Identifier
Mp00050:
Ordered trees
—to binary tree: right brother = right child⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0021;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]
[[[]],[]]=>[[.,.],[.,.]]=>[3,1,2]=>[1,2]
[[[],[]]]=>[[.,[.,.]],.]=>[2,1,3]=>[1,2]
[[[[]]]]=>[[[.,.],.],.]=>[1,2,3]=>[3]
[[],[],[],[]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]
[[],[],[[]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]
[[],[[]],[]]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,2,1]
[[],[[],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,2,1]
[[],[[[]]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]
[[[]],[],[]]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2]
[[[]],[[]]]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2]
[[[],[]],[]]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[1,1,2]
[[[[]]],[]]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,3]
[[[],[],[]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[1,1,2]
[[[],[[]]]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,2]
[[[[]],[]]]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3]
[[[[],[]]]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[1,3]
[[[[[]]]]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4]
[[],[],[],[],[]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]
[[],[],[],[[]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]
[[],[],[[]],[]]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,1,1]
[[],[],[[],[]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,1,1]
[[],[],[[[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[[],[[]],[],[]]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1]
[[],[[]],[[]]]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1]
[[],[[],[]],[]]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,1,2,1]
[[],[[[]]],[]]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,1]
[[],[[],[],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,1,2,1]
[[],[[],[[]]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[2,2,1]
[[],[[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,3,1]
[[],[[[],[]]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,1]
[[],[[[[]]]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]
[[[]],[],[],[]]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2]
[[[]],[],[[]]]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2]
[[[]],[[]],[]]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2]
[[[]],[[],[]]]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,2,2]
[[[]],[[[]]]]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2]
[[[],[]],[],[]]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[1,1,1,2]
[[[[]]],[],[]]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3]
[[[],[]],[[]]]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,1,2]
[[[[]]],[[]]]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3]
[[[],[],[]],[]]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[1,1,1,2]
[[[],[[]]],[]]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[1,2,2]
[[[[]],[]],[]]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,1,3]
[[[[],[]]],[]]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[1,1,3]
[[[[[]]]],[]]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,4]
[[[],[],[],[]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[1,1,1,2]
[[[],[],[[]]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,1,2]
[[[],[[]],[]]]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[1,2,2]
[[[],[[],[]]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[1,2,2]
[[[],[[[]]]]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[3,2]
[[[[]],[],[]]]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,1,3]
[[[[]],[[]]]]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,3]
[[[[],[]],[]]]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[1,1,3]
[[[[[]]],[]]]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,4]
[[[[],[],[]]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[1,1,3]
[[[[],[[]]]]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3]
[[[[[]],[]]]]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[1,4]
[[[[[],[]]]]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[1,4]
[[[[[[]]]]]]=>[[[[[.,.],.],.],.],.]=>[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]
[[],[],[],[[]],[]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,1,1,1]
[[],[],[],[[],[]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[[],[],[],[[[]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[],[],[[]],[],[]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1]
[[],[],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1]
[[],[],[[],[]],[]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,1,2,1,1]
[[],[],[[[]]],[]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,3,1,1]
[[],[],[[],[],[]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[[],[],[[],[[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,2,1,1]
[[],[],[[[]],[]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,3,1,1]
[[],[],[[[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,3,1,1]
[[],[],[[[[]]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]
[[],[[]],[],[],[]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1]
[[],[[]],[],[[]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1]
[[],[[]],[[]],[]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1]
[[],[[]],[[],[]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,2,2,1]
[[],[[]],[[[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1]
[[],[[],[]],[],[]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,1,1,2,1]
[[],[[[]]],[],[]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1]
[[],[[],[]],[[]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,1,2,1]
[[],[[[]]],[[]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,3,1]
[[],[[],[],[]],[]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,1,1,2,1]
[[],[[],[[]]],[]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,2,2,1]
[[],[[[]],[]],[]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,1,3,1]
[[],[[[],[]]],[]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,1,3,1]
[[],[[[[]]]],[]]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,4,1]
[[],[[],[],[],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[[],[[],[],[[]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[2,1,2,1]
[[],[[],[[]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,2,2,1]
[[],[[],[[],[]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,2,2,1]
[[],[[],[[[]]]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,2,1]
[[],[[[]],[],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,1,3,1]
[[],[[[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[2,3,1]
[[],[[[],[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,1,3,1]
[[],[[[[]]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,4,1]
[[],[[[],[],[]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,1,3,1]
[[],[[[],[[]]]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[2,3,1]
[[],[[[[]],[]]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,4,1]
[[],[[[[],[]]]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,4,1]
[[],[[[[[]]]]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]
[[[]],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[[[]],[],[],[[]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2]
[[[]],[],[[]],[]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2]
[[[]],[],[[],[]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,2,1,2]
[[[]],[],[[[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2]
[[[]],[[]],[],[]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2]
[[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2]
[[[]],[[],[]],[]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,1,2,2]
[[[]],[[[]]],[]]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2]
[[[]],[[],[],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,1,2,2]
[[[]],[[],[[]]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,2,2]
[[[]],[[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2]
[[[]],[[[],[]]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[1,3,2]
[[[]],[[[[]]]]]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2]
[[[],[]],[],[],[]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[[[[]]],[],[],[]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3]
[[[],[]],[],[[]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,1,1,2]
[[[[]]],[],[[]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3]
[[[],[]],[[]],[]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[1,2,1,2]
[[[[]]],[[]],[]]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3]
[[[],[]],[[],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[1,2,1,2]
[[[],[]],[[[]]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2]
[[[[]]],[[],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,3]
[[[[]]],[[[]]]]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3]
[[[],[],[]],[],[]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[[[],[[]]],[],[]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[1,1,2,2]
[[[[]],[]],[],[]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3]
[[[[],[]]],[],[]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[1,1,1,3]
[[[[[]]]],[],[]]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4]
[[[],[],[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,1,1,2]
[[[],[[]]],[[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,2,2]
[[[[]],[]],[[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,3]
[[[[],[]]],[[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,3]
[[[[[]]]],[[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,4]
[[[],[],[],[]],[]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[[[],[],[[]]],[]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[1,2,1,2]
[[[],[[]],[]],[]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[1,1,2,2]
[[[],[[],[]]],[]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[1,1,2,2]
[[[],[[[]]]],[]]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[1,3,2]
[[[[]],[],[]],[]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,1,1,3]
[[[[]],[[]]],[]]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,2,3]
[[[[],[]],[]],[]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[1,1,1,3]
[[[[[]]],[]],[]]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4]
[[[[],[],[]]],[]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[1,1,1,3]
[[[[],[[]]]],[]]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[1,2,3]
[[[[[]],[]]],[]]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,1,4]
[[[[[],[]]]],[]]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[1,1,4]
[[[[[[]]]]],[]]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,5]
[[[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[[],[],[],[[]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,1,1,2]
[[[],[],[[]],[]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[1,2,1,2]
[[[],[],[[],[]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[1,2,1,2]
[[[],[],[[[]]]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,2]
[[[],[[]],[],[]]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[1,1,2,2]
[[[],[[]],[[]]]]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[2,2,2]
[[[],[[],[]],[]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[1,1,2,2]
[[[],[[[]]],[]]]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[1,3,2]
[[[],[[],[],[]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[1,1,2,2]
[[[],[[],[[]]]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[2,2,2]
[[[],[[[]],[]]]]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[1,3,2]
[[[],[[[],[]]]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[1,3,2]
[[[],[[[[]]]]]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[4,2]
[[[[]],[],[],[]]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,1,1,3]
[[[[]],[],[[]]]]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,1,3]
[[[[]],[[]],[]]]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,2,3]
[[[[]],[[],[]]]]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[1,2,3]
[[[[]],[[[]]]]]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,3]
[[[[],[]],[],[]]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[1,1,1,3]
[[[[[]]],[],[]]]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4]
[[[[],[]],[[]]]]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,1,3]
[[[[[]]],[[]]]]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,4]
[[[[],[],[]],[]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[1,1,1,3]
[[[[],[[]]],[]]]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[1,2,3]
[[[[[]],[]],[]]]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,1,4]
[[[[[],[]]],[]]]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[1,1,4]
[[[[[[]]]],[]]]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,5]
[[[[],[],[],[]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[[],[],[[]]]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,1,3]
[[[[],[[]],[]]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[1,2,3]
[[[[],[[],[]]]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[1,2,3]
[[[[],[[[]]]]]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[3,3]
[[[[[]],[],[]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,1,4]
[[[[[]],[[]]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4]
[[[[[],[]],[]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[1,1,4]
[[[[[[]]],[]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,5]
[[[[[],[],[]]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[1,1,4]
[[[[[],[[]]]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,4]
[[[[[[]],[]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[1,5]
[[[[[[],[]]]]]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[1,5]
[[[[[[[]]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[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]
[[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]
[[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[]],[],[]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]
[[],[],[],[[]],[[]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[[],[],[],[[],[]],[]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]
[[],[],[],[[[]]],[]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]
[[],[],[],[[],[],[]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[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]
[[],[],[],[[[]],[]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1]
[[],[],[],[[[],[]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[[],[],[],[[[[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[],[],[[]],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]
[[],[],[[]],[],[[]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]
[[],[],[[]],[[]],[]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]
[[],[],[[]],[[],[]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]
[[],[],[[]],[[[]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1]
[[],[],[[],[]],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]
[[],[],[[[]]],[],[]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]
[[],[],[[],[]],[[]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]
[[],[],[[[]]],[[]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,3,1,1]
[[],[],[[],[],[]],[]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]
[[],[],[[],[[]]],[]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,2,1,1]
[[],[],[[[]],[]],[]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1]
[[],[],[[[],[]]],[]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,1,3,1,1]
[[],[],[[[[]]]],[]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,4,1,1]
