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>[4,2,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[5,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[4,1,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[6,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[5,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[4,2,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[5,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[3,4]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>[3,3,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>[3,2,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>[3,3,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[4,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>[4,2,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[3,1,3]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>[3,1,2,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[5,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[4,1,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[3,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[4,1,2]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[6,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[5,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[4,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[5,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[3,3,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[4,2,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[3,1,2,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[5,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[3,2,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[2,5]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>[2,4,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>[2,3,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>[2,4,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>[2,3,1,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>[2,2,3]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>[2,3,2]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>[2,2,1,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>[2,4,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>[2,3,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>[2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>[2,3,1,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[2,2,1,1,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[3,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>[3,3,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>[3,2,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>[3,3,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>[3,2,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[2,1,4]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>[2,1,2,2]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>[2,1,3,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>[2,1,2,1,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[4,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>[4,2,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[3,1,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>[3,1,2,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[2,2,3]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>[2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[3,1,3]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>[3,1,2,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>[2,1,1,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[5,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[4,1,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[3,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[4,1,2]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[3,1,1,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[2,3,2]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>[2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[3,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[2,1,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[4,1,2]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[3,1,1,2]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[2,2,1,2]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[3,1,1,2]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[6,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[5,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[4,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[5,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[3,3,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>[3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[4,2,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[3,1,2,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[5,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[3,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[2,4,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>[2,3,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>[2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>[2,3,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[2,2,1,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[3,3,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>[3,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[2,1,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>[2,1,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[4,2,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[3,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[3,1,2,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[5,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[3,2,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[2,3,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[2,2,1,1,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[3,2,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[2,2,1,1,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[1,6]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>[1,5,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>[1,4,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>[1,5,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>[1,4,1,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>[1,3,3]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>[1,3,2,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>[1,4,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>[1,5,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>[1,4,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>[1,3,2,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[1,4,1,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>[1,3,1,1,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>[1,2,4]