Identifier
Mp00018:
Binary trees
—left border symmetry⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
[.,.]=>[.,.]=>[1]=>[1]
[.,[.,.]]=>[.,[.,.]]=>[2,1]=>[1,1]
[[.,.],.]=>[[.,.],.]=>[1,2]=>[2]
[.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>[1,1,1]
[.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>[2,1]
[[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>[1,2]
[[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>[2,1]
[[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>[3]
[.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]
[.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]
[.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,2,1]
[.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[2,1,1]
[.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]
[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[1,1,2]
[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,2]
[[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[1,2,1]
[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[1,3]
[[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,1,1]
[[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1]
[[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,2]
[[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,1]
[[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4]
[.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]
[.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,1,1]
[.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,1,1,1]
[.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,1,2,1]
[.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[2,2,1]
[.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,2,1,1]
[.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,1]
[.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[2,1,1,1]
[.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,1,1]
[.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[2,2,1]
[.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[3,1,1]
[.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]
[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[1,1,1,2]
[[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,1,2]
[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[1,2,2]
[[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[2,1,2]
[[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[3,2]
[[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[1,1,2,1]
[[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[2,2,1]
[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[1,1,3]
[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3]
[[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[1,2,1,1]
[[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[1,3,1]
[[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[1,2,2]
[[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[1,3,1]
[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[1,4]
[[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,1,1,1]
[[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,1,1]
[[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,2,1]
[[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,1,1]
[[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[4,1]
[[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[2,1,2]
[[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,2]
[[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[2,2,1]
[[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3]
[[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,1,1]
[[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1]
[[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[3,2]
[[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,1]
[[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]
[.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,2,1,1]
[.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,1,1,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,3,1,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[3,1,1,1]
[.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,2,1,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[3,1,1,1]
[.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]
[.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[2,1,2,1]
[.,[[.,.],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,2,2,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[2,1,2,1]
[.,[[.,.],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,2,1]
[.,[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,1,2,1,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[2,2,1,1]
[.,[[[.,.],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,1,3,1]
[.,[[[.,.],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[2,3,1]
[.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,2,1,1,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,3,1,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,2,2,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,3,1,1]
[.,[[[[.,.],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,1,1,1]
[.,[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[2,2,1,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,1,1,1]
[.,[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,1,1]
[.,[[[.,.],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[2,1,2,1]
[.,[[[.,.],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[3,2,1]
[.,[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[2,2,1,1]
[.,[[[[.,.],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[2,3,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[3,1,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,1,1]
[.,[[[[.,.],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[3,2,1]
[.,[[[[.,[.,.]],.],.],.]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[4,1,1]
[.,[[[[[.,.],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]
[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[.,.],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,1,1,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[1,2,1,2]
[[.,.],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,1,1,2]
[[.,.],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,2]
[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[1,1,2,2]
[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[2,2,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[1,2,1,2]
[[.,.],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[1,3,2]
[[.,.],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[2,1,1,2]
[[.,.],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,1,2]
[[.,.],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[2,2,2]
[[.,.],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[3,1,2]
[[.,.],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[4,2]
[[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,1,2,1]
[[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[1,2,2,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[2,1,2,1]
[[.,[.,.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[3,2,1]
[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[.,.],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,1,3]
[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[1,2,3]
[[[.,.],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[2,1,3]
[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[3,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[2,2,1,1]
[[.,[[.,.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[1,1,3,1]
[[.,[[.,.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[2,3,1]
[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[1,1,2,2]
[[[.,.],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[2,2,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[1,1,3,1]
[[[.,[.,.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[2,3,1]
[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[1,1,4]
[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,4]
[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[1,3,1,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[1,2,2,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[1,3,1,1]
[[.,[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[1,4,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[1,2,1,2]
[[[.,.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[1,3,2]
[[[.,[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[1,2,2,1]
[[[[.,.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[1,2,3]
[[[.,[.,[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[1,3,1,1]
[[[.,[[.,.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[1,4,1]
[[[[.,.],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[1,3,2]
[[[[.,[.,.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[1,4,1]
[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[1,5]
[[.,[.,[.,[.,[.,.]]]]],.]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[3,1,1,1]
[[.,[.,[[.,.],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,2,1,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[3,1,1,1]
[[.,[.,[[[.,.],.],.]]],.]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,1,1]
[[.,[[.,.],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,1,2,1]
[[.,[[.,.],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,2,1]
[[.,[[.,[.,.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,2,1,1]
[[.,[[[.,.],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,3,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[3,1,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[4,1,1]
[[.,[[[.,.],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,2,1]
[[.,[[[.,[.,.]],.],.]],.]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[4,1,1]
[[.,[[[[.,.],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[5,1]
[[[.,.],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[2,1,1,2]
[[[.,.],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,1,2]
[[[.,.],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[2,2,2]
[[[.,.],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,1,2]
[[[.,.],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[4,2]
[[[.,[.,.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[2,1,2,1]
[[[.,[.,.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,2,1]
[[[[.,.],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[2,1,3]
[[[[.,.],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,3]
[[[.,[.,[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[2,2,1,1]
[[[.,[[.,.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[2,3,1]
[[[[.,.],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[2,2,2]
[[[[.,[.,.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[2,3,1]
[[[[[.,.],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,4]
[[[.,[.,[.,[.,.]]]],.],.]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,1,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[4,1,1]
[[[.,[[.,.],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,2,1]
[[[.,[[.,[.,.]],.]],.],.]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[4,1,1]