[[],[],[[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[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]
[[],[],[[],[[]],[]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,2,1,1]
[[],[],[[],[[],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[[],[],[[],[[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[[],[],[[[]],[],[]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1]
[[],[],[[[]],[[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,3,1,1]
[[],[],[[[],[]],[]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,1,3,1,1]
[[],[],[[[[]]],[]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,4,1,1]
[[],[],[[[],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[[],[],[[[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[[],[],[[[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,4,1,1]
[[],[],[[[[],[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[[],[],[[[[[]]]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[],[[]],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]
[[],[[]],[],[],[[]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]
[[],[[]],[],[[]],[]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]
[[],[[]],[],[[],[]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]
[[],[[]],[],[[[]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1]
[[],[[]],[[]],[],[]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]
[[],[[]],[[]],[[]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1]
[[],[[]],[[],[]],[]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]
[[],[[]],[[[]]],[]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1]
[[],[[]],[[],[],[]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]
[[],[[]],[[],[[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[2,2,2,1]
[[],[[]],[[[]],[]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1]
[[],[[]],[[[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,1]
[[],[[]],[[[[]]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1]
[[],[[],[]],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]
[[],[[[]]],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]
[[],[[],[]],[],[[]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]
[[],[[[]]],[],[[]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1]
[[],[[],[]],[[]],[]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]
[[],[[[]]],[[]],[]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1]
[[],[[],[]],[[],[]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]
[[],[[],[]],[[[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[3,1,2,1]
[[],[[[]]],[[],[]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,2,3,1]
[[],[[[]]],[[[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1]
[[],[[],[],[]],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]
[[],[[],[[]]],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,1,2,2,1]
[[],[[[]],[]],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1]
[[],[[[],[]]],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,1,1,3,1]
[[],[[[[]]]],[],[]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1]
[[],[[],[],[]],[[]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]
[[],[[],[[]]],[[]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[2,2,2,1]
[[],[[[]],[]],[[]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,3,1]
[[],[[[],[]]],[[]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[2,1,3,1]
[[],[[[[]]]],[[]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,4,1]
[[],[[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]
[[],[[],[],[[]]],[]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,2,1,2,1]
[[],[[],[[]],[]],[]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,1,2,2,1]
[[],[[],[[],[]]],[]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,1,2,2,1]
[[],[[],[[[]]]],[]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,3,2,1]
[[],[[[]],[],[]],[]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1]
[[],[[[]],[[]]],[]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,2,3,1]
[[],[[[],[]],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,1,1,3,1]
[[],[[[[]]],[]],[]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1]
[[],[[[],[],[]]],[]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,1,1,3,1]
[[],[[[],[[]]]],[]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,2,3,1]
[[],[[[[]],[]]],[]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,1,4,1]
[[],[[[[],[]]]],[]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,1,4,1]
[[],[[[[[]]]]],[]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,5,1]
[[],[[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[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]
[[],[[],[],[[]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,2,1,2,1]
[[],[[],[],[[],[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[[],[[],[],[[[]]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[[],[[],[[]],[],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,1,2,2,1]
[[],[[],[[]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[2,2,2,1]
[[],[[],[[],[]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,1,2,2,1]
[[],[[],[[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,3,2,1]
[[],[[],[[],[],[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[[],[[],[[],[[]]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[[],[[],[[[]],[]]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,3,2,1]
[[],[[],[[[],[]]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[[],[[],[[[[]]]]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[4,2,1]
[[],[[[]],[],[],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1]
[[],[[[]],[],[[]]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[2,1,3,1]
[[],[[[]],[[]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,2,3,1]
[[],[[[]],[[],[]]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,2,3,1]
[[],[[[]],[[[]]]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[3,3,1]
[[],[[[],[]],[],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,1,1,3,1]
[[],[[[[]]],[],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1]
[[],[[[],[]],[[]]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[2,1,3,1]
[[],[[[[]]],[[]]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,4,1]
[[],[[[],[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,1,1,3,1]
[[],[[[],[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,2,3,1]
[[],[[[[]],[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,1,4,1]
[[],[[[[],[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,1,4,1]
[[],[[[[[]]]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,5,1]
[[],[[[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[[],[[[],[],[[]]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[[],[[[],[[]],[]]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,2,3,1]
[[],[[[],[[],[]]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[[],[[[],[[[]]]]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,3,1]
[[],[[[[]],[],[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,1,4,1]
[[],[[[[]],[[]]]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[2,4,1]
[[],[[[[],[]],[]]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,1,4,1]
[[],[[[[[]]],[]]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,5,1]
[[],[[[[],[],[]]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[[],[[[[],[[]]]]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[2,4,1]
[[],[[[[[]],[]]]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,5,1]
[[],[[[[[],[]]]]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,5,1]
[[],[[[[[[]]]]]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]
[[[]],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[[[]],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]
[[[]],[],[],[[]],[]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]
[[[]],[],[],[[],[]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]
[[[]],[],[],[[[]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2]
[[[]],[],[[]],[],[]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]
[[[]],[],[[]],[[]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2]
[[[]],[],[[],[]],[]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]
[[[]],[],[[[]]],[]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2]
[[[]],[],[[],[],[]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]
[[[]],[],[[],[[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,2,1,2]
[[[]],[],[[[]],[]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2]
[[[]],[],[[[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[1,3,1,2]
[[[]],[],[[[[]]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2]
[[[]],[[]],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]
[[[]],[[]],[],[[]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2]
[[[]],[[]],[[]],[]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2]
[[[]],[[]],[[],[]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,2,2,2]
[[[]],[[]],[[[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2]
[[[]],[[],[]],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]
[[[]],[[[]]],[],[]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2]
[[[]],[[],[]],[[]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,2,2]
[[[]],[[[]]],[[]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2]
[[[]],[[],[],[]],[]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]
[[[]],[[],[[]]],[]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,2,2,2]
[[[]],[[[]],[]],[]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2]
[[[]],[[[],[]]],[]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,1,3,2]
[[[]],[[[[]]]],[]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2]
[[[]],[[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]
[[[]],[[],[],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,2,2]
[[[]],[[],[[]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,2,2,2]
[[[]],[[],[[],[]]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[1,2,2,2]
[[[]],[[],[[[]]]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[3,2,2]
[[[]],[[[]],[],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2]
[[[]],[[[]],[[]]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2]
[[[]],[[[],[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[1,1,3,2]
[[[]],[[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2]
[[[]],[[[],[],[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[1,1,3,2]
[[[]],[[[],[[]]]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,3,2]
[[[]],[[[[]],[]]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,4,2]
[[[]],[[[[],[]]]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[1,4,2]
[[[]],[[[[[]]]]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2]
[[[],[]],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[[[[]]],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[[[],[]],[],[],[[]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]
[[[[]]],[],[],[[]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3]
[[[],[]],[],[[]],[]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]
[[[[]]],[],[[]],[]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3]
[[[],[]],[],[[],[]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]
[[[],[]],[],[[[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,1,2]
[[[[]]],[],[[],[]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,1,3]
[[[[]]],[],[[[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3]
[[[],[]],[[]],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]
[[[[]]],[[]],[],[]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3]
[[[],[]],[[]],[[]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,2,1,2]
[[[[]]],[[]],[[]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3]
[[[],[]],[[],[]],[]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]
[[[],[]],[[[]]],[]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[1,3,1,2]
[[[[]]],[[],[]],[]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,1,2,3]
[[[[]]],[[[]]],[]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3]
[[[],[]],[[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]
[[[],[]],[[],[[]]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,2,1,2]
[[[],[]],[[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[1,3,1,2]
[[[],[]],[[[],[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[1,3,1,2]
[[[],[]],[[[[]]]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,1,2]
[[[[]]],[[],[],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,1,2,3]
[[[[]]],[[],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,2,3]
[[[[]]],[[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3]
[[[[]]],[[[],[]]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[1,3,3]
[[[[]]],[[[[]]]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3]
[[[],[],[]],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[[[],[[]]],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[1,1,1,2,2]
[[[[]],[]],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[[[[],[]]],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[[[[[]]]],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[[[],[],[]],[],[[]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]
[[[],[[]]],[],[[]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[2,1,2,2]
[[[[]],[]],[],[[]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3]
[[[[],[]]],[],[[]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,1,1,3]
[[[[[]]]],[],[[]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4]
[[[],[],[]],[[]],[]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]
[[[],[[]]],[[]],[]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[1,2,2,2]
[[[[]],[]],[[]],[]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3]
[[[[],[]]],[[]],[]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[1,2,1,3]
[[[[[]]]],[[]],[]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4]
[[[],[],[]],[[],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]
[[[],[],[]],[[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[3,1,1,2]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[1,2,2,2]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,2,2]
[[[[]],[]],[[],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,2,1,3]
[[[[]],[]],[[[]]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,3]
[[[[],[]]],[[],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[1,2,1,3]
[[[[],[]]],[[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,3]
[[[[[]]]],[[],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,4]
[[[[[]]]],[[[]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,4]
[[[],[],[],[]],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[[[],[],[[]]],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[1,1,2,1,2]
[[[],[[]],[]],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[1,1,1,2,2]
[[[],[[],[]]],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[1,1,1,2,2]
[[[],[[[]]]],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[1,1,3,2]
[[[[]],[],[]],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[[[[]],[[]]],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3]
[[[[],[]],[]],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[[[[[]]],[]],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[[[[],[],[]]],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[[[[],[[]]]],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[1,1,2,3]
[[[[[]],[]]],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[[[[[],[]]]],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[[[[[[]]]]],[],[]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5]
[[[],[],[],[]],[[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]
[[[],[],[[]]],[[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,2,1,2]