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>[1,2,3,1]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>[1,2,3,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>[1,2,2,1,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>[1,3,3]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>[1,3,2,1]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>[1,2,1,3]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>[1,2,1,2,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>[1,4,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>[1,3,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>[1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>[1,3,1,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>[1,2,1,1,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>[1,5,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[1,4,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>[1,3,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>[1,4,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>[1,3,1,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>[1,2,3,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>[1,2,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>[1,3,2,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>[1,2,1,2,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>[1,4,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>[1,3,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>[1,2,2,1,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>[1,3,1,1,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[2,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>[2,4,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>[2,3,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>[2,4,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>[2,3,1,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>[2,2,3]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>[2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>[2,3,2]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>[2,2,1,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>[2,4,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>[2,3,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>[2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>[2,3,1,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>[2,2,1,1,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>[1,1,4,1]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>[1,1,3,2]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>[1,1,4,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>[1,1,3,1,1]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>[1,1,2,2,1]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>[1,1,3,2]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>[1,1,2,1,2]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>[1,1,4,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>[1,1,3,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>[1,1,2,2,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>[1,1,3,1,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[3,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>[3,3,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>[3,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>[3,3,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>[3,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[2,1,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>[2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>[2,1,2,2]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>[2,1,3,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>[2,1,2,1,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[1,2,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>[1,2,3,1]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>[1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>[1,2,3,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>[1,2,2,1,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[2,1,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>[2,1,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>[2,1,2,2]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>[2,1,3,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>[2,1,2,1,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>[1,1,1,2,2]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>[1,1,1,3,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>[4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[3,1,3]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>[3,1,2,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[2,2,3]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>[2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[3,1,3]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>[3,1,2,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[2,1,1,3]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>[2,1,1,2,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[1,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>[1,3,2,1]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>[1,2,1,3]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>[1,2,1,2,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[2,2,3]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>[2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>[1,1,2,2,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[3,1,3]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>[3,1,2,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[2,1,1,3]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>[2,1,1,2,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>[1,2,1,2,1]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>[2,1,1,2,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[5,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[4,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[3,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[4,1,2]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[3,1,1,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[2,3,2]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>[2,2,1,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[3,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[2,1,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[4,1,2]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[3,1,1,2]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[2,2,1,2]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[3,1,1,2]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[1,4,2]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>[1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>[1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