Identifier
Mp00050:
Ordered trees
—to binary tree: right brother = right child⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0002;cc-rep-3
[[]]=>[.,.]=>[1]=>[1]
[[],[]]=>[.,[.,.]]=>[2,1]=>[1,1]
[[[]]]=>[[.,.],.]=>[1,2]=>[2]
[[],[],[]]=>[.,[.,[.,.]]]=>[3,2,1]=>[1,1,1]
[[],[[]]]=>[.,[[.,.],.]]=>[2,3,1]=>[2,1]
[[[]],[]]=>[[.,.],[.,.]]=>[3,1,2]=>[2,1]
[[[],[]]]=>[[.,[.,.]],.]=>[2,1,3]=>[2,1]
[[[[]]]]=>[[[.,.],.],.]=>[1,2,3]=>[3]
[[],[],[],[]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]
[[],[],[[]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]
[[],[[]],[]]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[2,1,1]
[[],[[],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[2,1,1]
[[],[[[]]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]
[[[]],[],[]]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,1]
[[[]],[[]]]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2]
[[[],[]],[]]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,1,1]
[[[[]]],[]]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,1]
[[[],[],[]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,1,1]
[[[],[[]]]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1]
[[[[]],[]]]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1]
[[[[],[]]]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,1]
[[[[[]]]]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4]
[[],[],[],[],[]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]
[[],[],[],[[]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]
[[],[],[[]],[]]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,1,1,1]
[[],[],[[],[]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,1,1,1]
[[],[],[[[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[[],[[]],[],[]]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[2,1,1,1]
[[],[[]],[[]]]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1]
[[],[[],[]],[]]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[2,1,1,1]
[[],[[[]]],[]]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[3,1,1]
[[],[[],[],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[2,1,1,1]
[[],[[],[[]]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,1,1]
[[],[[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[3,1,1]
[[],[[[],[]]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,1,1]
[[],[[[[]]]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]
[[[]],[],[],[]]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,1,1]
[[[]],[],[[]]]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,2,1]
[[[]],[[]],[]]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,2,1]
[[[]],[[],[]]]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,2,1]
[[[]],[[[]]]]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2]
[[[],[]],[],[]]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,1,1,1]
[[[[]]],[],[]]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,1,1]
[[[],[]],[[]]]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,2,1]
[[[[]]],[[]]]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2]
[[[],[],[]],[]]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,1,1,1]
[[[],[[]]],[]]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,1,1]
[[[[]],[]],[]]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,1]
[[[[],[]]],[]]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,1]
[[[[[]]]],[]]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,1]
[[[],[],[],[]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,1,1,1]
[[[],[],[[]]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,1,1]
[[[],[[]],[]]]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,1,1]
[[[],[[],[]]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,1,1]
[[[],[[[]]]]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1]
[[[[]],[],[]]]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,1]
[[[[]],[[]]]]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,2]
[[[[],[]],[]]]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,1]
[[[[[]]],[]]]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1]
[[[[],[],[]]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,1]
[[[[],[[]]]]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,1]
[[[[[]],[]]]]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[4,1]
[[[[[],[]]]]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[4,1]
[[[[[[]]]]]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5]
[[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[[],[],[],[],[[]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[[],[],[],[[]],[]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,1,1,1,1]
[[],[],[],[[],[]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,1,1,1,1]
[[],[],[],[[[]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[],[],[[]],[],[]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,1,1,1,1]
[[],[],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1]
[[],[],[[],[]],[]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,1,1,1,1]
[[],[],[[[]]],[]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[3,1,1,1]
[[],[],[[],[],[]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,1,1,1,1]
[[],[],[[],[[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[3,1,1,1]
[[],[],[[[]],[]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[3,1,1,1]
[[],[],[[[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[3,1,1,1]
[[],[],[[[[]]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]
[[],[[]],[],[],[]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[2,1,1,1,1]
[[],[[]],[],[[]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,2,1,1]
[[],[[]],[[]],[]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[2,2,1,1]
[[],[[]],[[],[]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[2,2,1,1]
[[],[[]],[[[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1]
[[],[[],[]],[],[]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[2,1,1,1,1]
[[],[[[]]],[],[]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[3,1,1,1]
[[],[[],[]],[[]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,2,1,1]
[[],[[[]]],[[]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[3,2,1]
[[],[[],[],[]],[]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[2,1,1,1,1]
[[],[[],[[]]],[]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[3,1,1,1]
[[],[[[]],[]],[]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[3,1,1,1]
[[],[[[],[]]],[]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[3,1,1,1]
[[],[[[[]]]],[]]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[4,1,1]
[[],[[],[],[],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[2,1,1,1,1]
[[],[[],[],[[]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[3,1,1,1]
[[],[[],[[]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[3,1,1,1]
[[],[[],[[],[]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[3,1,1,1]
[[],[[],[[[]]]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[4,1,1]
[[],[[[]],[],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[3,1,1,1]
[[],[[[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[3,2,1]
[[],[[[],[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[3,1,1,1]
[[],[[[[]]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[4,1,1]
[[],[[[],[],[]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[3,1,1,1]
[[],[[[],[[]]]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[4,1,1]
[[],[[[[]],[]]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[4,1,1]
[[],[[[[],[]]]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[4,1,1]
[[],[[[[[]]]]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]
[[[]],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,1,1,1]
[[[]],[],[],[[]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,2,1,1]
[[[]],[],[[]],[]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,2,1,1]
[[[]],[],[[],[]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,2,1,1]
[[[]],[],[[[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,2,1]
[[[]],[[]],[],[]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,2,1,1]
[[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2]
[[[]],[[],[]],[]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,2,1,1]
[[[]],[[[]]],[]]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,2,1]
[[[]],[[],[],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,2,1,1]
[[[]],[[],[[]]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[3,2,1]
[[[]],[[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[3,2,1]
[[[]],[[[],[]]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[3,2,1]
[[[]],[[[[]]]]]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2]
[[[],[]],[],[],[]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,1,1,1,1]
[[[[]]],[],[],[]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,1,1,1]
[[[],[]],[],[[]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,2,1,1]
[[[[]]],[],[[]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1]
[[[],[]],[[]],[]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,2,1,1]
[[[[]]],[[]],[]]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1]
[[[],[]],[[],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,2,1,1]
[[[],[]],[[[]]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,2,1]
[[[[]]],[[],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1]
[[[[]]],[[[]]]]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3]
[[[],[],[]],[],[]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,1,1,1,1]
[[[],[[]]],[],[]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,1,1,1]
[[[[]],[]],[],[]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,1,1]
[[[[],[]]],[],[]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[3,1,1,1]
[[[[[]]]],[],[]]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,1,1]
[[[],[],[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,2,1,1]
[[[],[[]]],[[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,2,1]
[[[[]],[]],[[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,2,1]
[[[[],[]]],[[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,2,1]
[[[[[]]]],[[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,2]
[[[],[],[],[]],[]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,1,1,1,1]
[[[],[],[[]]],[]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[3,1,1,1]
[[[],[[]],[]],[]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,1,1,1]
[[[],[[],[]]],[]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[3,1,1,1]
[[[],[[[]]]],[]]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,1,1]
[[[[]],[],[]],[]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,1,1]
[[[[]],[[]]],[]]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,2,1]
[[[[],[]],[]],[]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[3,1,1,1]
[[[[[]]],[]],[]]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,1]