[[[],[[]],[]],[[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[2,1,2,2]
[[[],[[],[]]],[[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[2,1,2,2]
[[[],[[[]]]],[[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[2,3,2]
[[[[]],[],[]],[[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,1,3]
[[[[]],[[]]],[[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,2,3]
[[[[],[]],[]],[[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,1,1,3]
[[[[[]]],[]],[[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4]
[[[[],[],[]]],[[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,1,1,3]
[[[[],[[]]]],[[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[2,2,3]
[[[[[]],[]]],[[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,1,4]
[[[[[],[]]]],[[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,1,4]
[[[[[[]]]]],[[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,5]
[[[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[[[],[],[],[[]]],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[1,2,1,1,2]
[[[],[],[[]],[]],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[1,1,2,1,2]
[[[],[],[[],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[1,1,2,1,2]
[[[],[],[[[]]]],[]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[1,3,1,2]
[[[],[[]],[],[]],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[1,1,1,2,2]
[[[],[[]],[[]]],[]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[1,2,2,2]
[[[],[[],[]],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[1,1,1,2,2]
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[1,1,3,2]
[[[],[[],[],[]]],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[1,1,1,2,2]
[[[],[[],[[]]]],[]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[1,2,2,2]
[[[],[[[]],[]]],[]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[1,1,3,2]
[[[],[[[],[]]]],[]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[1,1,3,2]
[[[],[[[[]]]]],[]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[1,4,2]
[[[[]],[],[],[]],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[[[[]],[],[[]]],[]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,2,1,3]
[[[[]],[[]],[]],[]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3]
[[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,1,2,3]
[[[[]],[[[]]]],[]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,3,3]
[[[[],[]],[],[]],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[[[[[]]],[],[]],[]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[[[[],[]],[[]]],[]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[1,2,1,3]
[[[[[]]],[[]]],[]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4]
[[[[],[],[]],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[[[[],[[]]],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[1,1,2,3]
[[[[[]],[]],[]],[]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[[[[[],[]]],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[[[[[[]]]],[]],[]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5]
[[[[],[],[],[]]],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[[[[],[],[[]]]],[]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[1,2,1,3]
[[[[],[[]],[]]],[]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[1,1,2,3]
[[[[],[[],[]]]],[]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[1,1,2,3]
[[[[],[[[]]]]],[]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[1,3,3]
[[[[[]],[],[]]],[]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[[[[[]],[[]]]],[]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,2,4]
[[[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[[[[[[]]],[]]],[]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,1,5]
[[[[[],[],[]]]],[]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[[[[[],[[]]]]],[]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[1,2,4]
[[[[[[]],[]]]],[]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,1,5]
[[[[[[],[]]]]],[]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[1,1,5]
[[[[[[[]]]]]],[]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,6]
[[[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[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]
[[[],[],[],[[]],[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[1,2,1,1,2]
[[[],[],[],[[],[]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[[[],[],[],[[[]]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[[[],[],[[]],[],[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[1,1,2,1,2]
[[[],[],[[]],[[]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,2,1,2]
[[[],[],[[],[]],[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[1,1,2,1,2]
[[[],[],[[[]]],[]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[1,3,1,2]
[[[],[],[[],[],[]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[[[],[],[[],[[]]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[[[],[],[[[]],[]]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[1,3,1,2]
[[[],[],[[[],[]]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[[[],[],[[[[]]]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[4,1,2]
[[[],[[]],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[1,1,1,2,2]
[[[],[[]],[],[[]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[2,1,2,2]
[[[],[[]],[[]],[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[1,2,2,2]
[[[],[[]],[[],[]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[1,2,2,2]
[[[],[[]],[[[]]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,2,2]
[[[],[[],[]],[],[]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[1,1,1,2,2]
[[[],[[[]]],[],[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[1,1,3,2]
[[[],[[],[]],[[]]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[2,1,2,2]
[[[],[[[]]],[[]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[2,3,2]
[[[],[[],[],[]],[]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[1,1,1,2,2]
[[[],[[],[[]]],[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[1,2,2,2]
[[[],[[[]],[]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[1,1,3,2]
[[[],[[[],[]]],[]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[1,1,3,2]
[[[],[[[[]]]],[]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[1,4,2]
[[[],[[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[[[],[[],[],[[]]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[[[],[[],[[]],[]]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[1,2,2,2]
[[[],[[],[[],[]]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[[[],[[],[[[]]]]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,2,2]
[[[],[[[]],[],[]]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[1,1,3,2]
[[[],[[[]],[[]]]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[2,3,2]
[[[],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[1,1,3,2]
[[[],[[[[]]],[]]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[1,4,2]
[[[],[[[],[],[]]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[[[],[[[],[[]]]]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[2,3,2]
[[[],[[[[]],[]]]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[1,4,2]
[[[],[[[[],[]]]]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[1,4,2]
[[[],[[[[[]]]]]]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[5,2]
[[[[]],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[[[[]],[],[],[[]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,1,1,3]
[[[[]],[],[[]],[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,2,1,3]
[[[[]],[],[[],[]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[1,2,1,3]
[[[[]],[],[[[]]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,3]
[[[[]],[[]],[],[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3]
[[[[]],[[]],[[]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,2,3]
[[[[]],[[],[]],[]]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[1,1,2,3]
[[[[]],[[[]]],[]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,3,3]
[[[[]],[[],[],[]]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[1,1,2,3]
[[[[]],[[],[[]]]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,2,3]
[[[[]],[[[]],[]]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,3,3]
[[[[]],[[[],[]]]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[1,3,3]
[[[[]],[[[[]]]]]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[4,3]
[[[[],[]],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[[[[[]]],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[[[[],[]],[],[[]]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,1,1,3]
[[[[[]]],[],[[]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4]
[[[[],[]],[[]],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[1,2,1,3]
[[[[[]]],[[]],[]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4]
[[[[],[]],[[],[]]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[1,2,1,3]
[[[[],[]],[[[]]]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,3]
[[[[[]]],[[],[]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,4]
[[[[[]]],[[[]]]]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[3,4]
[[[[],[],[]],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[[[[],[[]]],[],[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[1,1,2,3]
[[[[[]],[]],[],[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[[[[[],[]]],[],[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[[[[[[]]]],[],[]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5]
[[[[],[],[]],[[]]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,1,1,3]
[[[[],[[]]],[[]]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[2,2,3]
[[[[[]],[]],[[]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,1,4]
[[[[[],[]]],[[]]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,1,4]
[[[[[[]]]],[[]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,5]
[[[[],[],[],[]],[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[[[[],[],[[]]],[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[1,2,1,3]
[[[[],[[]],[]],[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[1,1,2,3]
[[[[],[[],[]]],[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[1,1,2,3]
[[[[],[[[]]]],[]]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[1,3,3]
[[[[[]],[],[]],[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[[[[[]],[[]]],[]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[1,2,4]
[[[[[],[]],[]],[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[[[[[[]]],[]],[]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,1,5]
[[[[[],[],[]]],[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[[[[[],[[]]]],[]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[1,2,4]
[[[[[[]],[]]],[]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,1,5]
[[[[[[],[]]]],[]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[1,1,5]
[[[[[[[]]]]],[]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,6]
[[[[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[[],[],[],[[]]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[[[[],[],[[]],[]]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[1,2,1,3]
[[[[],[],[[],[]]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[[[[],[],[[[]]]]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,3]
[[[[],[[]],[],[]]]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[1,1,2,3]
[[[[],[[]],[[]]]]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[2,2,3]
[[[[],[[],[]],[]]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[1,1,2,3]
[[[[],[[[]]],[]]]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[1,3,3]
[[[[],[[],[],[]]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[[[[],[[],[[]]]]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[2,2,3]
[[[[],[[[]],[]]]]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[1,3,3]
[[[[],[[[],[]]]]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[1,3,3]
[[[[],[[[[]]]]]]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[4,3]
[[[[[]],[],[],[]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[[[[[]],[],[[]]]]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,1,4]
[[[[[]],[[]],[]]]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[1,2,4]
[[[[[]],[[],[]]]]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[1,2,4]
[[[[[]],[[[]]]]]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4]
[[[[[],[]],[],[]]]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[[[[[[]]],[],[]]]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,1,5]
[[[[[],[]],[[]]]]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,1,4]
[[[[[[]]],[[]]]]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,5]
[[[[[],[],[]],[]]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[[[[[],[[]]],[]]]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[1,2,4]
[[[[[[]],[]],[]]]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,1,5]
[[[[[[],[]]],[]]]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[1,1,5]
[[[[[[[]]]],[]]]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,6]
[[[[[],[],[],[]]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[[[],[],[[]]]]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,1,4]
[[[[[],[[]],[]]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[1,2,4]
[[[[[],[[],[]]]]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[1,2,4]
[[[[[],[[[]]]]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[3,4]
[[[[[[]],[],[]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,1,5]
[[[[[[]],[[]]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,5]
[[[[[[],[]],[]]]]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[1,1,5]
[[[[[[[]]],[]]]]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[1,6]
[[[[[[],[],[]]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[[[[],[[]]]]]]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,5]
[[[[[[[]],[]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[1,6]
[[[[[[[],[]]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[1,6]
[[[[[[[[]]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7]
[[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[]],[],[]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]
[[],[],[],[],[[]],[[]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]
[[],[],[],[],[[],[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]
[[],[],[],[],[[[]]],[]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,3,1,1,1,1]
[[],[],[],[],[[],[],[]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[[],[],[],[],[[],[[]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,3,1,1,1,1]
[[],[],[],[],[[[],[]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]
[[],[],[],[],[[[[]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]
[[],[],[],[[]],[[]],[]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]
[[],[],[],[[]],[[],[]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]
[[],[],[],[[]],[[[]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]
[[],[],[],[[],[]],[],[]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]
[[],[],[],[[[]]],[[]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]
[[],[],[],[[],[],[]],[]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]
[[],[],[],[[],[[]]],[]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,2,1,1,1]
[[],[],[],[[[]],[]],[]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,1,3,1,1,1]
[[],[],[],[[[],[]]],[]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,1,3,1,1,1]
[[],[],[],[[[[]]]],[]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]
[[],[],[],[[],[],[],[]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[[],[],[],[[],[],[[]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]
[[],[],[],[[],[[]],[]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,2,1,1,1]
[[],[],[],[[],[[],[]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[[],[],[],[[],[[[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]