>[1,3,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>[1,2,1,1,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[2,3,2]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>[2,2,1,2]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>[1,1,2,1,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[3,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[2,1,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[4,1,2]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[3,1,1,2]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[2,2,1,2]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[3,1,1,2]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>[1,2,1,1,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[6,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[5,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[4,2,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[5,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[3,3,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>[3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[4,2,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[3,1,2,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[5,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[3,2,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[2,4,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>[2,3,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>[2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>[2,3,1,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>[2,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[3,3,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>[3,2,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[2,1,3,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>[2,1,2,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[4,2,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[3,1,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[3,1,2,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[5,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[3,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[2,3,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>[2,2,1,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[3,2,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[2,2,1,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[1,5,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>[1,4,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>[1,3,2,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>[1,4,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>[1,3,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>[1,2,3,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>[1,2,2,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>[1,3,2,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>[1,2,1,2,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>[1,4,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>[1,3,1,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>[1,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>[1,3,1,1,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>[1,2,1,1,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[2,4,1]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>[2,3,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>[2,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>[2,3,1,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>[2,2,1,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>[1,1,3,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>[1,1,2,2,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>[1,1,3,1,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>[1,1,2,1,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[3,3,1]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>[3,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[2,1,3,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>[2,1,2,1,1]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>[1,2,2,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>[2,1,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>[1,1,1,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[4,2,1]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[3,1,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[2,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[3,1,2,1]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>[1,2,1,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[3,2,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[2,3,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>[2,2,1,1,1]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[2,2,1,1,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>[1,3,1,1,1]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>[1,2,2,1,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>[1,3,1,1,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>[1,2,1,1,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>[2,2,1,1,1]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>[1,1,2,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[2,2,1,1,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>[1,2,1,1,1,1]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[7,1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>[6,2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[7,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>[5,3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[1,2,3,4,7,5,8,6]=>[5,2,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>[6,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[7,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>[5,2,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[4,4]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[8,7,6,3,5,4,1,2]=>[1,2,3,6,4,5,8,7]=>[4,3,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>[1,2,3,6,4,7,5,8]=>[4,2,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[1,2,3,6,4,7,8,5]=>[4,3,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[8,7,6,2,5,1,3,4]=>[1,2,3,7,4,8,6,5]=>[4,2,1,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[8,7,6,2,3,5,1,4]=>[1,2,3,7,6,4,8,5]=>[4,1,2,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>[4,2,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[7,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>[5,2,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>[4,3,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[8,7,6,2,4,1,3,5]=>[1,2,3,7,5,8,6,4]=>[4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>[5,2,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>[4,2,1,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>[3,5]