[[[[],[],[]]],[]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[3,1,1,1]
[[[[],[[]]]],[]]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,1,1]
[[[[[]],[]]],[]]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[4,1,1]
[[[[[],[]]]],[]]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[4,1,1]
[[[[[[]]]]],[]]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,1]
[[[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,1,1,1,1]
[[[],[],[],[[]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[3,1,1,1]
[[[],[],[[]],[]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[3,1,1,1]
[[[],[],[[],[]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[3,1,1,1]
[[[],[],[[[]]]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[4,1,1]
[[[],[[]],[],[]]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,1,1,1]
[[[],[[]],[[]]]]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,2,1]
[[[],[[],[]],[]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[3,1,1,1]
[[[],[[[]]],[]]]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,1,1]
[[[],[[],[],[]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[3,1,1,1]
[[[],[[],[[]]]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[4,1,1]
[[[],[[[]],[]]]]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[4,1,1]
[[[],[[[],[]]]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[4,1,1]
[[[],[[[[]]]]]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1]
[[[[]],[],[],[]]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,1,1]
[[[[]],[],[[]]]]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,2,1]
[[[[]],[[]],[]]]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[3,2,1]
[[[[]],[[],[]]]]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[3,2,1]
[[[[]],[[[]]]]]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[4,2]
[[[[],[]],[],[]]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[3,1,1,1]
[[[[[]]],[],[]]]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,1]
[[[[],[]],[[]]]]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,2,1]
[[[[[]]],[[]]]]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[4,2]
[[[[],[],[]],[]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[3,1,1,1]
[[[[],[[]]],[]]]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,1,1]
[[[[[]],[]],[]]]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[4,1,1]
[[[[[],[]]],[]]]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[4,1,1]
[[[[[[]]]],[]]]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1]
[[[[],[],[],[]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[3,1,1,1]
[[[[],[],[[]]]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,1]
[[[[],[[]],[]]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,1,1]
[[[[],[[],[]]]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,1,1]
[[[[],[[[]]]]]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[5,1]
[[[[[]],[],[]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,1,1]
[[[[[]],[[]]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,2]
[[[[[],[]],[]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,1,1]
[[[[[[]]],[]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[5,1]
[[[[[],[],[]]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[4,1,1]
[[[[[],[[]]]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[5,1]
[[[[[[]],[]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[5,1]
[[[[[[],[]]]]]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[5,1]
[[[[[[[]]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6]
[[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[]],[],[]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[[]],[[]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[[],[],[],[[],[]],[]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[[[]]],[]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[],[],[]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,1,1,1,1,1]
[[],[],[],[[],[[]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[[]],[]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[[],[]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[3,1,1,1,1]
[[],[],[],[[[[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[],[],[[]],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,1,1,1,1,1]
[[],[],[[]],[],[[]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,2,1,1,1]
[[],[],[[]],[[]],[]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,2,1,1,1]
[[],[],[[]],[[],[]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,2,1,1,1]
[[],[],[[]],[[[]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1]
[[],[],[[],[]],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,1,1,1,1,1]
[[],[],[[[]]],[],[]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[3,1,1,1,1]
[[],[],[[],[]],[[]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,2,1,1,1]
[[],[],[[[]]],[[]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[3,2,1,1]
[[],[],[[],[],[]],[]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,1,1,1,1,1]
[[],[],[[],[[]]],[]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[3,1,1,1,1]
[[],[],[[[]],[]],[]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[3,1,1,1,1]
[[],[],[[[],[]]],[]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[3,1,1,1,1]
[[],[],[[[[]]]],[]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[4,1,1,1]
[[],[],[[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,1,1,1,1,1]
[[],[],[[],[],[[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[3,1,1,1,1]
[[],[],[[],[[]],[]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[3,1,1,1,1]
[[],[],[[],[[],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[3,1,1,1,1]
[[],[],[[],[[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,1,1,1]
[[],[],[[[]],[],[]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[3,1,1,1,1]
[[],[],[[[]],[[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[3,2,1,1]
[[],[],[[[],[]],[]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[3,1,1,1,1]
[[],[],[[[[]]],[]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[4,1,1,1]
[[],[],[[[],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[3,1,1,1,1]
[[],[],[[[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,1,1,1]
[[],[],[[[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[4,1,1,1]
[[],[],[[[[],[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,1,1,1]
[[],[],[[[[[]]]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[],[[]],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[2,1,1,1,1,1]
[[],[[]],[],[],[[]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,2,1,1,1]
[[],[[]],[],[[]],[]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[2,2,1,1,1]
[[],[[]],[],[[],[]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[2,2,1,1,1]
[[],[[]],[],[[[]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,2,1,1]
[[],[[]],[[]],[],[]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[2,2,1,1,1]
[[],[[]],[[]],[[]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1]
[[],[[]],[[],[]],[]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[2,2,1,1,1]
[[],[[]],[[[]]],[]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,2,1,1]
[[],[[]],[[],[],[]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[2,2,1,1,1]
[[],[[]],[[],[[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,2,1,1]
[[],[[]],[[[]],[]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,2,1,1]
[[],[[]],[[[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,2,1,1]
[[],[[]],[[[[]]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1]
[[],[[],[]],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[2,1,1,1,1,1]
[[],[[[]]],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[3,1,1,1,1]
[[],[[],[]],[],[[]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[2,2,1,1,1]
[[],[[[]]],[],[[]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[3,2,1,1]
[[],[[],[]],[[]],[]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[2,2,1,1,1]
[[],[[[]]],[[]],[]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[3,2,1,1]
[[],[[],[]],[[],[]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[2,2,1,1,1]
[[],[[],[]],[[[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[3,2,1,1]
[[],[[[]]],[[],[]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[3,2,1,1]
[[],[[[]]],[[[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1]
[[],[[],[],[]],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[2,1,1,1,1,1]
[[],[[],[[]]],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[3,1,1,1,1]
[[],[[[]],[]],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[3,1,1,1,1]
[[],[[[],[]]],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[3,1,1,1,1]
[[],[[[[]]]],[],[]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[4,1,1,1]
[[],[[],[],[]],[[]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[2,2,1,1,1]
[[],[[],[[]]],[[]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[3,2,1,1]
[[],[[[]],[]],[[]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[3,2,1,1]
[[],[[[],[]]],[[]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[3,2,1,1]
[[],[[[[]]]],[[]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[4,2,1]
[[],[[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[2,1,1,1,1,1]
[[],[[],[],[[]]],[]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[3,1,1,1,1]
[[],[[],[[]],[]],[]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[3,1,1,1,1]
[[],[[],[[],[]]],[]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[3,1,1,1,1]
[[],[[],[[[]]]],[]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[4,1,1,1]
[[],[[[]],[],[]],[]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[3,1,1,1,1]
[[],[[[]],[[]]],[]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[3,2,1,1]
[[],[[[],[]],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[3,1,1,1,1]
[[],[[[[]]],[]],[]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[4,1,1,1]
[[],[[[],[],[]]],[]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[3,1,1,1,1]
[[],[[[],[[]]]],[]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[4,1,1,1]
[[],[[[[]],[]]],[]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[4,1,1,1]
[[],[[[[],[]]]],[]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[4,1,1,1]
[[],[[[[[]]]]],[]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[5,1,1]
[[],[[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[2,1,1,1,1,1]
[[],[[],[],[],[[]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[3,1,1,1,1]
[[],[[],[],[[]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[3,1,1,1,1]
[[],[[],[],[[],[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[3,1,1,1,1]
[[],[[],[],[[[]]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,1,1,1]
[[],[[],[[]],[],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[3,1,1,1,1]