[[],[],[],[[[]],[],[]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,1,3,1,1,1]
[[],[],[],[[[]],[[]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[2,3,1,1,1]
[[],[],[],[[[],[]],[]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,1,3,1,1,1]
[[],[],[],[[[[]]],[]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,4,1,1,1]
[[],[],[],[[[],[],[]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]
[[],[],[],[[[],[[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]
[[],[],[],[[[[]],[]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,4,1,1,1]
[[],[],[],[[[[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]
[[],[],[],[[[[[]]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]
[[],[],[[]],[],[],[[]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]
[[],[],[[]],[],[[],[]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]
[[],[],[[]],[],[[[]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]
[[],[],[[]],[[]],[],[]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]
[[],[],[[]],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]
[[],[],[[]],[[],[]],[]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,1,2,2,1,1]
[[],[],[[]],[[[]]],[]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]
[[],[],[[]],[[],[],[]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]
[[],[],[[]],[[],[[]]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,2,2,1,1]
[[],[],[[]],[[[],[]]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,3,2,1,1]
[[],[],[[]],[[[[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]
[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,1,1,3,1,1]
[[],[],[[],[]],[],[[]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]
[[],[],[[[]]],[],[[]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[2,1,3,1,1]
[[],[],[[[]]],[[]],[]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,2,3,1,1]
[[],[],[[],[]],[[],[]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,1,2,1,1]
[[],[],[[],[]],[[[]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[3,1,2,1,1]
[[],[],[[[]]],[[],[]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,3,1,1]
[[],[],[[[]]],[[[]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]
[[],[],[[],[],[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]
[[],[],[[[],[]]],[],[]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,1,1,3,1,1]
[[],[],[[[[]]]],[],[]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,1,4,1,1]
[[],[],[[],[],[]],[[]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]
[[],[],[[[]],[]],[[]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,1,3,1,1]
[[],[],[[[],[]]],[[]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,1,3,1,1]
[[],[],[[],[],[],[]],[]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]
[[],[],[[],[[],[]]],[]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,1,2,2,1,1]
[[],[],[[[],[],[]]],[]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,1,1,3,1,1]
[[],[],[[],[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[[],[],[[],[],[],[[]]]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]
[[],[],[[],[],[[]],[]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[1,2,1,2,1,1]
[[],[],[[],[],[[],[]]]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[[],[],[[],[[]],[],[]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,1,2,2,1,1]
[[],[],[[],[[]],[[]]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[2,2,2,1,1]
[[],[],[[],[[],[]],[]]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,1,2,2,1,1]
[[],[],[[],[[[]]],[]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,3,2,1,1]
[[],[],[[],[[],[],[]]]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[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]
[[],[],[[],[[[]],[]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,3,2,1,1]
[[],[],[[],[[[],[]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[[],[],[[],[[[[]]]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[[],[],[[[]],[],[[]]]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[2,1,3,1,1]
[[],[],[[[]],[[],[]]]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,3,1,1]
[[],[],[[[[]]],[],[]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,1,4,1,1]
[[],[],[[[],[],[]],[]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,1,1,3,1,1]
[[],[],[[[[]],[]],[]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,1,4,1,1]
[[],[],[[[],[],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]
[[],[],[[[[[]]],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,5,1,1]
[[],[],[[[[],[[]]]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[[],[],[[[[[]],[]]]]]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,5,1,1]
[[],[],[[[[[],[]]]]]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[[],[[]],[],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]
[[],[[]],[],[],[[]],[]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]
[[],[[]],[],[],[[],[]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]
[[],[[]],[],[[[]]],[]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,1,2,1]
[[],[[]],[],[[],[],[]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]
[[],[[]],[],[[],[[]]]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[2,2,1,2,1]
[[],[[]],[],[[[]],[]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,1,2,1]
[[],[[]],[],[[[],[]]]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,2,3,1]=>[1,3,1,2,1]
[[],[[]],[],[[[[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,1,2,1]
[[],[[]],[[]],[],[],[]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]
[[],[[]],[[]],[[]],[]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]
[[],[[]],[[]],[[],[]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]
[[],[[]],[[],[]],[],[]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]
[[],[[]],[[[]]],[],[]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,1,3,2,1]
[[],[[]],[[[]]],[[]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[2,3,2,1]
[[],[[]],[[],[],[]],[]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]
[[],[[]],[[],[[]]],[]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,2,2,2,1]
[[],[[]],[[[]],[]],[]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,1,3,2,1]
[[],[[]],[[],[],[],[]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]
[[],[[]],[[],[],[[]]]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[2,1,2,2,1]
[[],[[]],[[],[[]],[]]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,2,2,2,1]
[[],[[]],[[],[[],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,2,2,2,1]
[[],[[]],[[],[[[]]]]]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[3,2,2,1]
[[],[[]],[[[]],[],[]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]
[[],[[]],[[[],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,1,3,2,1]
[[],[[]],[[[[],[]]]]]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,4,2,1]
[[],[[]],[[[[[]]]]]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[5,2,1]
[[],[[],[]],[],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]
[[],[[[]]],[],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1]
[[],[[],[]],[],[],[[]]]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[2,1,1,1,2,1]
[[],[[],[]],[],[[]],[]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,2,1,1,2,1]
[[],[[[]]],[],[[]],[]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,2,1,3,1]
[[],[[],[]],[],[[],[]]]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,2,1,1,2,1]
[[],[[],[]],[],[[[]]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[3,1,1,2,1]
[[],[[[]]],[],[[],[]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,2,1,3,1]
[[],[[[]]],[],[[[]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[3,1,3,1]
[[],[[],[]],[[]],[],[]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]
[[],[[[]]],[[]],[],[]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[1,1,2,3,1]
[[],[[],[]],[[]],[[]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]
[[],[[[]]],[[]],[[]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[2,2,3,1]
[[],[[],[]],[[],[]],[]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]
[[],[[],[]],[[[]]],[]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,3,1,2,1]
[[],[[[]]],[[],[]],[]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[1,1,2,3,1]
[[],[[[]]],[[[]]],[]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]
[[],[[],[]],[[],[],[]]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]
[[],[[],[]],[[],[[]]]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[2,2,1,2,1]
[[],[[],[]],[[[]],[]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,3,1,2,1]
[[],[[],[]],[[[],[]]]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,3,1,2,1]
[[],[[],[]],[[[[]]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,1,2,1]
[[],[[[]]],[[],[],[]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,1,2,3,1]
[[],[[[]]],[[],[[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[2,2,3,1]
[[],[[[]]],[[[],[]]]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[1,3,3,1]
[[],[[[]]],[[[[]]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,3,1]
[[],[[],[],[]],[],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]
[[],[[],[[]]],[],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,1,1,2,2,1]
[[],[[[]],[]],[],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,1,1,1,3,1]
[[],[[[],[]]],[],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,1,1,1,3,1]
[[],[[[[]]]],[],[],[]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,1,1,4,1]
[[],[[],[],[]],[],[[]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[2,1,1,1,2,1]
[[],[[[]],[]],[],[[]]]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[2,1,1,3,1]
[[],[[[[]]]],[],[[]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[2,1,4,1]
[[],[[],[],[]],[[]],[]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]
[[],[[],[[]]],[[]],[]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,2,2,2,1]
[[],[[[]],[]],[[]],[]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,2,1,3,1]
[[],[[[],[]]],[[]],[]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,2,1,3,1]
[[],[[[[]]]],[[]],[]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,2,4,1]
[[],[[],[],[]],[[],[]]]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,2,1,1,2,1]
[[],[[],[],[]],[[[]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[3,1,1,2,1]
[[],[[],[[]]],[[],[]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,2,2,2,1]
[[],[[[]],[]],[[],[]]]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,2,1,3,1]
[[],[[[]],[]],[[[]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[3,1,3,1]
[[],[[[],[]]],[[[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[3,1,3,1]
[[],[[[[]]]],[[],[]]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[1,2,4,1]
[[],[[[[]]]],[[[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[3,4,1]
[[],[[],[],[],[]],[],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]
[[],[[],[[]],[]],[],[]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,1,1,2,2,1]
[[],[[[]],[],[]],[],[]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,1,1,1,3,1]
[[],[[[],[]],[]],[],[]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,1,1,1,3,1]
[[],[[[],[],[]]],[],[]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,1,1,1,3,1]
[[],[[],[],[],[]],[[]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[2,1,1,1,2,1]
[[],[[],[[]],[]],[[]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[2,1,2,2,1]
[[],[[[]],[[]]],[[]]]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[2,2,3,1]
[[],[[[[]]],[]],[[]]]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[2,1,4,1]
[[],[[[],[],[]]],[[]]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[2,1,1,3,1]
[[],[[[],[[]]]],[[]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[2,2,3,1]
[[],[[[[],[]]]],[[]]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[2,1,4,1]
[[],[[],[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]
[[],[[],[[]],[[]]],[]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,2,2,2,1]
[[],[[],[[],[]],[]],[]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,1,1,2,2,1]
[[],[[],[[[]]],[]],[]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,1,3,2,1]
[[],[[],[[],[],[]]],[]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,1,1,2,2,1]
[[],[[],[[],[[]]]],[]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,2,2,2,1]
[[],[[],[[[],[]]]],[]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[1,1,3,2,1]
[[],[[[]],[],[[]]],[]]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,2,1,3,1]
[[],[[[]],[[]],[]],[]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,1,2,3,1]
[[],[[[[]],[]],[]],[]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,1,1,4,1]
[[],[[[],[],[],[]]],[]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,3,1]
[[],[[[],[[]],[]]],[]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,1,2,3,1]
[[],[[[],[[[]]]]],[]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[1,3,3,1]
[[],[[[[]],[],[]]],[]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,1,1,4,1]
[[],[[[[]],[[]]]],[]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,2,4,1]
[[],[[[[[]]],[]]],[]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[1,1,5,1]
[[],[[[[],[],[]]]],[]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,1,1,4,1]
[[],[[[[],[[]]]]],[]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,2,4,1]
[[],[[],[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[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]
[[],[[],[],[],[[[]]]]]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[[],[[],[],[[]],[],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,1,2,1,2,1]
[[],[[],[],[[],[]],[]]]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,1,2,1,2,1]
[[],[[],[],[[[]]],[]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,3,1,2,1]
[[],[[],[],[[],[[]]]]]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]
[[],[[],[],[[[]],[]]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,3,1,2,1]
[[],[[],[],[[[],[]]]]]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[[],[[],[],[[[[]]]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[[],[[],[[]],[[]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,2,2,2,1]
[[],[[],[[]],[[],[]]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,2,2,2,1]
[[],[[],[[],[]],[],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,1,1,2,2,1]
[[],[[],[[],[],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,1,1,2,2,1]
[[],[[],[[],[[]]],[]]]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,2,2,2,1]
[[],[[],[[],[],[],[]]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[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]
[[],[[],[[],[[]],[]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,2,2,2,1]
[[],[[],[[],[[],[]]]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[[],[[],[[],[[[]]]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[[],[[],[[[]],[],[]]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,1,3,2,1]
[[],[[],[[[]],[[]]]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[2,3,2,1]
[[],[[],[[[],[],[]]]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]
[[],[[],[[[[]],[]]]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,4,2,1]
[[],[[[]],[],[],[[]]]]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[2,1,1,3,1]
[[],[[[]],[],[[]],[]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[1,2,1,3,1]
[[],[[[]],[],[[],[]]]]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,2,1,3,1]
[[],[[[]],[],[[[]]]]]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[3,1,3,1]
[[],[[[]],[[]],[],[]]]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,1,2,3,1]
[[],[[[]],[[]],[[]]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[2,2,3,1]