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[1,2,6,3,7,4,8,5]=>[3,2,2,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,7,3,6,2,4,5,1]=>[1,2,6,3,7,5,4,8]=>[3,2,1,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[1,2,5,3,6,7,8,4]=>[3,4,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[8,7,3,6,4,1,2,5]=>[1,2,6,3,5,8,7,4]=>[3,3,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,7,2,6,1,3,4,5]=>[1,2,7,3,8,6,5,4]=>[3,2,1,1,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,7,3,2,6,1,4,5]=>[1,2,6,7,3,8,5,4]=>[4,2,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,4,5,6,3,2,1]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,7,2,3,6,1,4,5]=>[1,2,7,6,3,8,5,4]=>[3,1,2,1,1]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>[1,2,5,7,6,3,8,4]=>[4,1,2,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[8,7,3,2,4,6,1,5]=>[1,2,6,7,5,3,8,4]=>[4,1,2,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[8,7,2,3,4,6,1,5]=>[1,2,7,6,5,3,8,4]=>[3,1,1,2,1]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[8,7,5,2,3,4,6,1]=>[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>[4,2,2]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>[5,1,2]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[7,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[1,2,4,6,5,7,8,3]=>[4,3,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>[6,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>[2,6]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[8,5,7,6,4,2,1,3]=>[1,4,2,3,5,7,8,6]=>[2,5,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,3,7,6,1,2,4,5]=>[1,6,2,3,8,7,5,4]=>[2,3,1,1,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,5,7,4,6,3,2,1]=>[1,4,2,5,3,6,7,8]=>[2,2,4]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4,8]=>[2,2,2,2]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[8,3,7,2,6,1,4,5]=>[1,6,2,7,3,8,5,4]=>[2,2,2,1,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[8,3,7,2,4,6,1,5]=>[1,6,2,7,5,3,8,4]=>[2,2,1,2,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[8,4,7,5,2,3,6,1]=>[1,5,2,4,7,6,3,8]=>[2,3,1,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,4,7,3,5,2,6,1]=>[1,5,2,6,4,7,3,8]=>[2,2,2,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[8,5,7,4,3,2,1,6]=>[1,4,2,5,6,7,8,3]=>[2,5,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[8,4,7,3,5,2,1,6]=>[1,5,2,6,4,7,8,3]=>[2,2,3,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[8,4,7,3,2,1,5,6]=>[1,5,2,6,7,8,4,3]=>[2,4,1,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>[3,5]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[8,5,4,7,6,2,3,1]=>[1,4,5,2,3,7,6,8]=>[3,3,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[8,3,2,7,1,4,5,6]=>[1,6,7,2,8,5,4,3]=>[3,2,1,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[8,3,4,7,6,1,2,5]=>[1,6,5,2,3,8,7,4]=>[2,1,3,1,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[8,3,4,7,2,6,1,5]=>[1,6,5,2,7,3,8,4]=>[2,1,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,2,3,7,1,4,5,6]=>[1,7,6,2,8,5,4,3]=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>[4,4]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[8,5,4,3,7,6,1,2]=>[1,4,5,6,2,3,8,7]=>[4,3,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,6,4,5,7,3,2,1]=>[1,3,5,4,2,6,7,8]=>[3,1,4]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,4,5,3,7,2,6,1]=>[1,5,4,6,2,7,3,8]=>[2,2,2,2]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,7,1,5,6]=>[1,7,6,5,2,8,4,3]=>[2,1,1,2,1,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[8,5,4,3,2,7,1,6]=>[1,4,5,6,7,2,8,3]=>[5,2,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>[4,1,3]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[8,4,6,3,5,7,2,1]=>[1,5,3,6,4,2,7,8]=>[2,2,1,3]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,5,4,3,6,7,2,1]=>[1,4,5,6,3,2,7,8]=>[4,1,3]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[8,4,5,3,6,7,2,1]=>[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>[6,2]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[8,6,3,5,2,4,7,1]=>[1,3,6,4,7,5,2,8]=>[3,2,1,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,4,6,3,5,2,7,1]=>[1,5,3,6,4,7,2,8]=>[2,2,2,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,3,4,5,6,2,7,1]=>[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,5,4,3,2,6,7,1]=>[1,4,5,6,7,3,2,8]=>[5,1,2]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[1,3,4,6,5,7,8,2]=>[4,3,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[1,3,6,4,7,5,8,2]=>[3,2,2,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[8,6,2,5,1,3,4,7]=>[1,3,7,4,8,6,5,2]=>[3,2,1,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>[4,3,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>[5,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,6,2,4,1,3,5,7]=>[1,3,7,5,8,6,4,2]=>[3,2,1,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[8,6,2,3,1,4,5,7]=>[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,3,6,2,4,1,5,7]=>[1,6,3,7,5,8,4,2]=>[2,2,2,1,1]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[8,4,3,6,5,1,2,7]=>[1,5,6,3,4,8,7,2]=>[3,3,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,4,3,6,2,1,5,7]=>[1,5,6,3,7,8,4,2]=>[3,3,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[8,3,4,6,2,5,1,7]=>[1,6,5,3,7,4,8,2]=>[2,1,2,2,1]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[8,4,3,2,6,1,5,7]=>[1,5,6,7,3,8,4,2]=>[4,2,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[8,5,4,3,2,6,1,7]=>[1,4,5,6,7,3,8,2]=>[5,2,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>[4,1,2,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[8,5,2,4,1,3,6,7]=>[1,4,7,5,8,6,3,2]=>[3,2,1,1,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,3,5,2,1,4,6,7]=>[1,6,4,7,8,5,3,2]=>[2,3,1,1,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[8,3,4,2,5,1,6,7]=>[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[8,4,2,3,1,5,6,7]=>[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,3,4,2,1,5,6,7]=>[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[8,2,4,1,3,5,6,7]=>[1,7,5,8,6,4,3,2]=>[2,2,1,1,1,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[5,8,7,6,4,1,2,3]=>[4,1,2,3,5,8,7,6]=>[1,5,1,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[6,8,7,5,3,2,1,4]=>[3,1,2,4,6,7,8,5]=>[1,6,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[5,8,7,6,3,1,2,4]=>[4,1,2,3,6,8,7,5]=>[1,5,1,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[5,8,7,6,2,3,1,4]=>[4,1,2,3,7,6,8,5]=>[1,4,2,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[5,8,7,6,2,1,3,4]=>[4,1,2,3,7,8,6,5]=>[1,5,1,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[4,8,7,6,1,2,3,5]=>[5,1,2,3,8,7,6,4]=>[1,4,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[5,8,7,3,6,4,1,2]=>[4,1,2,6,3,5,8,7]=>[1,3,3,1]