[[],[[],[[]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[3,2,1,1]
[[],[[],[[],[]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[3,1,1,1,1]
[[],[[],[[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[4,1,1,1]
[[],[[],[[],[],[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[3,1,1,1,1]
[[],[[],[[],[[]]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,1,1,1]
[[],[[],[[[]],[]]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[4,1,1,1]
[[],[[],[[[],[]]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,1,1,1]
[[],[[],[[[[]]]]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[5,1,1]
[[],[[[]],[],[],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[3,1,1,1,1]
[[],[[[]],[],[[]]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[3,2,1,1]
[[],[[[]],[[]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[3,2,1,1]
[[],[[[]],[[],[]]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[3,2,1,1]
[[],[[[]],[[[]]]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,2,1]
[[],[[[],[]],[],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[3,1,1,1,1]
[[],[[[[]]],[],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[4,1,1,1]
[[],[[[],[]],[[]]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[3,2,1,1]
[[],[[[[]]],[[]]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[4,2,1]
[[],[[[],[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[3,1,1,1,1]
[[],[[[],[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[4,1,1,1]
[[],[[[[]],[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[4,1,1,1]
[[],[[[[],[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[4,1,1,1]
[[],[[[[[]]]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[5,1,1]
[[],[[[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[3,1,1,1,1]
[[],[[[],[],[[]]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,1,1,1]
[[],[[[],[[]],[]]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[4,1,1,1]
[[],[[[],[[],[]]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,1,1,1]
[[],[[[],[[[]]]]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[5,1,1]
[[],[[[[]],[],[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[4,1,1,1]
[[],[[[[]],[[]]]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,2,1]
[[],[[[[],[]],[]]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[4,1,1,1]
[[],[[[[[]]],[]]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[5,1,1]
[[],[[[[],[],[]]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,1,1,1]
[[],[[[[],[[]]]]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[5,1,1]
[[],[[[[[]],[]]]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[5,1,1]
[[],[[[[[],[]]]]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[5,1,1]
[[],[[[[[[]]]]]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]
[[[]],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,1,1,1,1]
[[[]],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,2,1,1,1]
[[[]],[],[],[[]],[]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,2,1,1,1]
[[[]],[],[],[[],[]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,2,1,1,1]
[[[]],[],[],[[[]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,2,1,1]
[[[]],[],[[]],[],[]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,2,1,1,1]
[[[]],[],[[]],[[]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,2,1]
[[[]],[],[[],[]],[]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,2,1,1,1]
[[[]],[],[[[]]],[]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,2,1,1]
[[[]],[],[[],[],[]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,2,1,1,1]
[[[]],[],[[],[[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,2,1,1]
[[[]],[],[[[]],[]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,2,1,1]
[[[]],[],[[[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,2,1,1]
[[[]],[],[[[[]]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,2,1]
[[[]],[[]],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,2,1,1,1]
[[[]],[[]],[],[[]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,2,2,1]
[[[]],[[]],[[]],[]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,2,2,1]
[[[]],[[]],[[],[]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,2,2,1]
[[[]],[[]],[[[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2]
[[[]],[[],[]],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,2,1,1,1]
[[[]],[[[]]],[],[]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[3,2,1,1]
[[[]],[[],[]],[[]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,2,2,1]
[[[]],[[[]]],[[]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[3,2,2]
[[[]],[[],[],[]],[]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,2,1,1,1]
[[[]],[[],[[]]],[]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[3,2,1,1]
[[[]],[[[]],[]],[]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[3,2,1,1]
[[[]],[[[],[]]],[]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[3,2,1,1]
[[[]],[[[[]]]],[]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[4,2,1]
[[[]],[[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,2,1,1,1]
[[[]],[[],[],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[3,2,1,1]
[[[]],[[],[[]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[3,2,1,1]
[[[]],[[],[[],[]]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[3,2,1,1]
[[[]],[[],[[[]]]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,2,1]
[[[]],[[[]],[],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[3,2,1,1]
[[[]],[[[]],[[]]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[3,2,2]
[[[]],[[[],[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[3,2,1,1]
[[[]],[[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[4,2,1]
[[[]],[[[],[],[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[3,2,1,1]
[[[]],[[[],[[]]]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,2,1]
[[[]],[[[[]],[]]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[4,2,1]
[[[]],[[[[],[]]]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,2,1]
[[[]],[[[[[]]]]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2]
[[[],[]],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,1,1,1,1,1]
[[[[]]],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,1,1,1,1]
[[[],[]],[],[],[[]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,2,1,1,1]
[[[[]]],[],[],[[]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,1]
[[[],[]],[],[[]],[]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,2,1,1,1]
[[[[]]],[],[[]],[]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,1]
[[[],[]],[],[[],[]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,2,1,1,1]
[[[],[]],[],[[[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,2,1,1]
[[[[]]],[],[[],[]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,1]
[[[[]]],[],[[[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,3,1]
[[[],[]],[[]],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,2,1,1,1]
[[[[]]],[[]],[],[]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,1]
[[[],[]],[[]],[[]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,2,2,1]
[[[[]]],[[]],[[]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,2]
[[[],[]],[[],[]],[]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,2,1,1,1]
[[[],[]],[[[]]],[]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,2,1,1]
[[[[]]],[[],[]],[]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,1]
[[[[]]],[[[]]],[]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,3,1]
[[[],[]],[[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,2,1,1,1]
[[[],[]],[[],[[]]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,2,1,1]
[[[],[]],[[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,2,1,1]
[[[],[]],[[[],[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,2,1,1]
[[[],[]],[[[[]]]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,2,1]
[[[[]]],[[],[],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,1]
[[[[]]],[[],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,3,1]
[[[[]]],[[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,3,1]
[[[[]]],[[[],[]]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,3,1]
[[[[]]],[[[[]]]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3]
[[[],[],[]],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,1,1,1,1,1]
[[[],[[]]],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,1,1,1,1]
[[[[]],[]],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,1,1,1]
[[[[],[]]],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[3,1,1,1,1]
[[[[[]]]],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,1,1,1]
[[[],[],[]],[],[[]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,2,1,1,1]
[[[],[[]]],[],[[]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,2,1,1]
[[[[]],[]],[],[[]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,2,1,1]
[[[[],[]]],[],[[]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[3,2,1,1]
[[[[[]]]],[],[[]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,2,1]
[[[],[],[]],[[]],[]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,2,1,1,1]
[[[],[[]]],[[]],[]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,2,1,1]
[[[[]],[]],[[]],[]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,2,1,1]
[[[[],[]]],[[]],[]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[3,2,1,1]
[[[[[]]]],[[]],[]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,2,1]
[[[],[],[]],[[],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,2,1,1,1]
[[[],[],[]],[[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[3,2,1,1]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,2,1,1]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,3,1]
[[[[]],[]],[[],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,2,1,1]
[[[[]],[]],[[[]]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,3,1]
[[[[],[]]],[[],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[3,2,1,1]
[[[[],[]]],[[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,3,1]
[[[[[]]]],[[],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,2,1]
[[[[[]]]],[[[]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3]
[[[],[],[],[]],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,1,1,1,1,1]
[[[],[],[[]]],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[3,1,1,1,1]
[[[],[[]],[]],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,1,1,1,1]
[[[],[[],[]]],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[3,1,1,1,1]
[[[],[[[]]]],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,1,1,1]
[[[[]],[],[]],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,1,1,1]
[[[[]],[[]]],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[3,2,1,1]
[[[[],[]],[]],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[3,1,1,1,1]
[[[[[]]],[]],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,1,1]