[[],[[[]],[[],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,1,2,3,1]
[[],[[[]],[[[]]],[]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[1,3,3,1]
[[],[[[]],[[],[],[]]]]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[1,1,2,3,1]
[[],[[[]],[[],[[]]]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[2,2,3,1]
[[],[[[]],[[[]],[]]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,3,3,1]
[[],[[[]],[[[],[]]]]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,3,3,1]
[[],[[[]],[[[[]]]]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[4,3,1]
[[],[[[[]]],[],[],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,1,1,4,1]
[[],[[[],[]],[],[[]]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[2,1,1,3,1]
[[],[[[],[]],[[],[]]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,2,1,3,1]
[[],[[[[]]],[[[]]]]]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[3,4,1]
[[],[[[],[],[]],[],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[1,1,1,1,3,1]
[[],[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[1,1,2,3,1]
[[],[[[[]],[]],[],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,1,1,4,1]
[[],[[[[],[]]],[],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[1,1,1,4,1]
[[],[[[[[]]]],[],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,1,5,1]
[[],[[[],[],[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[2,1,1,3,1]
[[],[[[[]],[]],[[]]]]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[2,1,4,1]
[[],[[[[],[]]],[[]]]]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[2,1,4,1]
[[],[[[[[]]]],[[]]]]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[2,5,1]
[[],[[[],[],[],[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,1,1,1,3,1]
[[],[[[],[[[]]]],[]]]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[1,3,3,1]
[[],[[[[]],[],[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,1,1,4,1]
[[],[[[[],[]],[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,1,1,4,1]
[[],[[[[[]]],[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[1,1,5,1]
[[],[[[],[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[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]
[[],[[[],[[]],[[]]]]]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[2,2,3,1]
[[],[[[],[[[]]],[]]]]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,3,3,1]
[[],[[[],[[],[],[]]]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]
[[],[[[],[[[[]]]]]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[[],[[[[]],[],[],[]]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,1,1,4,1]
[[],[[[[]],[],[[]]]]]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[2,1,4,1]
[[],[[[[]],[[]],[]]]]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,2,4,1]
[[],[[[[]],[[],[]]]]]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,2,4,1]
[[],[[[[]],[[[]]]]]]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[3,4,1]
[[],[[[[],[]],[],[]]]]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,1,1,4,1]
[[],[[[[[]]],[],[]]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,1,5,1]
[[],[[[[[]],[]],[]]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,1,5,1]
[[],[[[[],[],[],[]]]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[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]
[[],[[[[],[[]],[]]]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,2,4,1]
[[],[[[[],[[],[]]]]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,2,4,1]
[[],[[[[],[[[]]]]]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,1]
[[],[[[[[]],[],[]]]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,1,5,1]
[[],[[[[[]],[[]]]]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[2,5,1]
[[],[[[[[],[]],[]]]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,1,5,1]
[[],[[[[[[]]],[]]]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,6,1]
[[],[[[[[],[],[]]]]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[[],[[[[[],[[]]]]]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[2,5,1]
[[],[[[[[[]],[]]]]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,6,1]
[[],[[[[[[],[]]]]]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,6,1]
[[],[[[[[[[]]]]]]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[[]],[],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[[[]],[],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]
[[[]],[],[],[],[[[]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,1,1,1,2]
[[[]],[],[],[[]],[],[]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]
[[[]],[],[],[[]],[[]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]
[[[]],[],[],[[],[]],[]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]
[[[]],[],[],[[[]]],[]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2]=>[1,3,1,1,2]
[[[]],[],[],[[],[],[]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]
[[[]],[],[],[[],[[]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,2,1,1,2]
[[[]],[],[],[[[]],[]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[1,3,1,1,2]
[[[]],[],[],[[[],[]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[1,3,1,1,2]
[[[]],[],[],[[[[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[4,1,1,2]
[[[]],[],[[]],[],[],[]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]
[[[]],[],[[]],[],[[]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]
[[[]],[],[[]],[[]],[]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[1,2,2,1,2]
[[[]],[],[[]],[[[]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[3,2,1,2]
[[[]],[],[[],[]],[],[]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[1,1,1,2,1,2]
[[[]],[],[[[]]],[],[]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]
[[[]],[],[[[]]],[[]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,3,1,2]
[[[]],[],[[],[[]]],[]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[1,2,2,1,2]
[[[]],[],[[[]],[]],[]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[1,1,3,1,2]
[[[]],[],[[[],[]]],[]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[1,1,3,1,2]
[[[]],[],[[],[],[],[]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]
[[[]],[],[[],[[]],[]]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[1,2,2,1,2]
[[[]],[],[[],[[],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[1,2,2,1,2]
[[[]],[],[[[]],[],[]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[1,1,3,1,2]
[[[]],[],[[[]],[[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,3,1,2]
[[[]],[],[[[],[]],[]]]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[1,1,3,1,2]
[[[]],[],[[[[]]],[]]]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[1,4,1,2]
[[[]],[],[[[],[[]]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,3,1,2]
[[[]],[],[[[[]],[]]]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[1,4,1,2]
[[[]],[],[[[[],[]]]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[1,4,1,2]
[[[]],[],[[[[[]]]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[5,1,2]
[[[]],[[]],[],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]
[[[]],[[]],[],[],[[]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]
[[[]],[[]],[],[[],[]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[1,2,1,2,2]
[[[]],[[]],[],[[[]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[3,1,2,2]
[[[]],[[]],[[]],[],[]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]
[[[]],[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[[[]],[[]],[[],[]],[]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]
[[[]],[[]],[[[]]],[]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[1,3,2,2]
[[[]],[[]],[[],[],[]]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[1,1,2,2,2]
[[[]],[[]],[[],[[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,2,2,2]
[[[]],[[]],[[[]],[]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[1,3,2,2]
[[[]],[[]],[[[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[1,3,2,2]
[[[]],[[]],[[[[]]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[[[]],[[],[]],[],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]
[[[]],[[[]]],[],[],[]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]
[[[]],[[],[]],[],[[]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]
[[[]],[[[]]],[],[[]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,3,2]
[[[]],[[],[]],[[]],[]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[1,2,1,2,2]
[[[]],[[[]]],[[]],[]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[1,2,3,2]
[[[]],[[],[]],[[],[]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[1,2,1,2,2]
[[[]],[[],[]],[[[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[3,1,2,2]
[[[]],[[[]]],[[],[]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[1,2,3,2]
[[[]],[[],[],[]],[],[]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]
[[[]],[[],[[]]],[],[]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[1,1,2,2,2]
[[[]],[[[]],[]],[],[]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[1,1,1,3,2]
[[[]],[[[],[]]],[],[]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[1,1,1,3,2]
[[[]],[[[[]]]],[],[]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[1,1,4,2]
[[[]],[[],[],[]],[[]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]
[[[]],[[],[[]]],[[]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,2,2,2]
[[[]],[[[]],[]],[[]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,3,2]
[[[]],[[[],[]]],[[]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,3,2]
[[[]],[[[[]]]],[[]]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,4,2]
[[[]],[[[]],[[]]],[]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[8,5,6,3,4,7,1,2]=>[1,2,3,2]
[[[]],[[[],[]],[]],[]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[1,1,1,3,2]
[[[]],[[[],[],[]]],[]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[1,1,1,3,2]
[[[]],[[[[]],[]]],[]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[1,1,4,2]
[[[]],[[[[],[]]]],[]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,1,4,2]
[[[]],[[[[[]]]]],[]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,5,2]
[[[]],[[],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]
[[[]],[[],[],[[],[]]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[1,2,1,2,2]
[[[]],[[],[],[[[]]]]]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[3,1,2,2]
[[[]],[[],[[]],[],[]]]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,3,8,1,2]=>[1,1,2,2,2]
[[[]],[[],[[]],[[]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,2,2,2]
[[[]],[[],[[[]]],[]]]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[1,3,2,2]
[[[]],[[],[[],[],[]]]]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[1,1,2,2,2]
[[[]],[[],[[],[[]]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,2,2,2]
[[[]],[[],[[[]],[]]]]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[1,3,2,2]
[[[]],[[],[[[],[]]]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[1,3,2,2]
[[[]],[[],[[[[]]]]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[4,2,2]
[[[]],[[[]],[],[[]]]]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,3,2]
[[[]],[[[]],[[]],[]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[1,2,3,2]
[[[]],[[[]],[[],[]]]]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[1,2,3,2]
[[[]],[[[[]]],[],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[1,1,4,2]
[[[]],[[[],[]],[[]]]]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,3,2]
[[[]],[[[],[],[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[1,1,1,3,2]
[[[]],[[[[]],[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[1,1,4,2]
[[[]],[[[[[]]]],[]]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[1,5,2]
[[[]],[[[],[],[],[]]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[1,1,1,3,2]
[[[]],[[[],[[],[]]]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[1,2,3,2]
[[[]],[[[],[[[]]]]]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[3,3,2]
[[[]],[[[[]],[[]]]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,4,2]
[[[]],[[[[],[]],[]]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[1,1,4,2]
[[[]],[[[[[]]],[]]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[1,5,2]
[[[]],[[[[],[],[]]]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[1,1,4,2]
[[[]],[[[[],[[]]]]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,4,2]
[[[]],[[[[[]],[]]]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[1,5,2]
[[[]],[[[[[],[]]]]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[1,5,2]
[[[]],[[[[[[]]]]]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,2]
[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[[[[]]],[],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[[[[]]],[],[],[],[[]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,1,1,1,3]
[[[],[]],[],[],[[]],[]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]
[[[],[]],[],[],[[],[]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]
[[[],[]],[],[],[[[]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[3,1,1,1,2]
[[[[]]],[],[],[[],[]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[1,2,1,1,3]
[[[[]]],[],[],[[[]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]
[[[],[]],[],[[]],[],[]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[1,1,2,1,1,2]
[[[],[]],[],[[]],[[]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]
[[[[]]],[],[[]],[[]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,2,1,3]
[[[],[]],[],[[],[]],[]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]
[[[],[]],[],[[[]]],[]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[1,3,1,1,2]
[[[[]]],[],[[],[]],[]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,1,2,1,3]
[[[[]]],[],[[[]]],[]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,3,1,3]
[[[],[]],[],[[],[],[]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]
[[[],[]],[],[[],[[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,2,1,1,2]
[[[],[]],[],[[[]],[]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[1,3,1,1,2]
[[[],[]],[],[[[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[1,3,1,1,2]
[[[],[]],[],[[[[]]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,1,1,2]
[[[[]]],[],[[],[],[]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[1,1,2,1,3]
[[[[]]],[],[[],[[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[2,2,1,3]
[[[[]]],[],[[[]],[]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[1,3,1,3]
[[[[]]],[],[[[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[1,3,1,3]
[[[[]]],[],[[[[]]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,3]
[[[],[]],[[]],[],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]
[[[[]]],[[]],[],[],[]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,1,1,2,3]
[[[],[]],[[]],[],[[]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]
[[[[]]],[[]],[],[[]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,1,2,3]
[[[],[]],[[]],[[]],[]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]
[[[[]]],[[]],[[]],[]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,2,2,3]
[[[],[]],[[]],[[],[]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]
[[[],[]],[[]],[[[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[3,2,1,2]
[[[],[]],[[],[]],[],[]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[1,1,1,2,1,2]
[[[],[]],[[[]]],[],[]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[1,1,3,1,2]
[[[[]]],[[],[]],[],[]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,1,1,2,3]
[[[[]]],[[[]]],[],[]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,1,3,3]
[[[],[]],[[],[]],[[]]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]
[[[],[]],[[[]]],[[]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,3,1,2]
[[[[]]],[[],[]],[[]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,1,2,3]
[[[[]]],[[[]]],[[]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,3,3]
[[[],[]],[[],[],[]],[]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[1,1,1,2,1,2]