[[[.,[[[.,.],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[5,1]
[[[[.,.],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,1,2]
[[[[.,.],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,2]
[[[[.,[.,.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,2,1]
[[[[[.,.],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[3,3]
[[[[.,[.,[.,.]]],.],.],.]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1]
[[[[[.,.],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[4,2]
[[[[[.,[.,.]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,1]
[[[[[[.,.],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[2,2,1,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,2,1,1,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,3,1,1,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,2,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,3,1,1,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[2,2,1,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[3,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,2,1,1,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[2,3,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[3,2,1,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,2,1,2,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[3,1,2,1]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[2,2,2,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[3,1,2,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[4,2,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[2,1,2,1,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,2,2,1,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[2,1,2,1,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[3,2,1,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[2,1,3,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,3,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[2,2,1,1,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,1,3,1,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[2,3,1,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,1,2,2,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[2,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,1,3,1,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[2,3,1,1]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[2,4,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,3,1,1,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,2,2,1,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,3,1,1,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,1,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,2,1,2,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,3,2,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,2,2,1,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,2,3,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,3,1,1,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,4,1,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,3,2,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,4,1,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[2,2,1,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[2,2,1,1,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[2,3,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[3,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[5,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[3,1,2,1]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[2,2,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[3,1,2,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[4,2,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[2,1,2,1,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[3,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[2,1,3,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[3,3,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[2,2,1,1,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[2,3,1,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[2,2,2,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[2,3,1,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[2,4,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[3,2,1,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[5,1,1]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[3,1,2,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[4,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[3,2,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[3,3,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,1,1]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[4,2,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[5,1,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[1,2,1,1,2]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[3,1,1,2]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[2,2,1,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[3,1,1,2]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[4,1,2]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[2,1,2,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,2,2]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[1,1,2,1,2]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[2,2,1,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[2,3,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[1,2,1,1,2]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[1,3,1,2]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[1,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[1,3,1,2]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[1,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[3,1,1,2]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[2,2,1,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[3,1,1,2]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,1,2]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[2,1,2,2]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[3,2,2]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[2,2,1,2]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[2,3,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[3,1,1,2]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[4,1,2]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[3,2,2]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[4,1,2]
[[.,.],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[5,2]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[2,1,1,2,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[1,2,1,2,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[2,1,1,2,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[3,1,2,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[1,1,2,2,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[2,2,2,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[1,2,1,2,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[1,3,2,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[2,1,1,2,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[3,1,2,1]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[2,2,2,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[3,1,2,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[4,2,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,1,1,3]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[2,2,3]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[1,2,1,3]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[1,3,3]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[2,1,1,3]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,1,3]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[2,2,3]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[3,1,3]
[[[.,.],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[4,3]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,1,2,1,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[1,2,2,1,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[2,1,2,1,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[3,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[1,1,1,3,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[1,2,3,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[2,1,3,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[3,3,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,1,2,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[1,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[2,1,2,2]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[3,2,2]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[2,1,3,1]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[1,2,3,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[2,1,3,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[3,3,1]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,1,4]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[1,2,4]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[2,1,4]
[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[3,4]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[2,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[1,1,3,1,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[2,3,1,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[1,1,2,2,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[2,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[1,1,3,1,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[2,3,1,1]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[1,1,4,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[2,4,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[2,2,1,2]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[1,1,3,2]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[2,3,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[2,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[2,2,3]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[2,3,1,1]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[1,1,4,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[2,4,1]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[2,3,2]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[2,4,1]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,5]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[1,3,1,1,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[1,2,2,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[1,3,1,1,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[1,4,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[1,2,1,2,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[1,3,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[1,2,2,1,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[1,2,3,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[1,3,1,1,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[1,4,1,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[1,3,2,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[1,4,1,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[1,5,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[1,3,1,2]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[1,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