[[[[],[],[]]],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[3,1,1,1,1]
[[[[],[[]]]],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,1,1,1]
[[[[[]],[]]],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[4,1,1,1]
[[[[[],[]]]],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,1,1,1]
[[[[[[]]]]],[],[]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,1,1]
[[[],[],[],[]],[[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,2,1,1,1]
[[[],[],[[]]],[[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[3,2,1,1]
[[[],[[]],[]],[[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,2,1,1]
[[[],[[],[]]],[[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[3,2,1,1]
[[[],[[[]]]],[[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,2,1]
[[[[]],[],[]],[[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,2,1,1]
[[[[]],[[]]],[[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[3,2,2]
[[[[],[]],[]],[[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[3,2,1,1]
[[[[[]]],[]],[[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,2,1]
[[[[],[],[]]],[[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[3,2,1,1]
[[[[],[[]]]],[[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[4,2,1]
[[[[[]],[]]],[[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[4,2,1]
[[[[[],[]]]],[[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,2,1]
[[[[[[]]]]],[[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,2]
[[[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,1,1,1,1,1]
[[[],[],[],[[]]],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[3,1,1,1,1]
[[[],[],[[]],[]],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[3,1,1,1,1]
[[[],[],[[],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[3,1,1,1,1]
[[[],[],[[[]]]],[]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[4,1,1,1]
[[[],[[]],[],[]],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,1,1,1,1]
[[[],[[]],[[]]],[]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,2,1,1]
[[[],[[],[]],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[3,1,1,1,1]
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,1,1,1]
[[[],[[],[],[]]],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[3,1,1,1,1]
[[[],[[],[[]]]],[]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[4,1,1,1]
[[[],[[[]],[]]],[]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[4,1,1,1]
[[[],[[[],[]]]],[]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[4,1,1,1]
[[[],[[[[]]]]],[]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,1,1]
[[[[]],[],[],[]],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,1,1,1]
[[[[]],[],[[]]],[]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,2,1,1]
[[[[]],[[]],[]],[]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[3,2,1,1]
[[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[3,2,1,1]
[[[[]],[[[]]]],[]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[4,2,1]
[[[[],[]],[],[]],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[3,1,1,1,1]
[[[[[]]],[],[]],[]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,1,1]
[[[[],[]],[[]]],[]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[3,2,1,1]
[[[[[]]],[[]]],[]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,2,1]
[[[[],[],[]],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[3,1,1,1,1]
[[[[],[[]]],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[4,1,1,1]
[[[[[]],[]],[]],[]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[4,1,1,1]
[[[[[],[]]],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,1,1,1]
[[[[[[]]]],[]],[]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,1]
[[[[],[],[],[]]],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[3,1,1,1,1]
[[[[],[],[[]]]],[]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[4,1,1,1]
[[[[],[[]],[]]],[]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[4,1,1,1]
[[[[],[[],[]]]],[]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,1,1,1]
[[[[],[[[]]]]],[]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,1,1]
[[[[[]],[],[]]],[]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,1,1,1]
[[[[[]],[[]]]],[]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,2,1]
[[[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,1,1,1]
[[[[[[]]],[]]],[]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[5,1,1]
[[[[[],[],[]]]],[]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,1,1,1]
[[[[[],[[]]]]],[]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[5,1,1]
[[[[[[]],[]]]],[]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[5,1,1]
[[[[[[],[]]]]],[]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[5,1,1]
[[[[[[[]]]]]],[]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,1]
[[[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,1,1,1,1,1]
[[[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[3,1,1,1,1]
[[[],[],[],[[]],[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[3,1,1,1,1]
[[[],[],[],[[],[]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[3,1,1,1,1]
[[[],[],[],[[[]]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,1,1,1]
[[[],[],[[]],[],[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[3,1,1,1,1]
[[[],[],[[]],[[]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[3,2,1,1]
[[[],[],[[],[]],[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[3,1,1,1,1]
[[[],[],[[[]]],[]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[4,1,1,1]
[[[],[],[[],[],[]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[3,1,1,1,1]
[[[],[],[[],[[]]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,1,1,1]
[[[],[],[[[]],[]]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[4,1,1,1]
[[[],[],[[[],[]]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,1,1,1]
[[[],[],[[[[]]]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[5,1,1]
[[[],[[]],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,1,1,1,1]
[[[],[[]],[],[[]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,2,1,1]
[[[],[[]],[[]],[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,2,1,1]
[[[],[[]],[[],[]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,2,1,1]
[[[],[[]],[[[]]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,2,1]
[[[],[[],[]],[],[]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[3,1,1,1,1]
[[[],[[[]]],[],[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,1,1,1]
[[[],[[],[]],[[]]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[3,2,1,1]
[[[],[[[]]],[[]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,2,1]
[[[],[[],[],[]],[]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[3,1,1,1,1]
[[[],[[],[[]]],[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[4,1,1,1]
[[[],[[[]],[]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[4,1,1,1]
[[[],[[[],[]]],[]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[4,1,1,1]
[[[],[[[[]]]],[]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,1,1]
[[[],[[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[3,1,1,1,1]
[[[],[[],[],[[]]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,1,1,1]
[[[],[[],[[]],[]]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[4,1,1,1]
[[[],[[],[[],[]]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,1,1,1]
[[[],[[],[[[]]]]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[5,1,1]
[[[],[[[]],[],[]]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[4,1,1,1]
[[[],[[[]],[[]]]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,2,1]
[[[],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[4,1,1,1]
[[[],[[[[]]],[]]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[5,1,1]
[[[],[[[],[],[]]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,1,1,1]
[[[],[[[],[[]]]]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[5,1,1]
[[[],[[[[]],[]]]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[5,1,1]
[[[],[[[[],[]]]]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[5,1,1]
[[[],[[[[[]]]]]]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1]
[[[[]],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,1,1,1]
[[[[]],[],[],[[]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,2,1,1]
[[[[]],[],[[]],[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,2,1,1]
[[[[]],[],[[],[]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,2,1,1]
[[[[]],[],[[[]]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,2,1]
[[[[]],[[]],[],[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[3,2,1,1]
[[[[]],[[]],[[]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[3,2,2]
[[[[]],[[],[]],[]]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[3,2,1,1]
[[[[]],[[[]]],[]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[4,2,1]
[[[[]],[[],[],[]]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[3,2,1,1]
[[[[]],[[],[[]]]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,2,1]
[[[[]],[[[]],[]]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[4,2,1]
[[[[]],[[[],[]]]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,2,1]
[[[[]],[[[[]]]]]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,2]
[[[[],[]],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[3,1,1,1,1]
[[[[[]]],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,1,1]
[[[[],[]],[],[[]]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,2,1,1]
[[[[[]]],[],[[]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,2,1]
[[[[],[]],[[]],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[3,2,1,1]
[[[[[]]],[[]],[]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[4,2,1]
[[[[],[]],[[],[]]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,2,1,1]
[[[[],[]],[[[]]]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,2,1]
[[[[[]]],[[],[]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[4,2,1]
[[[[[]]],[[[]]]]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,3]
[[[[],[],[]],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[3,1,1,1,1]
[[[[],[[]]],[],[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[4,1,1,1]
[[[[[]],[]],[],[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[4,1,1,1]
[[[[[],[]]],[],[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,1,1,1]
[[[[[[]]]],[],[]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,1]
[[[[],[],[]],[[]]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[3,2,1,1]
[[[[],[[]]],[[]]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[4,2,1]
[[[[[]],[]],[[]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[4,2,1]
[[[[[],[]]],[[]]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,2,1]
[[[[[[]]]],[[]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[5,2]
[[[[],[],[],[]],[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[3,1,1,1,1]
[[[[],[],[[]]],[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[4,1,1,1]