[[[],[]],[[[]],[]],[]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[1,1,3,1,2]
[[[],[]],[[[],[]]],[]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[1,1,3,1,2]
[[[[]]],[[],[],[]],[]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[1,1,1,2,3]
[[[[]]],[[],[[]]],[]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[1,2,2,3]
[[[[]]],[[[]],[]],[]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[1,1,3,3]
[[[[]]],[[[],[]]],[]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[1,1,3,3]
[[[],[]],[[],[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]
[[[],[]],[[],[],[[]]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[2,1,2,1,2]
[[[],[]],[[],[[]],[]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[1,2,2,1,2]
[[[],[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[1,2,2,1,2]
[[[],[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,2,1,2]
[[[],[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[1,1,3,1,2]
[[[],[]],[[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[2,3,1,2]
[[[],[]],[[[],[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[1,1,3,1,2]
[[[],[]],[[[[],[]]]]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[1,4,1,2]
[[[],[]],[[[[[]]]]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[5,1,2]
[[[[]]],[[],[],[],[]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[1,1,1,2,3]
[[[[]]],[[],[],[[]]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[2,1,2,3]
[[[[]]],[[],[[]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[1,2,2,3]
[[[[]]],[[],[[],[]]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[1,2,2,3]
[[[[]]],[[],[[[]]]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,3]
[[[[]]],[[[]],[],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[1,1,3,3]
[[[[]]],[[[]],[[]]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[2,3,3]
[[[[]]],[[[],[]],[]]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[1,1,3,3]
[[[[]]],[[[[]]],[]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[1,4,3]
[[[[]]],[[[],[],[]]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[1,1,3,3]
[[[[]]],[[[],[[]]]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[2,3,3]
[[[[]]],[[[[]],[]]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[1,4,3]
[[[[]]],[[[[],[]]]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[1,4,3]
[[[[]]],[[[[[]]]]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[5,3]
[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2]
[[[[]],[]],[],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[[[[[]]]],[],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[[[],[],[]],[],[],[[]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]
[[[],[[]]],[],[],[[]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[2,1,1,2,2]
[[[[]],[]],[],[],[[]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[2,1,1,1,3]
[[[[],[]]],[],[],[[]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,1,1,3]
[[[[[]]]],[],[],[[]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]
[[[],[],[]],[],[[]],[]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[1,2,1,1,1,2]
[[[],[[]]],[],[[]],[]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[1,2,1,2,2]
[[[[]],[]],[],[[]],[]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,2,1,1,3]
[[[[],[]]],[],[[]],[]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[1,2,1,1,3]
[[[[[]]]],[],[[]],[]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,2,1,4]
[[[],[],[]],[],[[],[]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]
[[[],[],[]],[],[[[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[3,1,1,1,2]
[[[],[[]]],[],[[],[]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[1,2,1,2,2]
[[[],[[]]],[],[[[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[3,1,2,2]
[[[[],[]]],[],[[],[]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[1,2,1,1,3]
[[[[],[]]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,1,1,3]
[[[[[]]]],[],[[],[]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[1,2,1,4]
[[[[[]]]],[],[[[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[3,1,4]
[[[],[],[]],[[]],[],[]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[1,1,2,1,1,2]
[[[],[[]]],[[]],[],[]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[1,1,2,2,2]
[[[[]],[]],[[]],[],[]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,1,2,1,3]
[[[[],[]]],[[]],[],[]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[1,1,2,1,3]
[[[[[]]]],[[]],[],[]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]
[[[],[],[]],[[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,2,1,1,2]
[[[],[[]]],[[]],[[]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[2,2,2,2]
[[[[]],[]],[[]],[[]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,2,1,3]
[[[[],[]]],[[]],[[]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,2,1,3]
[[[[[]]]],[[]],[[]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,2,4]
[[[],[],[]],[[],[]],[]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]
[[[],[],[]],[[[]]],[]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[1,3,1,1,2]
[[[],[[]]],[[],[]],[]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[1,1,2,2,2]
[[[],[[]]],[[[]]],[]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[1,3,2,2]
[[[[]],[]],[[],[]],[]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,1,2,1,3]
[[[[]],[]],[[[]]],[]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[1,3,1,3]
[[[[],[]]],[[],[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[1,1,2,1,3]
[[[[],[]]],[[[]]],[]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[1,3,1,3]
[[[[[]]]],[[],[]],[]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,1,2,4]
[[[[[]]]],[[[]]],[]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,3,4]
[[[],[],[]],[[],[],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]
[[[],[],[]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,2,1,1,2]
[[[],[],[]],[[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[1,3,1,1,2]
[[[],[],[]],[[[],[]]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[1,3,1,1,2]
[[[],[],[]],[[[[]]]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,1,2]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[1,1,2,2,2]
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[2,2,2,2]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[1,3,2,2]
[[[],[[]]],[[[],[]]]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[1,3,2,2]
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,2,2]
[[[[]],[]],[[],[],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[1,1,2,1,3]
[[[[]],[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,2,1,3]
[[[[]],[]],[[[]],[]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[1,3,1,3]
[[[[]],[]],[[[],[]]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[1,3,1,3]
[[[[]],[]],[[[[]]]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,1,3]
[[[[],[]]],[[],[],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[1,1,2,1,3]
[[[[],[]]],[[],[[]]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,2,1,3]
[[[[],[]]],[[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[1,3,1,3]
[[[[],[]]],[[[],[]]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[1,3,1,3]
[[[[],[]]],[[[[]]]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,1,3]
[[[[[]]]],[[],[],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[1,1,2,4]
[[[[[]]]],[[],[[]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[2,2,4]
[[[[[]]]],[[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[1,3,4]
[[[[[]]]],[[[],[]]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[1,3,4]
[[[[[]]]],[[[[]]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,4]
[[[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[1,1,1,2,1,2]
[[[],[[]],[]],[],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[1,1,1,1,2,2]
[[[],[[],[]]],[],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[1,1,1,1,2,2]
[[[],[[[]]]],[],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[1,1,1,3,2]
[[[[]],[],[]],[],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[[[[]],[[]]],[],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[1,1,1,2,3]
[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[[[[[]]],[]],[],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[[[[],[[]]]],[],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[1,1,1,2,3]
[[[[[]],[]]],[],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[[[[[[]]]]],[],[],[]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[[[],[],[],[]],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]
[[[],[],[[]]],[],[[]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[2,1,2,1,2]
[[[],[[]],[]],[],[[]]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[2,1,1,2,2]
[[[[]],[],[]],[],[[]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[2,1,1,1,3]
[[[[]],[[]]],[],[[]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,1,2,3]
[[[[],[]],[]],[],[[]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[2,1,1,1,3]
[[[[[]]],[]],[],[[]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[2,1,1,4]
[[[[],[],[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,1,1,1,3]
[[[[],[[]]]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[2,1,2,3]
[[[[[]],[]]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,1,1,4]
[[[[[],[]]]],[],[[]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[2,1,1,4]
[[[[[[]]]]],[],[[]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,1,5]
[[[],[],[],[]],[[]],[]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]
[[[],[],[[]]],[[]],[]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[1,2,2,1,2]
[[[],[[]],[]],[[]],[]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[1,2,1,2,2]
[[[],[[],[]]],[[]],[]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[1,2,1,2,2]
[[[[]],[],[]],[[]],[]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[1,2,1,1,3]
[[[[]],[[]]],[[]],[]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[1,2,2,3]
[[[[],[]],[]],[[]],[]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[1,2,1,1,3]
[[[[[]]],[]],[[]],[]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[1,2,1,4]
[[[[],[],[]]],[[]],[]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[1,2,1,1,3]
[[[[[]],[]]],[[]],[]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[1,2,1,4]
[[[[[],[]]]],[[]],[]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[1,2,1,4]
[[[[[[]]]]],[[]],[]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,2,5]
[[[],[],[],[]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]
[[[],[],[],[]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[3,1,1,1,2]
[[[],[],[[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[3,2,1,2]
[[[],[[]],[]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[1,2,1,2,2]
[[[],[[]],[]],[[[]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,1,2,2]
[[[],[[],[]]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[1,2,1,2,2]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[3,1,2,2]
[[[],[[[]]]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[1,2,3,2]
[[[],[[[]]]],[[[]]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[3,3,2]
[[[[]],[],[]],[[[]]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,1,3]
[[[[]],[[]]],[[[]]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[3,2,3]
[[[[],[]],[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[1,2,1,1,3]
[[[[],[]],[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,1,1,3]
[[[[[]]],[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[1,2,1,4]
[[[[[]]],[]],[[[]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[3,1,4]
[[[[],[],[]]],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[1,2,1,1,3]
[[[[],[],[]]],[[[]]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[3,1,1,3]
[[[[],[[]]]],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[1,2,2,3]
[[[[],[[]]]],[[[]]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,2,3]
[[[[[]],[]]],[[[]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[3,1,4]
[[[[[],[]]]],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[1,2,1,4]
[[[[[],[]]]],[[[]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,1,4]
[[[[[[]]]]],[[],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[1,2,5]
[[[[[[]]]]],[[[]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[3,5]
[[[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[[[],[],[],[[]]],[],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[1,1,2,1,1,2]
[[[],[],[[]],[]],[],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[1,1,1,2,1,2]
[[[],[],[[],[]]],[],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[1,1,1,2,1,2]
[[[],[],[[[]]]],[],[]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[1,1,3,1,2]
[[[],[[]],[],[]],[],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[1,1,1,1,2,2]
[[[],[[]],[[]]],[],[]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[1,1,2,2,2]
[[[],[[],[]],[]],[],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[1,1,1,1,2,2]
[[[],[[[]]],[]],[],[]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[1,1,1,3,2]
[[[],[[],[],[]]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[1,1,1,1,2,2]
[[[],[[],[[]]]],[],[]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[1,1,2,2,2]
[[[],[[[]],[]]],[],[]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[1,1,1,3,2]
[[[],[[[],[]]]],[],[]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6]=>[1,1,1,3,2]
[[[],[[[[]]]]],[],[]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[1,1,4,2]
[[[[]],[],[],[]],[],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[[[[]],[[]],[]],[],[]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[1,1,1,2,3]
[[[[]],[[],[]]],[],[]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[1,1,1,2,3]
[[[[],[]],[],[]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[1,1,1,1,1,3]
[[[[[]]],[],[]],[],[]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]
[[[[[]]],[[]]],[],[]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,1,2,4]
[[[[],[],[]],[]],[],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[[[[],[[]]],[]],[],[]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[1,1,1,2,3]
[[[[[]],[]],[]],[],[]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]
[[[[[],[]]],[]],[],[]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[[[[[[]]]],[]],[],[]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[[[[],[],[],[]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]
[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[1,1,2,1,3]
[[[[],[[],[]]]],[],[]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[1,1,1,2,3]
[[[[],[[[]]]]],[],[]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[1,1,3,3]
[[[[[]],[],[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[1,1,1,1,4]
[[[[[]],[[]]]],[],[]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[1,1,2,4]
[[[[[[]]],[]]],[],[]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,1,1,5]
[[[[[],[],[]]]],[],[]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[[[[[[],[]]]]],[],[]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[[[[[[[]]]]]],[],[]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,1,6]
[[[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]
[[[],[],[[],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,1,2,1,2]
[[[],[],[[[]]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[2,3,1,2]
[[[],[[]],[[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[2,2,2,2]
[[[],[[],[]],[]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[2,1,1,2,2]
[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[2,1,3,2]
[[[],[[],[],[]]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[2,1,1,2,2]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[2,2,2,2]
[[[],[[[[]]]]],[[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[2,4,2]