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[5,8,7,3,6,2,4,1]=>[4,1,2,6,3,7,5,8]=>[1,3,2,2]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[4,8,7,2,6,1,3,5]=>[5,1,2,7,3,8,6,4]=>[1,3,2,1,1]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[5,8,7,3,2,6,1,4]=>[4,1,2,6,7,3,8,5]=>[1,4,2,1]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[4,8,7,2,3,6,1,5]=>[5,1,2,7,6,3,8,4]=>[1,3,1,2,1]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[5,8,7,3,4,2,6,1]=>[4,1,2,6,5,7,3,8]=>[1,3,2,2]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[5,8,7,3,2,4,6,1]=>[4,1,2,6,7,5,3,8]=>[1,4,1,2]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[5,8,7,3,2,1,4,6]=>[4,1,2,6,7,8,5,3]=>[1,5,1,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[4,8,7,2,1,3,5,6]=>[5,1,2,7,8,6,4,3]=>[1,4,1,1,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[6,8,5,7,4,3,2,1]=>[3,1,4,2,5,6,7,8]=>[1,2,5]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[5,8,4,7,6,2,3,1]=>[4,1,5,2,3,7,6,8]=>[1,2,3,2]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[4,8,3,7,6,1,2,5]=>[5,1,6,2,3,8,7,4]=>[1,2,3,1,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[5,8,4,7,3,6,2,1]=>[4,1,5,2,6,3,7,8]=>[1,2,2,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[4,8,3,7,2,5,1,6]=>[5,1,6,2,7,4,8,3]=>[1,2,2,2,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[4,8,3,7,2,1,5,6]=>[5,1,6,2,7,8,4,3]=>[1,2,3,1,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[3,8,2,7,1,4,5,6]=>[6,1,7,2,8,5,4,3]=>[1,2,2,1,1,1]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[5,8,4,3,7,6,1,2]=>[4,1,5,6,2,3,8,7]=>[1,3,3,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[5,8,4,6,7,3,2,1]=>[4,1,5,3,2,6,7,8]=>[1,2,1,4]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[4,8,3,5,7,2,1,6]=>[5,1,6,4,2,7,8,3]=>[1,2,1,3,1]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[3,8,2,4,7,1,5,6]=>[6,1,7,5,2,8,4,3]=>[1,2,1,2,1,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[6,8,5,4,3,7,2,1]=>[3,1,4,5,6,2,7,8]=>[1,4,3]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[4,8,3,5,2,7,1,6]=>[5,1,6,4,7,2,8,3]=>[1,2,2,2,1]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[5,8,4,3,6,7,2,1]=>[4,1,5,6,3,2,7,8]=>[1,3,1,3]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[4,8,3,2,5,7,1,6]=>[5,1,6,7,4,2,8,3]=>[1,3,1,2,1]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[4,8,3,5,6,7,2,1]=>[5,1,6,4,3,2,7,8]=>[1,2,1,1,3]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[5,8,6,3,4,2,7,1]=>[4,1,3,6,5,7,2,8]=>[1,3,2,2]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[5,8,4,6,3,2,7,1]=>[4,1,5,3,6,7,2,8]=>[1,2,3,2]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[5,8,4,3,2,6,7,1]=>[4,1,5,6,7,3,2,8]=>[1,4,1,2]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[5,8,6,4,3,1,2,7]=>[4,1,3,5,6,8,7,2]=>[1,5,1,1]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[4,8,3,6,2,5,1,7]=>[5,1,6,3,7,4,8,2]=>[1,2,2,2,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[4,8,3,5,2,6,1,7]=>[5,1,6,4,7,3,8,2]=>[1,2,2,2,1]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[4,8,3,2,5,1,6,7]=>[5,1,6,7,4,8,3,2]=>[1,3,2,1,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[4,8,3,2,1,5,6,7]=>[5,1,6,7,8,4,3,2]=>[1,4,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>[2,6]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[6,5,8,7,4,3,1,2]=>[3,4,1,2,5,6,8,7]=>[2,5,1]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[6,5,8,7,4,2,3,1]=>[3,4,1,2,5,7,6,8]=>[2,4,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[6,5,8,7,4,2,1,3]=>[3,4,1,2,5,7,8,6]=>[2,5,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[5,4,8,7,6,1,2,3]=>[4,5,1,2,3,8,7,6]=>[2,4,1,1]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[6,5,8,7,3,4,2,1]=>[3,4,1,2,6,5,7,8]=>[2,3,3]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[5,4,8,7,2,6,1,3]=>[4,5,1,2,7,3,8,6]=>[2,3,2,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[6,5,8,7,3,2,4,1]=>[3,4,1,2,6,7,5,8]=>[2,4,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[6,5,8,7,3,2,1,4]=>[3,4,1,2,6,7,8,5]=>[2,5,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[5,4,8,7,3,1,2,6]=>[4,5,1,2,6,8,7,3]=>[2,4,1,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[5,4,8,7,2,1,3,6]=>[4,5,1,2,7,8,6,3]=>[2,4,1,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[4,3,8,7,1,2,5,6]=>[5,6,1,2,8,7,4,3]=>[2,3,1,1,1]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[5,4,8,3,7,6,1,2]=>[4,5,1,6,2,3,8,7]=>[2,2,3,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[5,4,8,3,7,2,6,1]=>[4,5,1,6,2,7,3,8]=>[2,2,2,2]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[4,3,8,2,7,1,5,6]=>[5,6,1,7,2,8,4,3]=>[2,2,2,1,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[5,4,8,3,6,7,2,1]=>[4,5,1,6,3,2,7,8]=>[2,2,1,3]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[4,3,8,2,5,7,1,6]=>[5,6,1,7,4,2,8,3]=>[2,2,1,2,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[5,4,8,3,6,2,7,1]=>[4,5,1,6,3,7,2,8]=>[2,2,2,2]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[4,3,8,2,5,6,7,1]=>[5,6,1,7,4,3,2,8]=>[2,2,1,1,2]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[5,4,8,6,2,1,3,7]=>[4,5,1,3,7,8,6,2]=>[2,4,1,1]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[4,3,8,6,1,2,5,7]=>[5,6,1,3,8,7,4,2]=>[2,3,1,1,1]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[4,3,8,2,6,1,5,7]=>[5,6,1,7,3,8,4,2]=>[2,2,2,1,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[5,4,8,3,2,6,1,7]=>[4,5,1,6,7,3,8,2]=>[2,3,2,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,2,8,1,4,5,6,7]=>[6,7,1,8,5,4,3,2]=>[2,2,1,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[4,5,8,7,6,1,2,3]=>[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[5,6,8,7,3,2,1,4]=>[4,3,1,2,6,7,8,5]=>[1,1,5,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>[6,5,1,2,8,7,4,3]=>[1,1,3,1,1,1]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[4,5,8,3,7,6,1,2]=>[5,4,1,6,2,3,8,7]=>[1,1,2,3,1]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[4,5,8,3,7,2,6,1]=>[5,4,1,6,2,7,3,8]=>[1,1,2,2,2]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,4,8,2,7,1,5,6]=>[6,5,1,7,2,8,4,3]=>[1,1,2,2,1,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>[4,5,8,3,2,7,1,6]=>[5,4,1,6,7,2,8,3]=>[1,1,3,2,1]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[3,4,8,2,5,7,1,6]=>[6,5,1,7,4,2,8,3]=>[1,1,2,1,2,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[5,6,8,4,3,2,7,1]=>[4,3,1,5,6,7,2,8]=>[1,1,4,2]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[4,5,8,3,6,2,7,1]=>[5,4,1,6,3,7,2,8]=>[1,1,2,2,2]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[4,5,8,6,2,3,1,7]=>[5,4,1,3,7,6,8,2]=>[1,1,3,2,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[3,4,8,6,1,2,5,7]=>[6,5,1,3,8,7,4,2]=>[1,1,3,1,1,1