[[[[],[[]],[]],[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[4,1,1,1]
[[[[],[[],[]]],[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,1,1,1]
[[[[],[[[]]]],[]]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,1,1]
[[[[[]],[],[]],[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[4,1,1,1]
[[[[[]],[[]]],[]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,2,1]
[[[[[],[]],[]],[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,1,1,1]
[[[[[[]]],[]],[]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[5,1,1]
[[[[[],[],[]]],[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,1,1,1]
[[[[[],[[]]]],[]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[5,1,1]
[[[[[[]],[]]],[]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[5,1,1]
[[[[[[],[]]]],[]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[5,1,1]
[[[[[[[]]]]],[]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1]
[[[[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[3,1,1,1,1]
[[[[],[],[],[[]]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,1,1,1]
[[[[],[],[[]],[]]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[4,1,1,1]
[[[[],[],[[],[]]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,1,1,1]
[[[[],[],[[[]]]]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,1]
[[[[],[[]],[],[]]]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[4,1,1,1]
[[[[],[[]],[[]]]]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,2,1]
[[[[],[[],[]],[]]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,1,1,1]
[[[[],[[[]]],[]]]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,1,1]
[[[[],[[],[],[]]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,1,1,1]
[[[[],[[],[[]]]]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,1,1]
[[[[],[[[]],[]]]]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,1,1]
[[[[],[[[],[]]]]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,1,1]
[[[[],[[[[]]]]]]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,1]
[[[[[]],[],[],[]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[4,1,1,1]
[[[[[]],[],[[]]]]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,2,1]
[[[[[]],[[]],[]]]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,2,1]
[[[[[]],[[],[]]]]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,2,1]
[[[[[]],[[[]]]]]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,2]
[[[[[],[]],[],[]]]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,1,1,1]
[[[[[[]]],[],[]]]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[5,1,1]
[[[[[],[]],[[]]]]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,2,1]
[[[[[[]]],[[]]]]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,2]
[[[[[],[],[]],[]]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,1,1,1]
[[[[[],[[]]],[]]]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,1,1]
[[[[[[]],[]],[]]]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[5,1,1]
[[[[[[],[]]],[]]]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[5,1,1]
[[[[[[[]]]],[]]]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[6,1]
[[[[[],[],[],[]]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,1,1]
[[[[[],[],[[]]]]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,1,1]
[[[[[],[[]],[]]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[5,1,1]
[[[[[],[[],[]]]]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,1,1]
[[[[[],[[[]]]]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[6,1]
[[[[[[]],[],[]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[5,1,1]
[[[[[[]],[[]]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[5,2]
[[[[[[],[]],[]]]]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[5,1,1]
[[[[[[[]]],[]]]]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[6,1]
[[[[[[],[],[]]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[5,1,1]
[[[[[[],[[]]]]]]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[6,1]
[[[[[[[]],[]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[6,1]
[[[[[[[],[]]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[6,1]
[[[[[[[[]]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[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]=>[2,1,1,1,1,1,1]
[[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[]],[],[]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[],[[]],[[]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]
[[],[],[],[],[[],[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[],[[[]]],[]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[],[],[]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[],[[],[[]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[[],[]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[],[[[[]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[[[]],[]],[]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[],[],[],[]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,1,1,1,1,1,1]
[[],[],[],[[],[],[[]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[],[[]],[]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[],[[],[]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[],[[[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[[]],[],[]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[[]],[[]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[3,2,1,1,1]
[[],[],[],[[[],[]],[]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[[[]]],[]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[[],[],[]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[3,1,1,1,1,1]
[[],[],[],[[[],[[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[[[]],[]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[[[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[4,1,1,1,1]
[[],[],[],[[[[[]]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[2,1,1,1,1,1,1]
[[],[],[[]],[],[],[[]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,2,1,1,1,1]
[[],[],[[]],[],[[],[]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[2,2,1,1,1,1]
[[],[],[[]],[[]],[],[]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[2,2,1,1,1,1]
[[],[],[[]],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]
[[],[],[[]],[[[]]],[]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[3,2,1,1,1]
[[],[],[[]],[[],[],[]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[2,2,1,1,1,1]
[[],[],[[]],[[[[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[2,1,1,1,1,1,1]
[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[3,1,1,1,1,1]
[[],[],[[],[]],[],[[]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[2,2,1,1,1,1]
[[],[],[[[]]],[],[[]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[3,2,1,1,1]
[[],[],[[[]]],[[]],[]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[3,2,1,1,1]
[[],[],[[],[]],[[[]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[3,2,1,1,1]
[[],[],[[[]]],[[],[]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[3,2,1,1,1]
[[],[],[[[]]],[[[]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]
[[],[],[[],[],[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[2,1,1,1,1,1,1]
[[],[],[[[],[]]],[],[]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[3,1,1,1,1,1]
[[],[],[[[[]]]],[],[]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[4,1,1,1,1]
[[],[],[[],[],[]],[[]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[2,2,1,1,1,1]
[[],[],[[[]],[]],[[]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[3,2,1,1,1]
[[],[],[[],[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1]
[[],[],[[],[],[[]],[]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[3,1,1,1,1,1]
[[],[],[[],[[[]]],[]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[4,1,1,1,1]
[[],[],[[],[[[]],[]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[4,1,1,1,1]
[[],[],[[],[[[],[]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[4,1,1,1,1]
[[],[],[[],[[[[]]]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[5,1,1,1]
[[],[],[[[],[],[]],[]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[3,1,1,1,1,1]
[[],[],[[[[]],[]],[]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[4,1,1,1,1]
[[],[],[[[],[],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[3,1,1,1,1,1]
[[],[[]],[],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[2,1,1,1,1,1,1]
[[],[[]],[],[],[[]],[]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[2,2,1,1,1,1]
[[],[[]],[],[[[]]],[]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[3,2,1,1,1]
[[],[[]],[],[[[]],[]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[3,2,1,1,1]
[[],[[]],[],[[[[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,2,1,1]
[[],[[]],[[]],[[]],[]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[2,2,2,1,1]
[[],[[]],[[]],[[],[]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[2,2,2,1,1]
[[],[[]],[[[]]],[],[]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[3,2,1,1,1]
[[],[[]],[[],[[]]],[]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,2,1,1,1]
[[],[[]],[[[]],[]],[]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[3,2,1,1,1]
[[],[[]],[[],[[]],[]]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,2,1,1,1]
[[],[[]],[[],[[],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,2,1,1,1]
[[],[[],[]],[],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[2,1,1,1,1,1,1]
[[],[[[]]],[],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[3,1,1,1,1,1]
[[],[[[]]],[],[[]],[]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[3,2,1,1,1]
[[],[[],[]],[],[[[]]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[3,2,1,1,1]
[[],[[[]]],[],[[[]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[3,3,1,1]
[[],[[[]]],[[]],[],[]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[3,2,1,1,1]
[[],[[[]]],[[]],[[]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[3,2,2,1]
[[],[[],[]],[[],[]],[]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[2,2,1,1,1,1]
[[],[[],[]],[[[]]],[]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[3,2,1,1,1]
[[],[[[]]],[[],[]],[]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[3,2,1,1,1]
[[],[[[]]],[[[]]],[]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[3,3,1,1]
[[],[[],[]],[[[[]]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,2,1,1]
[[],[[[]]],[[],[[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[3,3,1,1]
[[],[[[]]],[[[],[]]]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[3,3,1,1]
[[],[[[]]],[[[[]]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,3,1]
[[],[[],[[]]],[],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[3,1,1,1,1,1]
[[],[[[[]]]],[],[],[]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[4,1,1,1,1]
[[],[[[[]]]],[],[[]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[4,2,1,1]
[[],[[],[[]]],[[]],[]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[3,2,1,1,1]