[[[[]],[],[],[]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[2,1,1,1,3]
[[[[]],[[]],[]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,1,2,3]
[[[[],[]],[],[]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,1,1,1,3]
[[[[[]]],[],[]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,1,1,4]
[[[[],[]],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,2,1,3]
[[[[[]]],[[]]],[[]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,2,4]
[[[[],[],[]],[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,1,1,1,3]
[[[[],[[]]],[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[2,1,2,3]
[[[[[]],[]],[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[2,1,1,4]
[[[[[],[]]],[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,1,1,4]
[[[[[[]]]],[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,1,5]
[[[[],[],[],[]]],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,1,1,1,3]
[[[[],[],[[]]]],[[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,2,1,3]
[[[[],[[]],[]]],[[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[2,1,2,3]
[[[[],[[],[]]]],[[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[2,1,2,3]
[[[[],[[[]]]]],[[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[2,3,3]
[[[[[]],[],[]]],[[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,1,1,4]
[[[[[]],[[]]]],[[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[2,2,4]
[[[[[],[]],[]]],[[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,1,1,4]
[[[[[[]]],[]]],[[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[2,1,5]
[[[[[],[],[]]]],[[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,1,1,4]
[[[[[],[[]]]]],[[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[2,2,4]
[[[[[[]],[]]]],[[]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[2,1,5]
[[[[[[],[]]]]],[[]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,1,5]
[[[[[[[]]]]]],[[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,6]
[[[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[[[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[1,2,1,1,1,2]
[[[],[],[],[[[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[1,3,1,1,2]
[[[],[],[[]],[],[]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[1,1,1,2,1,2]
[[[],[],[[]],[[]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[1,2,2,1,2]
[[[],[],[[],[],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[1,1,1,2,1,2]
[[[],[],[[],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[1,2,2,1,2]
[[[],[[]],[],[],[]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[1,1,1,1,2,2]
[[[],[[]],[],[[]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[1,2,1,2,2]
[[[],[[]],[[]],[]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[1,1,2,2,2]
[[[],[[]],[[[]]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[1,3,2,2]
[[[],[[],[]],[],[]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[1,1,1,1,2,2]
[[[],[[[]]],[],[]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[1,1,1,3,2]
[[[],[[[]]],[[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[1,2,3,2]
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[1,1,1,3,2]
[[[],[[[],[]]],[]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[1,1,1,3,2]
[[[],[[],[],[],[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[1,1,1,1,2,2]
[[[],[[],[],[[]]]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[1,2,1,2,2]
[[[],[[],[[],[]]]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[1,1,2,2,2]
[[[],[[],[[[]]]]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[1,3,2,2]
[[[],[[[]],[],[]]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>[1,1,1,3,2]
[[[],[[[[]]],[]]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[1,1,4,2]
[[[],[[[[]],[]]]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[1,1,4,2]
[[[[]],[],[],[],[]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]
[[[[]],[],[[]],[]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[1,1,2,1,3]
[[[[]],[],[[],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[1,1,2,1,3]
[[[[]],[[]],[[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,2,2,3]
[[[[]],[[],[]],[]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[8,6,4,3,5,1,2,7]=>[1,1,1,2,3]
[[[[]],[[[]]],[]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[1,1,3,3]
[[[[]],[[],[[]]]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[1,2,2,3]
[[[[]],[[[]],[]]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[1,1,3,3]
[[[[]],[[[],[]]]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[1,1,3,3]
[[[[],[]],[],[],[]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]
[[[[[]]],[],[],[]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]
[[[[],[]],[],[[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[1,2,1,1,3]
[[[[[]]],[],[[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[1,2,1,4]
[[[[],[]],[[]],[]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[1,1,2,1,3]
[[[[],[]],[[],[]]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[1,1,2,1,3]
[[[[[]]],[[[]]]],[]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[1,3,4]
[[[[],[],[]],[],[]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]
[[[[],[[]]],[],[]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[1,1,1,2,3]
[[[[[]],[]],[],[]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[1,1,1,1,4]
[[[[[],[]]],[],[]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]
[[[[[[]]]],[],[]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,1,1,5]
[[[[],[],[]],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[1,2,1,1,3]
[[[[],[[]]],[[]]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[1,2,2,3]
[[[[[]],[]],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[1,2,1,4]
[[[[[],[]]],[[]]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[1,2,1,4]
[[[[[[]]]],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,2,5]
[[[[],[],[],[]],[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[[[[],[],[[]]],[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[1,1,2,1,3]
[[[[],[[]],[]],[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[1,1,1,2,3]
[[[[],[[],[]]],[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[1,1,1,2,3]
[[[[],[[[]]]],[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[1,1,3,3]
[[[[[]],[],[]],[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,4]
[[[[[]],[[]]],[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[1,1,2,4]
[[[[[],[]],[]],[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[[[[[[]]],[]],[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[[[[[],[],[]]],[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[[[[[],[[]]]],[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[1,1,2,4]
[[[[[[[]]]]],[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,1,6]
[[[[],[],[],[],[]]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]
[[[[],[],[],[[]]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[1,2,1,1,3]
[[[[],[],[[],[]]]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[1,1,2,1,3]
[[[[],[],[[[]]]]],[]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[1,3,1,3]
[[[[],[[]],[],[]]],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[1,1,1,2,3]
[[[[],[[]],[[]]]],[]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[1,2,2,3]
[[[[],[[[]]],[]]],[]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[1,1,3,3]
[[[[],[[[]],[]]]],[]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[1,1,3,3]
[[[[[]],[[]],[]]],[]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[1,1,2,4]
[[[[[],[]],[],[]]],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]
[[[[[],[]],[[]]]],[]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[1,2,1,4]
[[[[[[]]],[[]]]],[]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[1,2,5]
[[[[[],[],[]],[]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[[[[[[]],[]],[]]],[]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[1,1,1,5]
[[[[[[],[]]],[]]],[]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[1,1,1,5]
[[[[[[[]]]],[]]],[]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,1,6]
[[[[[],[],[],[]]]],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[[[[[],[],[[]]]]],[]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[1,2,1,4]
[[[[[],[[]],[]]]],[]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[1,1,2,4]
[[[[[],[[],[]]]]],[]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[1,1,2,4]
[[[[[],[[[]]]]]],[]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[1,3,4]
[[[[[[]],[],[]]]],[]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[1,1,1,5]
[[[[[[]],[[]]]]],[]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[1,2,5]
[[[[[[],[]],[]]]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[[[[[[[]]],[]]]],[]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,1,6]
[[[[[[],[],[]]]]],[]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[[[[[[],[[]]]]]],[]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[1,2,5]
[[[[[[[]],[]]]]],[]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,1,6]
[[[[[[[[]]]]]]],[]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,7]
[[[],[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[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]
[[[],[],[],[],[[]],[]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[1,2,1,1,1,2]
[[[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[[[],[],[],[],[[[]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[[[],[],[],[[]],[],[]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[1,1,2,1,1,2]
[[[],[],[],[[]],[[]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[2,2,1,1,2]
[[[],[],[],[[[]]],[]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[1,3,1,1,2]
[[[],[],[],[[],[],[]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[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]
[[[],[],[],[[[],[]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[[[],[],[],[[[[]]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[[[],[],[[]],[],[],[]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[1,1,1,2,1,2]
[[[],[],[[]],[],[[]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[2,1,2,1,2]
[[[],[],[[]],[[]],[]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[1,2,2,1,2]
[[[],[],[[]],[[],[]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[1,2,2,1,2]
[[[],[],[[]],[[[]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[3,2,1,2]
[[[],[],[[],[]],[],[]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[1,1,1,2,1,2]
[[[],[],[[[]]],[],[]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[1,1,3,1,2]
[[[],[],[[],[[]]],[]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[1,2,2,1,2]
[[[],[],[[[[]]]],[]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[1,4,1,2]
[[[],[],[[],[],[],[]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[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]
[[[],[],[[],[[]],[]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[1,2,2,1,2]
[[[],[],[[],[[],[]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[[[],[],[[],[[[]]]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[[[],[],[[[]],[[]]]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[2,3,1,2]
[[[],[],[[[],[],[]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[[[],[[]],[],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[1,1,1,1,2,2]
[[[],[[]],[],[],[[]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]
[[[],[[]],[],[[]],[]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[1,2,1,2,2]
[[[],[[]],[],[[[]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,1,2,2]
[[[],[[]],[[]],[],[]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[1,1,2,2,2]
[[[],[[]],[[]],[[]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[2,2,2,2]
[[[],[[]],[[[]]],[]]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[1,3,2,2]
[[[],[[]],[[],[],[]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[1,1,2,2,2]
[[[],[[]],[[],[[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[2,2,2,2]
[[[],[[]],[[[],[]]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[1,3,2,2]
[[[],[[]],[[[[]]]]]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[4,2,2]
[[[],[[],[]],[],[],[]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[1,1,1,1,2,2]
[[[],[[[]]],[],[],[]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[1,1,1,3,2]
[[[],[[[]]],[],[[]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[2,1,3,2]
[[[],[[[]]],[[]],[]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[1,2,3,2]
[[[],[[],[]],[[],[]]]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]
[[[],[[],[]],[[[]]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[3,1,2,2]
[[[],[[[]]],[[],[]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[1,2,3,2]
[[[],[[[]]],[[[]]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[3,3,2]
[[[],[[],[],[]],[],[]]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[1,1,1,1,2,2]
[[[],[[[]],[]],[],[]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[1,1,1,3,2]
[[[],[[[],[]]],[],[]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[1,1,1,3,2]
[[[],[[[[]]]],[],[]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[1,1,4,2]
[[[],[[],[],[]],[[]]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[2,1,1,2,2]
[[[],[[],[[]]],[[]]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[2,2,2,2]
[[[],[[[],[]]],[[]]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[2,1,3,2]
[[[],[[[[]]]],[[]]]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[2,4,2]
[[[],[[],[],[],[]],[]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[1,1,1,1,2,2]
[[[],[[],[],[[]]],[]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[1,2,1,2,2]
[[[],[[],[[]],[]],[]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[1,1,2,2,2]
[[[],[[],[[],[]]],[]]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[1,1,2,2,2]
[[[],[[],[[[]]]],[]]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[1,3,2,2]
[[[],[[[]],[],[]],[]]]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[1,1,1,3,2]
[[[],[[[]],[[]]],[]]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[1,2,3,2]
[[[],[[[],[]],[]],[]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[1,1,1,3,2]
[[[],[[[[]]],[]],[]]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[7,5,2,3,4,6,1,8]=>[1,1,4,2]
[[[],[[[],[],[]]],[]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[1,1,1,3,2]
[[[],[[[[]],[]]],[]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[1,1,4,2]
[[[],[[],[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[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]
[[[],[[],[[]],[[]]]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[2,2,2,2]
[[[],[[],[[],[]],[]]]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[1,1,2,2,2]
[[[],[[],[[[]]],[]]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[1,3,2,2]
[[[],[[],[[],[],[]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[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]
[[[],[[],[[[[]]]]]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[[[],[[[]],[[],[]]]]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[1,2,3,2]
[[[],[[[]],[[[]]]]]]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[3,3,2]
[[[],[[[],[]],[],[]]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[1,1,1,3,2]
[[[],[[[[]]],[],[]]]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[1,1,4,2]
[[[],[[[[]]],[[]]]]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[2,4,2]
[[[],[[[[]],[]],[]]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[1,1,4,2]
[[[],[[[[],[]]],[]]]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[1,1,4,2]
[[[],[[[[[]]]],[]]]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[1,5,2]
[[[],[[[],[],[],[]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[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]