[1,3,1,2]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[1,4,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[1,3,2,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[1,3,3]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[1,2,3,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[1,2,4]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[1,4,1,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[1,3,2,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[1,4,1,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[1,5,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[1,4,2]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[1,3,3]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[1,5,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[1,4,2]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[1,5,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[1,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,2,1,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,2,1,1,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,3,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[3,2,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[5,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[3,1,2,1]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[3,1,2,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,2,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,1,2,1,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[3,2,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,1,3,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,3,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,2,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,3,1,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,3,1,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,4,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[3,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[3,1,2,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[4,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[3,2,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,3,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[5,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[4,2,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[5,1,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[6,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[3,1,1,2]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[2,2,1,2]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[3,1,1,2]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,1,2]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[2,1,2,2]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,2,2]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[2,2,1,2]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[2,3,2]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[3,1,1,2]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[4,1,2]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,2,2]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[4,1,2]
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[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
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[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
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[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[2,1,1,2,1,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[4,6,5,7,3,8,2,1]=>[2,2,2,1,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[4,5,7,6,3,8,2,1]=>[3,1,2,1,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,1,3,1,1,1]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[2,2,2,1,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,1,3,1,1,1]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,3,1,1,1,1]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[1,3,1,1,1,1]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[1,3,2,1,1]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[2,2,1,1,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[3,2,1,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[3,6,5,7,8,4,2,1]=>[2,3,1,1,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[2,1,1,2,1,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[3,1,2,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[3,3,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[2,2,2,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[3,2,1,1,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[2,1,2,2,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[1,1,2,1,2,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[4,1,2,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[3,1,1,2,1]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[4,1,2,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[3,2,2,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[2,2,3,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[3,4,5,2,8,7,6,1]=>[3,2,1,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[1,1,1,3,1,1]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[2,1,3,1,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[3,3,1,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[4,5,3,2,7,6,8,1]=>[2,1,2,2,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[3,2,2,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[1,1,1,3,1,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[3,3,1,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[2,1,4,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,2,4,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[2,1,4,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[2,3,1,1,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[3,4,2,7,6,8,5,1]=>[2,2,2,1,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[1,1,3,1,1,1]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[2,3,1,1,1]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,1,4,1,1]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[2,4,1,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[1,1,2,1,2,1]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[2,2,1,2,1]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[1,1,3,2,1]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>[1,1,2,3,1]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[2,2,3,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[1,1,3,1,1,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[2,4,1,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,1,3,2,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[1,1,4,1,1]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[2,4,1,1]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[2,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[1,3,1,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[1,2,2,1,1,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[3,2,6,5,7,8,4,1]=>[1,2,3,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[1,3,1,1,1,1]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>[1,3,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[1,4,1,1,1]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[1,5,1,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,3,1,2,1]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[1,2,2,2,1]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,4,2,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[1,2,4,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,3,1,1,1,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[3,2,4,6,7,8,5,1]=>[1,5,1,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[1,3,1,2,1]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[1,4,2,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,6,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[2,1,2,1,1,1]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[2,1,1,2,1,1]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[6,1,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[2,1,1,1,2,1]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[3,1,1,2,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[2,3,2,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[4,1,2,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[5,2,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[2,1,1,2,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[3,1,2,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[2,2,3,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[2,1,3,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[2,1,2,2,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[2,1,3,1,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[3,4,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[2,2,1,1,1,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[2,4,1,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[2,2,1,2,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[2,2,3,1]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[2,3,1,1,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[2,3,2,1]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[2,4,1,1]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[2,5,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[4,2,1,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[3,2,1,1,1]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[4,2,1,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[4,3,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[3,2,1,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[3,2,2,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[3,4,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[4,2,1,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[4,3,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[6,1,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[5,2,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[3,1,1,1,2]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[3,1,1,1,2]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[2,2,1,1,2]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[3,1,1,1,2]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[4,1,1,2]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[3,2,1,2]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[2,2,1,1,2]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[3,1,1,1,2]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>[3,2,1,2]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,3,2]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[2,2,1,1,2]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[2,3,1,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[2,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[1,4,1,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[2,1,1,1,1,2]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[2,6,5,7,4,3,1,8]=>[2,2,1,1,2]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[4,1,1,2]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[3,2,1,2]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[2,2,1,1,2]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