[[],[[[],[]]],[[]],[]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[3,2,1,1,1]
[[],[[[[]]]],[[]],[]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[4,2,1,1]
[[],[[],[[]]],[[],[]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[3,2,1,1,1]
[[],[[[]],[]],[[[]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[3,3,1,1]
[[],[[[],[]]],[[[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[3,3,1,1]
[[],[[[[]]]],[[],[]]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[4,2,1,1]
[[],[[[[]]]],[[[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[4,3,1]
[[],[[],[[]],[]],[],[]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[3,1,1,1,1,1]
[[],[[[],[]],[]],[],[]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[3,1,1,1,1,1]
[[],[[],[[]],[]],[[]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[3,2,1,1,1]
[[],[[[],[],[]]],[[]]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[3,2,1,1,1]
[[],[[[],[[]]]],[[]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[4,2,1,1]
[[],[[[[],[]]]],[[]]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[4,2,1,1]
[[],[[],[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[2,1,1,1,1,1,1]
[[],[[],[[]],[[]]],[]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[3,2,1,1,1]
[[],[[],[[],[]],[]],[]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[3,1,1,1,1,1]
[[],[[],[[],[[]]]],[]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[4,1,1,1,1]
[[],[[[[]],[]],[]],[]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[4,1,1,1,1]
[[],[[[],[[]],[]]],[]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[4,1,1,1,1]
[[],[[[[]],[],[]]],[]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[4,1,1,1,1]
[[],[[],[],[[[]]],[]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[4,1,1,1,1]
[[],[[],[],[[[[]]]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[5,1,1,1]
[[],[[],[[]],[[]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[3,2,1,1,1]
[[],[[],[[]],[[],[]]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[3,2,1,1,1]
[[],[[],[[],[[]]],[]]]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[4,1,1,1,1]
[[],[[],[[],[],[],[]]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[3,1,1,1,1,1]
[[],[[],[[],[[]],[]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[4,1,1,1,1]
[[],[[],[[],[[],[]]]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[4,1,1,1,1]
[[],[[],[[],[[[]]]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[5,1,1,1]
[[],[[],[[[]],[],[]]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[4,1,1,1,1]
[[],[[],[[[]],[[]]]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[4,2,1,1]
[[],[[[]],[],[],[[]]]]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[3,2,1,1,1]
[[],[[[]],[],[[]],[]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[3,2,1,1,1]
[[],[[[]],[],[[],[]]]]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[3,2,1,1,1]
[[],[[[]],[],[[[]]]]]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[4,2,1,1]
[[],[[[]],[[]],[[]]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[3,2,2,1]
[[],[[[]],[[[]]],[]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[4,2,1,1]
[[],[[[]],[[],[],[]]]]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[3,2,1,1,1]
[[],[[[]],[[],[[]]]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[4,2,1,1]
[[],[[[]],[[[],[]]]]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[4,2,1,1]
[[],[[[[]]],[],[],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[4,1,1,1,1]
[[],[[[],[]],[],[[]]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[3,2,1,1,1]
[[],[[[],[]],[[],[]]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[3,2,1,1,1]
[[],[[[[]]],[[[]]]]]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[4,3,1]
[[],[[[[]],[]],[],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[4,1,1,1,1]
[[],[[[],[],[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[3,2,1,1,1]
[[],[[[[[]]],[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[5,1,1,1]
[[],[[[],[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[3,1,1,1,1,1]
[[],[[[],[[],[],[]]]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[4,1,1,1,1]
[[],[[[[]],[[]],[]]]]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[4,2,1,1]
[[],[[[[],[],[],[]]]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[4,1,1,1,1]
[[],[[[[],[[],[]]]]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[5,1,1,1]
[[],[[[[[]],[],[]]]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[5,1,1,1]
[[],[[[[[]],[[]]]]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[5,2,1]
[[],[[[[[[]]],[]]]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[6,1,1]
[[],[[[[[],[[]]]]]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[6,1,1]
[[],[[[[[[],[]]]]]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[6,1,1]
[[],[[[[[[[]]]]]]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[[]],[],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1]
[[[]],[],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,2,1,1,1,1]
[[[]],[],[],[[]],[],[]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,2,1,1,1,1]
[[[]],[],[],[[]],[[]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,2,2,1,1]
[[[]],[],[],[[],[[]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,2,1,1,1]
[[[]],[],[],[[[]],[]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[3,2,1,1,1]
[[[]],[],[],[[[[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[4,2,1,1]
[[[]],[],[[]],[],[[]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,2,2,1,1]
[[[]],[],[[]],[[]],[]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[2,2,2,1,1]
[[[]],[],[[],[]],[],[]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,2,1,1,1,1]
[[[]],[],[[],[[]]],[]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[3,2,1,1,1]
[[[]],[],[[],[[],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[3,2,1,1,1]
[[[]],[],[[[]],[],[]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[3,2,1,1,1]
[[[]],[],[[[]],[[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[3,2,2,1]
[[[]],[],[[[],[[]]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[4,2,1,1]
[[[]],[],[[[[[]]]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[5,2,1]
[[[]],[[]],[],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,2,1,1,1,1]
[[[]],[[]],[],[],[[]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,2,2,1,1]
[[[]],[[]],[],[[[]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[3,2,2,1]
[[[]],[[]],[[]],[],[]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,2,2,1,1]
[[[]],[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[[[]],[[]],[[[]]],[]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[3,2,2,1]
[[[]],[[]],[[[]],[]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[3,2,2,1]
[[[]],[[]],[[[[]]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[[[]],[[[]]],[],[],[]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[3,2,1,1,1]
[[[]],[[],[[]]],[],[]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[3,2,1,1,1]
[[[]],[[[],[]]],[],[]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[3,2,1,1,1]
[[[]],[[],[],[]],[[]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,2,2,1,1]
[[[]],[[[],[]]],[[]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[3,2,2,1]
[[[]],[[[],[],[]]],[]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[3,2,1,1,1]
[[[]],[[[[]],[]]],[]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[4,2,1,1]
[[[]],[[[[],[]]]],[]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[4,2,1,1]
[[[]],[[],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,2,1,1,1,1]
[[[]],[[[[]]],[],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[4,2,1,1]
[[[]],[[[],[],[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[3,2,1,1,1]
[[[]],[[[[]],[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[4,2,1,1]
[[[]],[[[],[],[],[]]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[3,2,1,1,1]
[[[]],[[[],[[],[]]]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[4,2,1,1]
[[[]],[[[[]],[[]]]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[4,2,2]
[[[]],[[[[[]]],[]]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[5,2,1]
[[[]],[[[[],[[]]]]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[5,2,1]
[[[]],[[[[[],[]]]]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[5,2,1]
[[[]],[[[[[[]]]]]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,2]
[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,1,1,1,1,1,1]
[[[[]]],[],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,1,1,1,1,1]
[[[],[]],[],[],[[],[]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,2,1,1,1,1]
[[[[]]],[],[],[[[]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,3,1,1]
[[[],[]],[],[[]],[],[]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,2,1,1,1,1]
[[[],[]],[],[[]],[[]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,2,2,1,1]
[[[[]]],[],[[]],[[]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[3,2,2,1]
[[[[]]],[],[[[]]],[]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,3,1,1]
[[[],[]],[],[[[]],[]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,2,1,1,1]
[[[],[]],[],[[[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,2,1,1,1]
[[[],[]],[],[[[[]]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,2,1,1]
[[[[]]],[],[[[]],[]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,3,1,1]
[[[[]]],[],[[[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,3,1,1]
[[[[]]],[],[[[[]]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,3,1]
[[[],[]],[[]],[[],[]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,2,2,1,1]
[[[[]]],[[],[]],[],[]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,1,1]
[[[[]]],[[],[[]]],[]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,3,1,1]
[[[[]]],[[[]],[]],[]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,3,1,1]
[[[],[]],[[],[],[[]]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,2,1,1,1]
[[[],[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,2,1,1,1]
[[[[]]],[[[]],[[]]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,3,2]
[[[[]]],[[[],[],[]]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,3,1,1]
[[[[]]],[[[[],[]]]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[4,3,1]
[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,1,1,1,1,1,1]
[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,1,1,1,1,1]
[[[[]],[]],[],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,1,1,1,1]
[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[3,1,1,1,1,1]
[[[[[]]]],[],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,1,1,1,1]
[[[],[[]]],[],[],[[]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[3,2,1,1,1]
[[[[]],[]],[],[],[[]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[3,2,1,1,1]
[[[[[]]]],[],[],[[]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,2,1,1]