]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[4,5,8,3,6,2,1,7]=>[5,4,1,6,3,7,8,2]=>[1,1,2,3,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[4,5,8,3,2,1,6,7]=>[5,4,1,6,7,8,3,2]=>[1,1,4,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>[3,5]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[6,5,4,8,7,3,1,2]=>[3,4,5,1,2,6,8,7]=>[3,4,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[6,5,4,8,7,2,3,1]=>[3,4,5,1,2,7,6,8]=>[3,3,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[6,5,4,8,7,2,1,3]=>[3,4,5,1,2,7,8,6]=>[3,4,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[5,4,3,8,7,1,2,6]=>[4,5,6,1,2,8,7,3]=>[3,3,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[6,5,4,8,3,7,2,1]=>[3,4,5,1,6,2,7,8]=>[3,2,3]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[5,4,3,8,2,7,1,6]=>[4,5,6,1,7,2,8,3]=>[3,2,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[6,5,4,8,3,2,7,1]=>[3,4,5,1,6,7,2,8]=>[3,3,2]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[5,4,3,8,2,6,7,1]=>[4,5,6,1,7,3,2,8]=>[3,2,1,2]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[6,5,4,8,3,2,1,7]=>[3,4,5,1,6,7,8,2]=>[3,4,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[5,4,3,8,2,6,1,7]=>[4,5,6,1,7,3,8,2]=>[3,2,2,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[5,4,3,8,2,1,6,7]=>[4,5,6,1,7,8,3,2]=>[3,3,1,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,3,2,8,1,5,6,7]=>[5,6,7,1,8,4,3,2]=>[3,2,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>[2,1,5]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[6,4,5,8,7,2,3,1]=>[3,5,4,1,2,7,6,8]=>[2,1,3,2]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[6,4,5,8,7,2,1,3]=>[3,5,4,1,2,7,8,6]=>[2,1,4,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[5,3,4,8,7,1,2,6]=>[4,6,5,1,2,8,7,3]=>[2,1,3,1,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[6,4,5,8,3,2,7,1]=>[3,5,4,1,6,7,2,8]=>[2,1,3,2]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[5,3,4,8,2,6,1,7]=>[4,6,5,1,7,3,8,2]=>[2,1,2,2,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,2,3,8,1,5,6,7]=>[5,7,6,1,8,4,3,2]=>[2,1,2,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[4,5,3,8,2,7,1,6]=>[5,4,6,1,7,2,8,3]=>[1,2,2,2,1]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[5,6,4,8,3,2,1,7]=>[4,3,5,1,6,7,8,2]=>[1,2,4,1]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[4,5,3,8,2,6,1,7]=>[5,4,6,1,7,3,8,2]=>[1,2,2,2,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[4,5,3,8,2,1,6,7]=>[5,4,6,1,7,8,3,2]=>[1,2,3,1,1]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[5,4,6,8,7,3,1,2]=>[4,5,3,1,2,6,8,7]=>[2,1,4,1]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[5,4,6,8,7,2,3,1]=>[4,5,3,1,2,7,6,8]=>[2,1,3,2]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[4,5,6,8,7,2,3,1]=>[5,4,3,1,2,7,6,8]=>[1,1,1,3,2]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,5,6,8,7,2,1,3]=>[5,4,3,1,2,7,8,6]=>[1,1,1,4,1]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[4,5,6,8,3,7,2,1]=>[5,4,3,1,6,2,7,8]=>[1,1,1,2,3]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[3,4,5,8,2,7,1,6]=>[6,5,4,1,7,2,8,3]=>[1,1,1,2,2,1]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[4,5,6,8,3,2,7,1]=>[5,4,3,1,6,7,2,8]=>[1,1,1,3,2]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,5,6,8,3,2,1,7]=>[5,4,3,1,6,7,8,2]=>[1,1,1,4,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[3,4,5,8,2,1,6,7]=>[6,5,4,1,7,8,3,2]=>[1,1,1,3,1,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[6,5,4,3,8,7,1,2]=>[3,4,5,6,1,2,8,7]=>[4,3,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[6,5,4,3,8,2,7,1]=>[3,4,5,6,1,7,2,8]=>[4,2,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[6,5,4,3,8,2,1,7]=>[3,4,5,6,1,7,8,2]=>[4,3,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,8,1,6,7]=>[4,5,6,7,1,8,3,2]=>[4,2,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>[3,1,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[6,5,3,4,8,7,1,2]=>[3,4,6,5,1,2,8,7]=>[3,1,3,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[6,5,3,4,8,2,7,1]=>[3,4,6,5,1,7,2,8]=>[3,1,2,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,4,2,3,8,1,6,7]=>[4,5,7,6,1,8,3,2]=>[3,1,2,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>[2,2,4]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[6,4,5,3,8,2,7,1]=>[3,5,4,6,1,7,2,8]=>[2,2,2,2]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>[3,1,4]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[6,4,3,5,8,7,1,2]=>[3,5,6,4,1,2,8,7]=>[3,1,3,1]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[6,4,3,5,8,2,1,7]=>[3,5,6,4,1,7,8,2]=>[3,1,3,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,3,2,4,8,1,6,7]=>[4,6,7,5,1,8,3,2]=>[3,1,2,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[6,3,4,5,8,7,1,2]=>[3,6,5,4,1,2,8,7]=>[2,1,1,3,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[6,3,4,5,8,2,7,1]=>[3,6,5,4,1,7,2,8]=>[2,1,1,2,2]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[6,3,4,5,8,2,1,7]=>[3,6,5,4,1,7,8,2]=>[2,1,1,3,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,2,3,4,8,1,6,7]=>[4,7,6,5,1,8,3,2]=>[2,1,1,2,1,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[5,6,4,3,8,2,1,7]=>[4,3,5,6,1,7,8,2]=>[1,3,3,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[4,5,3,2,8,1,6,7]=>[5,4,6,7,1,8,3,2]=>[1,3,2,1,1]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,7,4,6,8,3,2,1]=>[4,2,5,3,1,6,7,8]=>[1,2,1,4]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[4,6,3,5,8,7,1,2]=>[5,3,6,4,1,2,8,7]=>[1,2,1,3,1]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[4,6,3,5,8,2,7,1]=>[5,3,6,4,1,7,2,8]=>[1,2,1,2,2]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[4,6,3,5,8,2,1,7]=>[5,3,6,4,1,7,8,2]=>[1,2,1,3,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,5,2,4,8,1,6,7]=>[6,4,7,5,1,8,3,2]=>[1,2,1,2,1,1]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,4,6,3,8,7,1,2]=>[4,5,3,6,1,2,8,7]=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,4,6,3,8,2,7,1]=>[4,5,3,6,1,7,2,8]=>[2,2,2,2]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,4,6,3,8,2,1,7]=>[4,5,3,6,1,7,8,2]=>[2,2,3,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[4,3,5,2,8,1,6,7]=>[5,6,4,7,1,8,3,2]=>[2,2,2,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[4,5,6,3,8,7,1,2]=>[5,4,3,6,1,2,8,7]=>[1,1,2,3,1]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[4,5,6,3,8,2,1,7]=>[5,4,3,6,1,7,8,2]=>[1,1,2,3,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[3,4,5,2,8,1,6,7]=>[6,5,4,7,1,8,3,2]=>[1,1,2,2,1,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,4,3,6,8,7,1,2]=>[4,5,6,3,1,2,8,7]=>[3,1,3,1]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[5,4,3,6,8,2,7,1]=>[4,5,6,3,1,7,2,8]=>[3,1,2,2]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[4,3,2,5,8,1,6