[3,1,1,1,2]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[5,1,2]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[2,2,2,2]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[2,4,3,5,7,6,1,8]=>[2,3,1,2]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[4,1,1,2]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[3,2,1,2]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[5,1,2]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[4,2,2]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[3,3,2]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[6,2]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[1,1,2,1,2,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[3,5,4,6,2,1,8,7]=>[2,2,1,2,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[4,1,2,1]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[3,2,2,1]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[1,1,3,2,1]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[2,3,2,1]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[3,1,1,2,1]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[2,1,2,2,1]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[3,2,2,1]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[3,1,1,2,1]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[4,1,2,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[5,2,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[1,2,1,1,3]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[4,5,3,6,2,1,7,8]=>[2,2,1,3]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>[1,2,1,1,3]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[2,1,2,3]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,2,3]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[1,1,2,1,3]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[2,2,1,3]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[2,2,1,3]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[4,1,3]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[3,2,3]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[5,3]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[1,3,2,1,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[2,2,2,1,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[4,2,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[1,1,1,1,3,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[4,5,3,2,1,7,8,6]=>[2,1,1,3,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[2,1,1,3,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[3,1,3,1]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[2,2,3,1]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[1,3,3,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[2,1,1,3,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[3,1,3,1]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[2,2,3,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[3,1,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[4,3,1]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[3,1,2,2]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[2,2,2,2]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[3,2,4,5,1,7,6,8]=>[1,3,2,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[2,1,1,2,2]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[3,1,2,2]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[2,2,2,2]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[3,1,2,2]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[4,2,2]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[2,1,1,3,1]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[3,1,3,1]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[2,2,3,1]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[3,1,3,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[4,3,1]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[1,2,1,4]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[3,1,4]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[2,2,4]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[3,1,4]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[1,1,1,3,1,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[3,3,1,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[2,1,2,2,1]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[3,2,2,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[1,1,1,3,1,1]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[3,3,1,1]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[1,1,1,4,1]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[2,1,4,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[1,2,4,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[2,1,4,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[3,4,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[3,2,1,2]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[1,2,3,2]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[3,3,2]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[3,2,2,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[1,2,2,3]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[3,2,3]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[2,1,3,1,1]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[1,2,3,1,1]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[3,3,1,1]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[1,1,1,4,1]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[1,2,4,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[2,1,4,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[3,4,1]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[1,2,3,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[3,3,2]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[1,2,4,1]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[2,1,4,1]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[3,4,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[2,1,5]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[3,5]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[1,1,3,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[1,1,2,2,1,1]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[1,1,3,1,1,1]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[1,1,4,1,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[2,4,1,1]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[2,3,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[1,1,2,3,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[2,2,3,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[1,1,3,1,1,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[1,1,4,1,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[2,4,1,1]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[1,1,3,2,1]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[2,3,2,1]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[1,1,4,1,1]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[2,4,1,1]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[1,1,5,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[2,5,1]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8]=>[2,2,1,1,2]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[2,3,1,2]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[2,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[1,1,4,2]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[2,4,2]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[1,1,2,1,3]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[2,2,1,3]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[1,1,3,3]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[2,3,3]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[2,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[2,2,4]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[1,1,4,1,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[2,4,1,1]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[1,1,3,2,1]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[2,3,2,1]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[1,1,4,1,1]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[2,4,1,1]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[1,1,5,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[2,5,1]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[1,1,4,2]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[2,4,2]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[2,4,1,1]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[1,1,5,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[2,5,1]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[1,1,4,2]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[1,3,1,1,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[1,3,1,1,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[1,3,1,1,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[1,5,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[1,3,1,2,1]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[1,4,2,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[1,3,3,1]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[1,2,2,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[1,2,4,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[1,3,1,1,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[1,5,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[1,3,1,2,1]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[1,4,2,1]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[1,5,1,1]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[1,5,1,1]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[1,6,1]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>[1,4,1,2]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[2,1,5,4,7,6,3,8]=>[1,2,2,1,2]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[1,2,3,2]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[1,3,1,1,2]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[1,4,1,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[1,4,2,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[1,3,1,3]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[1,3,1,3]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[2,1,4,5,6,3,7,8]=>[1,4,3]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[2,1,4,5,3,7,8,6]=>[1,3,3,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[1,3,3,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[1,3,4]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[1,2,4,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[1,2,4,1]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[1,5,1,1]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[1,3,1,2,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[1,4,2,1]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[1,3,3,1]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[1,5,1,1]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[1,4,2,1]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[2,1,3,5,6,8,7,4]=>[1,5,1,1]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[1,6,1]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>[1,4,1,2]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