[[[],[[]]],[],[[]],[]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,2,1,1,1]
[[[[[]]]],[],[[]],[]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,2,1,1]
[[[],[],[]],[],[[[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[3,2,1,1,1]
[[[],[[]]],[],[[],[]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[3,2,1,1,1]
[[[[],[]]],[],[[],[]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[3,2,1,1,1]
[[[[],[]]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,3,1,1]
[[[[[]]]],[],[[],[]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,2,1,1]
[[[[[]]]],[],[[[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,1]
[[[[[]]]],[[]],[],[]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,2,1,1]
[[[],[],[]],[[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,2,2,1,1]
[[[],[[]]],[[]],[[]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[3,2,2,1]
[[[[[]]]],[[]],[[]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,2,2]
[[[],[],[]],[[[]]],[]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[3,2,1,1,1]
[[[[],[]]],[[],[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[3,2,1,1,1]
[[[[],[]]],[[[]]],[]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[3,3,1,1]
[[[[[]]]],[[],[]],[]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,2,1,1]
[[[[[]]]],[[[]]],[]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,1]
[[[],[],[]],[[],[],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,2,1,1,1,1]
[[[],[],[]],[[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[3,2,1,1,1]
[[[],[],[]],[[[[]]]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,2,1,1]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[3,2,1,1,1]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[3,3,1,1]
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,3,1]
[[[[]],[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,3,1,1]
[[[[]],[]],[[[],[]]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,3,1,1]
[[[[]],[]],[[[[]]]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,3,1]
[[[[],[]]],[[],[],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[3,2,1,1,1]
[[[[],[]]],[[],[[]]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,3,1,1]
[[[[],[]]],[[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[3,3,1,1]
[[[[],[]]],[[[],[]]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[3,3,1,1]
[[[[],[]]],[[[[]]]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1]
[[[[[]]]],[[],[],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,2,1,1]
[[[[[]]]],[[],[[]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,1]
[[[[[]]]],[[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,1]
[[[[[]]]],[[[],[]]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,1]
[[[[[]]]],[[[[]]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,4]
[[[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,1,1,1,1,1,1]
[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[3,1,1,1,1,1]
[[[],[[]],[]],[],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[3,1,1,1,1,1]
[[[],[[],[]]],[],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[3,1,1,1,1,1]
[[[],[[[]]]],[],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[4,1,1,1,1]
[[[[]],[],[]],[],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[3,1,1,1,1,1]
[[[[]],[[]]],[],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[3,2,1,1,1]
[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[3,1,1,1,1,1]
[[[[[]]],[]],[],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,1,1,1]
[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[3,1,1,1,1,1]
[[[[],[[]]]],[],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[4,1,1,1,1]
[[[[[]],[]]],[],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[4,1,1,1,1]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[4,1,1,1,1]
[[[[[[]]]]],[],[],[]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,1,1,1]
[[[],[],[],[]],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,2,1,1,1,1]
[[[],[],[[]]],[],[[]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[3,2,1,1,1]
[[[[],[]],[]],[],[[]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[3,2,1,1,1]
[[[[[]]],[]],[],[[]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,2,1,1]
[[[[[]],[]]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[4,2,1,1]
[[[[[[]]]]],[],[[]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,2,1]
[[[],[],[],[]],[[]],[]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[2,2,1,1,1,1]
[[[],[[],[]]],[[]],[]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[3,2,1,1,1]
[[[[],[]],[]],[[]],[]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[3,2,1,1,1]
[[[[[[]]]]],[[]],[]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,2,1]
[[[],[],[],[]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,2,1,1,1,1]
[[[],[],[],[]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[3,2,1,1,1]
[[[],[],[[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[3,3,1,1]
[[[],[[]],[]],[[[]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,3,1,1]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[3,3,1,1]
[[[],[[[]]]],[[[]]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[4,3,1]
[[[[]],[],[]],[[[]]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,3,1,1]
[[[[]],[[]]],[[[]]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[3,3,2]
[[[[],[]],[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,3,1,1]
[[[[[]]],[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[4,2,1,1]
[[[[[]]],[]],[[[]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,3,1]
[[[[],[],[]]],[[[]]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[3,3,1,1]
[[[[],[[]]]],[[[]]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[4,3,1]
[[[[[]],[]]],[[[]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[4,3,1]
[[[[[],[]]]],[[[]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[4,3,1]
[[[[[[]]]]],[[],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,2,1]
[[[[[[]]]]],[[[]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,3]
[[[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[2,1,1,1,1,1,1]
[[[],[],[[]],[]],[],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[3,1,1,1,1,1]
[[[],[[]],[[]]],[],[]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,2,1,1,1]
[[[],[[],[]],[]],[],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[3,1,1,1,1,1]
[[[],[[],[],[]]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[3,1,1,1,1,1]
[[[[]],[],[],[]],[],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[3,1,1,1,1,1]
[[[[]],[[]],[]],[],[]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[3,2,1,1,1]
[[[[],[],[]],[]],[],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[3,1,1,1,1,1]
[[[[[]],[]],[]],[],[]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[4,1,1,1,1]
[[[[[],[]]],[]],[],[]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[4,1,1,1,1]
[[[[[[]]]],[]],[],[]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,1,1]
[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[4,1,1,1,1]
[[[[],[[],[]]]],[],[]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[4,1,1,1,1]
[[[[[]],[[]]]],[],[]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[4,2,1,1]
[[[[[],[],[]]]],[],[]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[4,1,1,1,1]
[[[[[[],[]]]]],[],[]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[5,1,1,1]
[[[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,2,1,1,1,1]
[[[],[[],[],[]]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[3,2,1,1,1]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[4,2,1,1]
[[[[]],[],[],[]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[3,2,1,1,1]
[[[[],[]],[],[]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[3,2,1,1,1]
[[[[],[],[]],[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[3,2,1,1,1]
[[[[[]],[]],[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[4,2,1,1]
[[[[[],[]]],[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[4,2,1,1]
[[[[[[]]]],[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,2,1]
[[[[],[],[[]]]],[[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[4,2,1,1]
[[[[],[[]],[]]],[[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[4,2,1,1]
[[[[[]],[],[]]],[[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[4,2,1,1]
[[[[[]],[[]]]],[[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[4,2,2]
[[[[[],[]],[]]],[[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[4,2,1,1]
[[[[[],[],[]]]],[[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[4,2,1,1]
[[[[[[[]]]]]],[[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,2]
[[[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[3,1,1,1,1,1]
[[[],[],[],[[[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[4,1,1,1,1]
[[[],[],[[]],[],[]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[3,1,1,1,1,1]
[[[],[],[[]],[[]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[3,2,1,1,1]
[[[],[],[[],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[4,1,1,1,1]
[[[],[[]],[],[],[]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[3,1,1,1,1,1]
[[[],[[]],[],[[]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[3,2,1,1,1]
[[[],[[],[]],[],[]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[3,1,1,1,1,1]
[[[],[[[]]],[],[]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[4,1,1,1,1]
[[[],[[[]]],[[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[4,2,1,1]
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[4,1,1,1,1]
[[[],[[[],[]]],[]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[4,1,1,1,1]
[[[],[[[[]]],[]]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[5,1,1,1]
[[[[]],[],[[]],[]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[3,2,1,1,1]
[[[[]],[[]],[[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[3,2,2,1]
[[[[]],[[[],[]]]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,2,1,1]
[[[[],[]],[],[],[]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[3,1,1,1,1,1]
[[[[],[]],[],[[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[3,2,1,1,1]
[[[[[]]],[],[[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[4,2,1,1]
[[[[[]]],[[[]]]],[]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[4,3,1]
[[[[],[],[]],[],[]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[3,1,1,1,1,1]
[[[[],[[]]],[],[]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[4,1,1,1,1]
[[[[[],[]]],[],[]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[4,1,1,1,1]
[[[[[[]]]],[],[]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,1,1]
[[[[],[],[]],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[3,2,1,1,1]
[[[[],[[]]],[[]]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[4,2,1,1]
[[[[[]],[]],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[4,2,1,1]