,7]=>[5,6,7,4,1,8,3,2]=>[3,1,2,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[5,3,4,6,8,7,1,2]=>[4,6,5,3,1,2,8,7]=>[2,1,1,3,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,3,4,6,8,2,1,7]=>[4,6,5,3,1,7,8,2]=>[2,1,1,3,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[4,2,3,5,8,1,6,7]=>[5,7,6,4,1,8,3,2]=>[2,1,1,2,1,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[4,5,3,6,8,2,7,1]=>[5,4,6,3,1,7,2,8]=>[1,2,1,2,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[3,4,2,5,8,1,6,7]=>[6,5,7,4,1,8,3,2]=>[1,2,1,2,1,1]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[4,3,5,6,8,2,1,7]=>[5,6,4,3,1,7,8,2]=>[2,1,1,3,1]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,8,1,6,7]=>[6,7,5,4,1,8,3,2]=>[2,1,1,2,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[3,4,5,6,8,7,1,2]=>[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[3,4,5,6,8,2,7,1]=>[6,5,4,3,1,7,2,8]=>[1,1,1,1,2,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[3,4,5,6,8,2,1,7]=>[6,5,4,3,1,7,8,2]=>[1,1,1,1,3,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,8,1,6,7]=>[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>[5,3]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,8,1,7]=>[3,4,5,6,7,1,8,2]=>[5,2,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>[3,2,3]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[6,5,2,3,4,8,1,7]=>[3,4,7,6,5,1,8,2]=>[3,1,1,2,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,4,5,3,2,8,1,7]=>[3,5,4,6,7,1,8,2]=>[2,3,2,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,4,3,5,2,8,1,7]=>[3,5,6,4,7,1,8,2]=>[3,2,2,1]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[7,4,5,6,3,8,2,1]=>[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[7,5,4,3,6,8,2,1]=>[2,4,5,6,3,1,7,8]=>[4,1,3]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[7,5,3,4,6,8,2,1]=>[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[6,4,2,3,5,8,1,7]=>[3,5,7,6,4,1,8,2]=>[3,1,1,2,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[7,4,5,3,6,8,2,1]=>[2,5,4,6,3,1,7,8]=>[2,2,1,3]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[4,6,3,5,2,8,1,7]=>[5,3,6,4,7,1,8,2]=>[1,2,2,2,1]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>[4,6,3,2,5,8,1,7]=>[5,3,6,7,4,1,8,2]=>[1,3,1,2,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[4,7,3,5,6,8,2,1]=>[5,2,6,4,3,1,7,8]=>[1,2,1,1,3]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[4,5,6,3,2,8,1,7]=>[5,4,3,6,7,1,8,2]=>[1,1,3,2,1]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[4,5,7,3,6,8,2,1]=>[5,4,2,6,3,1,7,8]=>[1,1,2,1,3]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[4,5,3,6,2,8,1,7]=>[5,4,6,3,7,1,8,2]=>[1,2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[5,4,6,7,3,8,2,1]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[4,5,6,7,3,8,2,1]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[3,4,5,6,2,8,1,7]=>[6,5,4,3,7,1,8,2]=>[1,1,1,2,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,8,1,7]=>[4,5,6,7,3,1,8,2]=>[4,1,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[6,4,3,5,7,8,2,1]=>[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,3,4,5,7,8,2,1]=>[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[5,2,3,4,6,8,1,7]=>[4,7,6,5,3,1,8,2]=>[2,1,1,1,2,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[5,6,4,3,7,8,2,1]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[4,6,3,5,7,8,2,1]=>[5,3,6,4,2,1,7,8]=>[1,2,1,1,3]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[3,5,2,4,6,8,1,7]=>[6,4,7,5,3,1,8,2]=>[1,2,1,1,2,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[3,4,5,2,6,8,1,7]=>[6,5,4,7,3,1,8,2]=>[1,1,2,1,2,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,8,1,7]=>[5,6,7,4,3,1,8,2]=>[3,1,1,2,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>[6,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>[3,3,2]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>[4,2,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>[5,1,2]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,6,4,2,3,5,8,1]=>[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[7,4,6,3,5,2,8,1]=>[2,5,3,6,4,7,1,8]=>[2,2,2,2]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[7,3,4,6,2,5,8,1]=>[2,6,5,3,7,4,1,8]=>[2,1,2,1,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,5,4,3,2,6,8,1]=>[2,4,5,6,7,3,1,8]=>[5,1,2]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,5,4,2,3,6,8,1]=>[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[7,5,2,3,4,6,8,1]=>[2,4,7,6,5,3,1,8]=>[3,1,1,1,2]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,4,3,5,2,6,8,1]=>[2,5,6,4,7,3,1,8]=>[3,2,1,2]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[5,7,6,3,2,4,8,1]=>[4,2,3,6,7,5,1,8]=>[1,4,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[6,5,7,4,3,2,8,1]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[5,4,7,6,2,3,8,1]=>[4,5,2,3,7,6,1,8]=>[2,3,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[5,4,7,3,6,2,8,1]=>[4,5,2,6,3,7,1,8]=>[2,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[5,4,7,3,2,6,8,1]=>[4,5,2,6,7,3,1,8]=>[2,3,1,2]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[4,3,7,2,5,6,8,1]=>[5,6,2,7,4,3,1,8]=>[2,2,1,1,2]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[5,4,6,7,3,2,8,1]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[4,5,6,7,3,2,8,1]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[6,5,3,4,7,2,8,1]=>[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[6,3,4,5,7,2,8,1]=>[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[4,5,3,6,7,2,8,1]=>[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[6,3,5,2,4,7,8,1]=>[3,6,4,7,5,2,1,8]=>[2,2,1,1,2]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[6,4,3,5,2,7,8,1]=>[3,5,6,4,7,2,1,8]=>[3,2,1,2]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>[3,6,2,4,5,7,8,1]=>[6,3,7,5,4,2,1,8]=>[1,2,1,1,1,2]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[4,3,6,2,5,7,8,1]=>[5,6,3,7,4,2,1,8]=>[2,2,1,1,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[4,5,6,3,2,7,8,1]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,8,1]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[5,3,2,4,6,7,8,1]=>[4,6,7,5,3,2,1,8]=>[3,1,1,1,2]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[4,5,3,2,6,7,8,1]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[3,5,2,4,6,7,8,1]=>[6,4,7,5,3,2,1,8]=>[1,2,1,1,1,2]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>[5,2,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>[6,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>[2,3,4,6,5,7,8,1]=>[4,3,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[7,3,6,5,1,2,4,8]=>[2,6,3,4,8,7,5,1]=>[2,3,1,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,3,6,2,5,1,4,8]=>[2,6,3,7,4,8,5,1]=>[2,2,2,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