[[[],[[[],[[]],[]]]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[1,2,3,2]
[[[],[[[],[[[]]]]]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,3,2]
[[[],[[[[]],[],[]]]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[1,1,4,2]
[[[],[[[[]],[[]]]]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[2,4,2]
[[[],[[[[],[]],[]]]]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[1,1,4,2]
[[[],[[[[[]]],[]]]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[1,5,2]
[[[],[[[[],[[]]]]]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[[[],[[[[[]],[]]]]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[1,5,2]
[[[],[[[[[[]]]]]]]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[6,2]
[[[[]],[],[],[],[[]]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[2,1,1,1,3]
[[[[]],[],[],[[]],[]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[1,2,1,1,3]
[[[[]],[],[],[[[]]]]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,1,3]
[[[[]],[],[[[]]],[]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[1,3,1,3]
[[[[]],[],[[[],[]]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[1,3,1,3]
[[[[]],[],[[[[]]]]]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[4,1,3]
[[[[]],[[]],[],[],[]]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[1,1,1,2,3]
[[[[]],[[]],[[]],[]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[1,2,2,3]
[[[[]],[[],[]],[[]]]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[6,7,4,3,5,1,2,8]=>[2,1,2,3]
[[[[]],[[],[],[]],[]]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[1,1,1,2,3]
[[[[]],[[],[[]]],[]]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[1,2,2,3]
[[[[]],[[[]],[]],[]]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[1,1,3,3]
[[[[]],[[],[],[],[]]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[1,1,1,2,3]
[[[[]],[[],[],[[]]]]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[2,1,2,3]
[[[[]],[[[]],[],[]]]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[1,1,3,3]
[[[[]],[[[]],[[]]]]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[2,3,3]
[[[[]],[[[],[]],[]]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[1,1,3,3]
[[[[]],[[[],[[]]]]]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[2,3,3]
[[[[]],[[[[[]]]]]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[5,3]
[[[[[]]],[],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[[[[[]]],[],[],[[]]]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[2,1,1,4]
[[[[[]]],[],[[]],[]]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[1,2,1,4]
[[[[],[]],[],[[[]]]]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[3,1,1,3]
[[[[[]]],[],[[],[]]]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[1,2,1,4]
[[[[[]]],[],[[[]]]]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[3,1,4]
[[[[[]]],[[]],[],[]]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[1,1,2,4]
[[[[],[]],[[]],[[]]]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[2,2,1,3]
[[[[],[]],[[],[]],[]]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[1,1,2,1,3]
[[[[],[]],[[[]]],[]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[1,3,1,3]
[[[[[]]],[[],[]],[]]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[1,1,2,4]
[[[[[]]],[[[]]],[]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[1,3,4]
[[[[],[]],[[],[],[]]]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[1,1,2,1,3]
[[[[],[]],[[[],[]]]]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[1,3,1,3]
[[[[],[]],[[[[]]]]]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[4,1,3]
[[[[[]]],[[],[],[]]]]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[1,1,2,4]
[[[[[]]],[[[]],[]]]]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[1,3,4]
[[[[[]]],[[[],[]]]]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[1,3,4]
[[[[[]]],[[[[]]]]]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[4,4]
[[[[],[],[]],[],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]
[[[[],[[]]],[],[],[]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[1,1,1,2,3]
[[[[[]],[]],[],[],[]]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[1,1,1,1,4]
[[[[[],[]]],[],[],[]]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[[[[[[]]]],[],[],[]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[[[[],[],[]],[],[[]]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[6,7,5,3,2,1,4,8]=>[2,1,1,1,3]
[[[[],[[]]],[],[[]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[2,1,2,3]
[[[[[[]]]],[],[[]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[2,1,5]
[[[[],[],[]],[[]],[]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[1,2,1,1,3]
[[[[],[[]]],[[]],[]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[1,2,2,3]
[[[[[]],[]],[[]],[]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[1,2,1,4]
[[[[[],[]]],[[]],[]]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[1,2,1,4]
[[[[[[]]]],[[]],[]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[1,2,5]
[[[[],[],[]],[[[]]]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[3,1,1,3]
[[[[],[[]]],[[],[]]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[1,2,2,3]
[[[[],[[]]],[[[]]]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,2,3]
[[[[[[]]]],[[],[]]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[1,2,5]
[[[[[[]]]],[[[]]]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[3,5]
[[[[],[],[],[]],[],[]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[[[[],[[],[]]],[],[]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[1,1,1,2,3]
[[[[],[[[]]]],[],[]]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[1,1,3,3]
[[[[[]],[],[]],[],[]]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]
[[[[[]],[[]]],[],[]]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[1,1,2,4]
[[[[[],[]],[]],[],[]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[[[[[[]]],[]],[],[]]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[1,1,1,5]
[[[[[],[],[]]],[],[]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[[[[[],[[]]]],[],[]]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[1,1,2,4]
[[[[[[]],[]]],[],[]]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[1,1,1,5]
[[[[[[[]]]]],[],[]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[1,1,6]
[[[[],[],[],[]],[[]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,1,1,1,3]
[[[[],[[],[]]],[[]]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[2,1,2,3]
[[[[],[[[]]]],[[]]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[2,3,3]
[[[[[]],[],[]],[[]]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[6,7,4,3,1,2,5,8]=>[2,1,1,4]
[[[[[]],[[]]],[[]]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[2,2,4]
[[[[[],[],[]]],[[]]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[2,1,1,4]
[[[[[],[[]]]],[[]]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[2,2,4]
[[[[[[]],[]]],[[]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[2,1,5]
[[[[[[[]]]]],[[]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[2,6]
[[[[],[],[],[],[]],[]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,3]
[[[[],[],[[]],[]],[]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[1,1,2,1,3]
[[[[],[],[[],[]]],[]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[1,1,2,1,3]
[[[[],[],[[[]]]],[]]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[1,3,1,3]
[[[[],[[]],[],[]],[]]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[1,1,1,2,3]
[[[[],[[],[]],[]],[]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[1,1,1,2,3]
[[[[],[[[]]],[]],[]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[1,1,3,3]
[[[[],[[[]],[]]],[]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[1,1,3,3]
[[[[],[[[[]]]]],[]]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[1,4,3]
[[[[[]],[[]],[]],[]]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[1,1,2,4]
[[[[[]],[[[]]]],[]]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[1,3,4]
[[[[[[]]],[],[]],[]]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[1,1,1,5]
[[[[[[]]],[[]]],[]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[1,2,5]
[[[[[],[],[]],[]],[]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[[[[[],[[]]],[]],[]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[1,1,2,4]
[[[[[[]],[]],[]],[]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[[[[[[],[]]],[]],[]]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[1,1,1,5]
[[[[[[[]]]],[]],[]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[1,1,6]
[[[[[],[],[],[]]],[]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[[[[[],[],[[]]]],[]]]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[1,2,1,4]
[[[[[],[[]],[]]],[]]]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[1,1,2,4]
[[[[[],[[],[]]]],[]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[1,1,2,4]
[[[[[],[[[]]]]],[]]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[1,3,4]
[[[[[[]],[],[]]],[]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[1,1,1,5]
[[[[[[]],[[]]]],[]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[1,2,5]
[[[[[[],[[]]]]],[]]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[1,2,5]
[[[[[[[]],[]]]],[]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[1,1,6]
[[[[[[[[]]]]]],[]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[1,7]
[[[[],[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[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]
[[[[],[],[[]],[],[]]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[1,1,2,1,3]
[[[[],[],[[]],[[]]]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[2,2,1,3]
[[[[],[],[[[]]],[]]]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[1,3,1,3]
[[[[],[],[[],[],[]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[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]
[[[[],[],[[[],[]]]]]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[[[[],[],[[[[]]]]]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[[[[],[[]],[],[[]]]]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[2,1,2,3]
[[[[],[[]],[[]],[]]]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[1,2,2,3]
[[[[],[[]],[[],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[1,2,2,3]
[[[[],[[]],[[[]]]]]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[4,5,6,2,3,1,7,8]=>[3,2,3]
[[[[],[[[]]],[],[]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[1,1,3,3]
[[[[],[[],[]],[[]]]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[2,1,2,3]
[[[[],[[[]]],[[]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[2,3,3]
[[[[],[[],[],[]],[]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[1,1,1,2,3]
[[[[],[[[],[]]],[]]]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[1,1,3,3]
[[[[],[[],[],[],[]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[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]
[[[[],[[],[[[]]]]]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,2,3]
[[[[],[[[]],[],[]]]]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[1,1,3,3]
[[[[],[[[],[]],[]]]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[1,1,3,3]
[[[[],[[[[]]],[]]]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[1,4,3]
[[[[],[[[],[],[]]]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[[[[],[[[[[]]]]]]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[5,3]
[[[[[]],[],[],[],[]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[[[[[]],[],[],[[]]]]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[2,1,1,4]
[[[[[]],[[]],[],[]]]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[1,1,2,4]
[[[[[]],[[]],[[]]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[2,2,4]
[[[[[]],[[],[]],[]]]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[1,1,2,4]
[[[[[]],[[],[],[]]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[1,1,2,4]
[[[[[]],[[],[[]]]]]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[4,5,3,6,1,2,7,8]=>[2,2,4]
[[[[[]],[[[]],[]]]]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[1,3,4]
[[[[[[]]],[],[],[]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[1,1,1,5]
[[[[[],[]],[],[[]]]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,1,1,4]
[[[[[],[]],[[]],[]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[1,2,1,4]
[[[[[],[[]]],[],[]]]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[1,1,2,4]
[[[[[[[]]]],[],[]]]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[1,1,6]
[[[[[],[],[]],[[]]]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,1,1,4]
[[[[[],[[]]],[[]]]]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[2,2,4]
[[[[[[[]]]],[[]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[2,6]
[[[[[],[],[],[]],[]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[[[[[],[],[[]]],[]]]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[1,2,1,4]
[[[[[],[[],[]]],[]]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[1,1,2,4]
[[[[[],[[[]]]],[]]]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[1,3,4]
[[[[[[]],[],[]],[]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[1,1,1,5]
[[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[1,1,6]
[[[[[[],[],[]]],[]]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[1,1,1,5]
[[[[[[[]],[]]],[]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[1,1,6]
[[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[1,7]
[[[[[],[],[],[],[]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[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]
[[[[[],[],[[]],[]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[1,2,1,4]
[[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[[[[[],[],[[[]]]]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[1,1,2,4]
[[[[[],[[]],[[]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[2,2,4]
[[[[[],[[],[]],[]]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[1,1,2,4]
[[[[[],[[[]]],[]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[1,3,4]
[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[[[[[],[[],[[]]]]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[1,3,4]
[[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[[[[[],[[[[]]]]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[4,4]
[[[[[[]],[],[],[]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[[[[[[]],[[]],[]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[1,2,5]
[[[[[[]],[[[]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[3,5]
[[[[[[],[]],[],[]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[1,1,1,5]
[[[[[[[]]],[],[]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[1,1,6]
[[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[2,6]
[[[[[[],[],[]],[]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[[[[[[],[[]]],[]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[1,2,5]
[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[1,1,6]
[[[[[[[],[]]],[]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[1,1,6]
[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[1,7]
[[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[[[[],[],[[]]]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[[[[[[],[[]],[]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[1,2,5]
[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[3,5]
[[[[[[[]],[],[]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[1,1,6]
[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[2,6]
[[[[[[[],[]],[]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[1,1,6]
[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[1,7]
[[[[[[[],[],[]]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[[[[[],[[]]]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,6]
[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[1,7]
[[[[[[[[],[]]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]
Map
to binary tree: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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