[[[[[],[]]],[[]]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[4,2,1,1]
[[[[[[]]]],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[5,2,1]
[[[[],[],[],[]],[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[3,1,1,1,1,1]
[[[[],[],[[]]],[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[4,1,1,1,1]
[[[[],[[]],[]],[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[4,1,1,1,1]
[[[[],[[],[]]],[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,1,1,1,1]
[[[[[]],[[]]],[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[4,2,1,1]
[[[[[],[]],[]],[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[4,1,1,1,1]
[[[[[[]]],[]],[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[5,1,1,1]
[[[[[],[],[]]],[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[4,1,1,1,1]
[[[[],[],[],[[]]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[4,1,1,1,1]
[[[[],[],[[],[]]]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[4,1,1,1,1]
[[[[],[[]],[[]]]],[]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[4,2,1,1]
[[[[],[[[]]],[]]],[]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[5,1,1,1]
[[[[],[[[]],[]]]],[]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,1,1,1]
[[[[[]],[[]],[]]],[]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[4,2,1,1]
[[[[[],[]],[],[]]],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[4,1,1,1,1]
[[[[[],[],[]],[]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[4,1,1,1,1]
[[[[[[]],[]],[]]],[]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[5,1,1,1]
[[[[[],[],[],[]]]],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[4,1,1,1,1]
[[[[[[]],[[]]]]],[]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[5,2,1]
[[[[[[],[]],[]]]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[5,1,1,1]
[[[[[[],[],[]]]]],[]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[5,1,1,1]
[[[[[[],[[]]]]]],[]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[6,1,1]
[[[[[[[]],[]]]]],[]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[6,1,1]
[[[[[[[[]]]]]]],[]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,1]
[[[],[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[],[],[[]],[]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[],[],[[[]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[4,1,1,1,1]
[[[],[],[],[[]],[],[]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[],[[],[],[]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[],[[],[[]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[4,1,1,1,1]
[[[],[],[],[[[[]]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[5,1,1,1]
[[[],[],[[]],[],[],[]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[3,1,1,1,1,1]
[[[],[],[[]],[],[[]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[3,2,1,1,1]
[[[],[],[[]],[[]],[]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[3,2,1,1,1]
[[[],[],[[]],[[],[]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[3,2,1,1,1]
[[[],[],[[]],[[[]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[4,2,1,1]
[[[],[],[[],[],[],[]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[3,1,1,1,1,1]
[[[],[[]],[],[[[]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[4,2,1,1]
[[[],[[]],[[]],[[]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,2,2,1]
[[[],[[]],[[],[],[]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,2,1,1,1]
[[[],[[]],[[],[[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[4,2,1,1]
[[[],[[]],[[[],[]]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[4,2,1,1]
[[[],[[[]]],[],[],[]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,1,1,1,1]
[[[],[[[]]],[],[[]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,2,1,1]
[[[],[[[]]],[[]],[]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,2,1,1]
[[[],[[],[]],[[[]]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,2,1,1]
[[[],[[[]]],[[],[]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,2,1,1]
[[[],[[[]]],[[[]]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,3,1]
[[[],[[[]],[]],[],[]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[4,1,1,1,1]
[[[],[[[],[]]],[],[]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[4,1,1,1,1]
[[[],[[],[],[]],[[]]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[3,2,1,1,1]
[[[],[[[],[]]],[[]]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[4,2,1,1]
[[[],[[],[],[[]]],[]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[4,1,1,1,1]
[[[],[[],[[],[]]],[]]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[4,1,1,1,1]
[[[],[[[],[]],[]],[]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[4,1,1,1,1]
[[[],[[[[]],[]]],[]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[5,1,1,1]
[[[],[[[],[]],[],[]]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[4,1,1,1,1]
[[[],[[[[]],[]],[]]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[5,1,1,1]
[[[],[[[],[],[],[]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[4,1,1,1,1]
[[[],[[[[]],[[]]]]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[5,2,1]
[[[[]],[],[[[],[]]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[4,2,1,1]
[[[[]],[[],[],[],[]]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[3,2,1,1,1]
[[[[[]]],[],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[4,1,1,1,1]
[[[[],[[]]],[],[],[]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[4,1,1,1,1]
[[[[[],[]]],[],[],[]]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[4,1,1,1,1]
[[[[[[]]]],[],[],[]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,1,1]
[[[[],[[]]],[],[[]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[4,2,1,1]
[[[[[[]]]],[],[[]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,2,1]
[[[[],[[]]],[[]],[]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[4,2,1,1]
[[[[[[]]]],[[]],[]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[5,2,1]
[[[[],[[]]],[[],[]]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[4,2,1,1]
[[[[],[[]]],[[[]]]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[4,3,1]
[[[[[[]]]],[[],[]]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[5,2,1]
[[[[[[]]]],[[[]]]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[5,3]
[[[[],[[]],[]],[],[]]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[4,1,1,1,1]
[[[[],[[[]]]],[],[]]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[5,1,1,1]
[[[[[],[]],[]],[],[]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[4,1,1,1,1]
[[[[[],[],[]]],[],[]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[4,1,1,1,1]
[[[[[],[[]]]],[],[]]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[5,1,1,1]
[[[[],[],[],[]],[[]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[3,2,1,1,1]
[[[[],[],[[]]],[[]]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[4,2,1,1]
[[[[],[[[]]]],[[]]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[5,2,1]
[[[[[],[],[]]],[[]]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[4,2,1,1]
[[[[[[]],[]]],[[]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[5,2,1]
[[[[[[[]]]]],[[]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[6,2]
[[[[],[[[]]],[]],[]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[5,1,1,1]
[[[[],[[[]],[]]],[]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[5,1,1,1]
[[[[[[]]],[[]]],[]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[5,2,1]
[[[[[],[],[]],[]],[]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[4,1,1,1,1]
[[[[[[]],[]],[]],[]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[5,1,1,1]
[[[[[[[]]]],[]],[]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[6,1,1]
[[[[[[]],[],[]]],[]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[5,1,1,1]
[[[[[[]],[[]]]],[]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[5,2,1]
[[[[[[[]],[]]]],[]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[6,1,1]
[[[[[[[[]]]]]],[]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1]
[[[[],[],[],[],[[]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[4,1,1,1,1]
[[[[],[],[],[[[]]]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[5,1,1,1]
[[[[],[[]],[[],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[4,2,1,1]
[[[[],[[[]]],[],[]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[5,1,1,1]
[[[[],[[],[]],[[]]]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,2,1,1]
[[[[],[[[]]],[[]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[5,2,1]
[[[[],[[],[],[]],[]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[4,1,1,1,1]
[[[[],[[],[],[],[]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[4,1,1,1,1]
[[[[[]],[],[],[],[]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[4,1,1,1,1]
[[[[[],[]],[[]],[]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[4,2,1,1]
[[[[[],[],[],[]],[]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[4,1,1,1,1]
[[[[[],[],[[]]],[]]]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[5,1,1,1]
[[[[[[]],[],[]],[]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[5,1,1,1]
[[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[5,1,1,1]
[[[[[],[],[],[],[]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[4,1,1,1,1]
[[[[[],[],[],[[]]]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,1,1]
[[[[[],[],[[]],[]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,1,1,1]
[[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,1,1,1]
[[[[[],[],[[[]]]]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[6,1,1]
[[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,1,1,1]
[[[[[],[[]],[[]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,2,1]
[[[[[],[[],[]],[]]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,1,1,1]
[[[[[],[[[]]],[]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[6,1,1]
[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,1,1,1]
[[[[[],[[],[[]]]]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[6,1,1]
[[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[6,1,1]
[[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[6,1,1]
[[[[[],[[[[]]]]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[7,1]
[[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[6,2]
[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[6,1,1]
[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[7,1]
[[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[5,1,1,1]
[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[6,1,1]
[[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[7,1]
[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[6,2]
[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[7,1]
[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[7,1]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[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
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
searching the database
Sorry, this map was not found in the database.