>[3,4,1]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[7,4,3,6,2,5,1,8]=>[2,5,6,3,7,4,8,1]=>[3,2,2,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,4,5,6,3,2,1,8]=>[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[7,3,4,6,5,1,2,8]=>[2,6,5,3,4,8,7,1]=>[2,1,3,1,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>[7,3,4,6,2,5,1,8]=>[2,6,5,3,7,4,8,1]=>[2,1,2,2,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[7,3,4,6,2,1,5,8]=>[2,6,5,3,7,8,4,1]=>[2,1,3,1,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[7,2,3,6,1,4,5,8]=>[2,7,6,3,8,5,4,1]=>[2,1,2,1,1,1]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[7,3,2,4,6,1,5,8]=>[2,6,7,5,3,8,4,1]=>[3,1,2,1,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,3,4,5,6,2,1,8]=>[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>[5,2,1]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,5,4,2,3,6,1,8]=>[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,3,5,2,1,4,6,8]=>[2,6,4,7,8,5,3,1]=>[2,3,1,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[7,3,4,2,5,1,6,8]=>[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[7,4,2,3,1,5,6,8]=>[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[7,3,4,2,1,5,6,8]=>[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[4,7,6,5,1,2,3,8]=>[5,2,3,4,8,7,6,1]=>[1,4,1,1,1]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[4,7,6,2,3,1,5,8]=>[5,2,3,7,6,8,4,1]=>[1,3,2,1,1]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>[5,2,6,3,7,4,8,1]=>[1,2,2,2,1]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[4,7,3,5,2,6,1,8]=>[5,2,6,4,7,3,8,1]=>[1,2,2,2,1]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[4,7,3,2,5,6,1,8]=>[5,2,6,7,4,3,8,1]=>[1,3,1,2,1]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[4,7,5,2,1,3,6,8]=>[5,2,4,7,8,6,3,1]=>[1,4,1,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[4,7,3,2,5,1,6,8]=>[5,2,6,7,4,8,3,1]=>[1,3,2,1,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[2,7,1,3,4,5,6,8]=>[7,2,8,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>[5,6,2,7,3,8,4,1]=>[2,2,2,1,1]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>[4,5,7,6,2,3,1,8]=>[5,4,2,3,7,6,8,1]=>[1,1,3,2,1]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[3,4,7,5,1,2,6,8]=>[6,5,2,4,8,7,3,1]=>[1,1,3,1,1,1]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[5,4,3,7,2,6,1,8]=>[4,5,6,2,7,3,8,1]=>[3,2,2,1]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>[5,4,3,7,2,1,6,8]=>[4,5,6,2,7,8,3,1]=>[3,3,1,1]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[4,3,2,7,1,5,6,8]=>[5,6,7,2,8,4,3,1]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[5,3,4,7,6,1,2,8]=>[4,6,5,2,3,8,7,1]=>[2,1,3,1,1]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[5,3,4,7,2,1,6,8]=>[4,6,5,2,7,8,3,1]=>[2,1,3,1,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[4,2,3,7,1,5,6,8]=>[5,7,6,2,8,4,3,1]=>[2,1,2,1,1,1]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[4,5,3,7,2,6,1,8]=>[5,4,6,2,7,3,8,1]=>[1,2,2,2,1]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[4,5,3,7,2,1,6,8]=>[5,4,6,2,7,8,3,1]=>[1,2,3,1,1]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[3,4,2,7,1,5,6,8]=>[6,5,7,2,8,4,3,1]=>[1,2,2,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[3,4,5,7,2,6,1,8]=>[6,5,4,2,7,3,8,1]=>[1,1,1,2,2,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[3,4,5,7,2,1,6,8]=>[6,5,4,2,7,8,3,1]=>[1,1,1,3,1,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[2,3,4,7,1,5,6,8]=>[7,6,5,2,8,4,3,1]=>[1,1,1,2,1,1,1]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,7,1,6,8]=>[4,5,6,7,2,8,3,1]=>[4,2,1,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[5,3,2,4,7,1,6,8]=>[4,6,7,5,2,8,3,1]=>[3,1,2,1,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[6,3,4,5,7,2,1,8]=>[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[4,5,3,2,7,1,6,8]=>[5,4,6,7,2,8,3,1]=>[1,3,2,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,5,2,4,7,1,6,8]=>[6,4,7,5,2,8,3,1]=>[1,2,1,2,1,1]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[4,3,5,2,7,1,6,8]=>[5,6,4,7,2,8,3,1]=>[2,2,2,1,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[4,5,3,6,7,2,1,8]=>[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[2,3,4,5,7,1,6,8]=>[7,6,5,4,2,8,3,1]=>[1,1,1,1,2,1,1]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>[3,2,2,1]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[6,3,5,2,4,7,1,8]=>[3,6,4,7,5,2,8,1]=>[2,2,1,2,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[6,4,2,3,5,7,1,8]=>[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[6,3,4,2,5,7,1,8]=>[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[4,6,3,5,2,7,1,8]=>[5,3,6,4,7,2,8,1]=>[1,2,2,2,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[4,6,3,2,5,7,1,8]=>[5,3,6,7,4,2,8,1]=>[1,3,1,2,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[4,5,3,2,6,7,1,8]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[3,5,2,4,6,7,1,8]=>[6,4,7,5,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[6,3,5,2,4,1,7,8]=>[3,6,4,7,5,8,2,1]=>[2,2,2,1,1]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[6,2,5,1,3,4,7,8]=>[3,7,4,8,6,5,2,1]=>[2,2,1,1,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[4,6,5,2,3,1,7,8]=>[5,3,4,7,6,8,2,1]=>[1,3,2,1,1]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[4,6,5,2,1,3,7,8]=>[5,3,4,7,8,6,2,1]=>[1,4,1,1,1]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>[6,3,7,4,8,5,2,1]=>[1,2,2,1,1,1]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>[5,3,6,7,4,8,2,1]=>[1,3,2,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[4,3,6,5,1,2,7,8]=>[5,6,3,4,8,7,2,1]=>[2,3,1,1,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[3,4,6,5,1,2,7,8]=>[6,5,3,4,8,7,2,1]=>[1,1,3,1,1,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[2,3,6,1,4,5,7,8]=>[7,6,3,8,5,4,2,1]=>[1,1,2,1,1,1,1]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>[5,6,7,3,8,4,2,1]=>[3,2,1,1,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[5,3,4,6,2,1,7,8]=>[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[2,3,4,6,1,5,7,8]=>[7,6,5,3,8,4,2,1]=>[1,1,1,2,1,1,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[4,3,5,2,6,1,7,8]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[3,4,2,5,6,1,7,8]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,5,7,6,8,3,2,1]=>[3,2,1,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[5,2,4,1,3,6,7,8]=>[4,7,5,8,6,3,2,1]=>[2,2,1,1,1,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[3,5,2,4,1,6,7,8]=>[6,4,7,5,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[2,5,1,3,4,6,7,8]=>[7,4,8,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[7,5,8,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
searching the database
Sorry, this map was not found in the database.