[2,1,3,5,6,4,7,8]=>[1,4,3]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[1,4,2,1]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[1,6,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[1,4,2,1]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[1,4,3]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[3,2,1,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[3,1,2,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[4,2,1,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[2,1,1,1,2,1]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[3,1,1,2,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[2,2,1,2,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[4,1,2,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[4,1,2,1]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[5,2,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[3,1,2,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[2,1,3,1,1]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,5,4,3,7,6,8,2]=>[2,1,2,2,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[2,1,3,1,1]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[3,3,1,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[3,4,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,2,2,1,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[2,4,1,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[2,3,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[2,2,3,1]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[2,4,1,1]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[2,3,2,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[4,1,2,1]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[5,2,1]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[4,3,1]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[3,2,1,1,1]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[3,3,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[3,2,2,1]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[3,4,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[5,1,1,1]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[4,1,2,1]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[5,2,1]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[4,3,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[6,1,1]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[7,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[3,2,1,2]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[4,1,1,2]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[5,1,2]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[3,2,1,2]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[2,1,3,2]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>[3,3,2]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[2,2,2,2]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[2,3,1,2]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[4,1,1,2]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[4,1,1,2]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[5,1,2]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[3,1,2,2]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[3,2,1,2]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[6,2]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,4,5,6,3,2,8,7]=>[4,1,2,1]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>[3,1,1,2,1]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>[5,2,1]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[3,1,1,3]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[3,1,1,3]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[4,1,3]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[2,2,1,3]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[3,1,1,3]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[4,1,3]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[4,2,1,1]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[2,1,1,3,1]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>[2,2,3,1]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[3,1,3,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[4,3,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[3,1,2,2]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[2,2,2,2]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[3,1,2,2]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[4,2,2]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[3,1,3,1]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>[4,3,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[3,1,4]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[4,4]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[3,3,1,1]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[2,1,2,2,1]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[3,2,2,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[2,1,3,1,1]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[3,3,1,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[2,1,4,1]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,4,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[3,2,1,2]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[2,1,3,2]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,3,2]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[3,2,2,1]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[3,3,1,1]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[2,1,4,1]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[3,4,1]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[2,1,3,2]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[3,3,2]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[2,1,4,1]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[3,4,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[3,5]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[2,3,1,1,1]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>[2,4,1,1]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[2,2,1,2,1]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[2,3,2,1]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[2,2,2,1,1]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[2,2,3,1]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[2,4,1,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[2,3,2,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[2,5,1]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[2,3,1,2]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[2,2,2,2]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[2,3,1,2]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[2,4,2]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[2,2,1,3]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[2,3,3]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[2,2,3,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[2,3,2,1]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[2,4,1,1]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[2,5,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[2,3,3]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[2,4,1,1]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[2,5,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[2,6]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[4,2,1,1]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[3,3,1,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[5,1,1,1]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[4,2,1,1]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[6,1,1]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[5,2,1]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[3,1,2,1,1]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,2,5,6,4,8,7,3]=>[4,2,1,1]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[4,3,1]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>[3,3,1,1]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,4,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[4,1,2,1]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[5,2,1]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[4,2,1,1]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[4,3,1]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[7,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[5,1,2]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[4,2,2]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[3,3,2]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[5,1,2]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,2,4,5,7,6,3,8]=>[5,1,2]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[6,2]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,2,5,6,4,3,8,7]=>[4,1,2,1]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[5,2,1]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[4,1,3]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[4,1,3]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[5,3]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[4,2,1,1]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[3,1,3,1]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[4,3,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[4,3,1]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[4,4]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[3,3,1,1]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[3,2,2,1]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[3,3,1,1]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[3,4,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[3,3,2]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[3,4,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[3,4,1]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[3,5]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,2,1,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[5,2,1]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[4,2,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[4,3,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[5,2,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[7,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[5,1,2]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[4,2,2]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[5,1,2]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[6,2]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[5,2,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[5,3]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[4,3,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[4,4]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[5,2,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[7,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[6,2]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[5,2,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[5,3]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[6,2]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[7,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
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
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.