Identifier
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0002;cc-rep-3
[[]]=>[.,.]=>[1]=>[1]
[[],[]]=>[[.,.],.]=>[1,2]=>[2]
[[[]]]=>[.,[.,.]]=>[2,1]=>[1,1]
[[],[],[]]=>[[[.,.],.],.]=>[1,2,3]=>[3]
[[],[[]]]=>[[.,.],[.,.]]=>[1,3,2]=>[2,1]
[[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>[2,1]
[[[],[]]]=>[.,[[.,.],.]]=>[2,3,1]=>[2,1]
[[[[]]]]=>[.,[.,[.,.]]]=>[3,2,1]=>[1,1,1]
[[],[],[],[]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4]
[[],[],[[]]]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,1]
[[],[[]],[]]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1]
[[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1]
[[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,1,1]
[[[]],[],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,1]
[[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,2]
[[[],[]],[]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1]
[[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,1,1]
[[[],[],[]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]
[[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[2,1,1]
[[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[2,1,1]
[[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]
[[[[[]]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]
[[],[],[],[],[]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5]
[[],[],[],[[]]]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,1]
[[],[],[[]],[]]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1]
[[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1]
[[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,1,1]
[[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[4,1]
[[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,2]
[[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[4,1]
[[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,1,1]
[[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[4,1]
[[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,1,1]
[[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,1,1]
[[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,1,1]
[[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,1,1,1]
[[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[4,1]
[[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2]
[[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2]
[[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2]
[[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,2,1]
[[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,1]
[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,1]
[[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2]
[[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,2,1]
[[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1]
[[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,1,1]
[[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,1,1]
[[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,1,1]
[[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,1,1,1]
[[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]
[[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[3,1,1]
[[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[3,1,1]
[[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,1,1]
[[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[2,1,1,1]
[[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,1,1]
[[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[2,2,1]
[[[[],[]],[]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,1,1]
[[[[[]]],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[2,1,1,1]
[[[[],[],[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[[[[],[[]]]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,1,1,1]
[[[[[]],[]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,1,1,1]
[[[[[],[]]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]
[[[[[[]]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]
[[],[],[],[],[],[]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6]
[[],[],[],[],[[]]]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,1]
[[],[],[],[[]],[]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1]
[[],[],[],[[],[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1]
[[],[],[],[[[]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,1,1]
[[],[],[[]],[],[]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[5,1]
[[],[],[[]],[[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[4,2]
[[],[],[[],[]],[]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[5,1]
[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[4,1,1]
[[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[5,1]
[[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[4,1,1]
[[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[4,1,1]
[[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[4,1,1]
[[],[],[[[[]]]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,1,1,1]
[[],[[]],[],[],[]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[5,1]
[[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[4,2]
[[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[4,2]
[[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[4,2]
[[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[3,2,1]
[[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[5,1]
[[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[4,1,1]
[[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[4,2]
[[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[3,2,1]
[[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[5,1]
[[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[4,1,1]
[[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,1,1]
[[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,1,1]
[[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[3,1,1,1]
[[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[5,1]
[[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[4,1,1]
[[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[4,1,1]
[[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[4,1,1]
[[],[[],[[[]]]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[3,1,1,1]
[[],[[[]],[],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,1,1]
[[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[3,2,1]
[[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,1,1]
[[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[3,1,1,1]
[[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,1,1]
[[],[[[],[[]]]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[3,1,1,1]
[[],[[[[]],[]]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[3,1,1,1]
[[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[3,1,1,1]
[[],[[[[[]]]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[[[]],[],[],[],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[5,1]
[[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[4,2]
[[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[4,2]
[[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[4,2]
[[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[3,2,1]
[[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2]
[[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[3,3]
[[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2]
[[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[3,2,1]
[[[]],[[],[],[]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2]
[[[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,2,1]
[[[]],[[[]],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,2,1]
[[[]],[[[],[]]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,2,1]
[[[]],[[[[]]]]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,2,1,1]
[[[],[]],[],[],[]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[5,1]
[[[[]]],[],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[4,1,1]
[[[],[]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2]
[[[[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1]
[[[],[]],[[]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2]
[[[[]]],[[]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1]
[[[],[]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2]
[[[],[]],[[[]]]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1]
[[[[]]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1]
[[[[]]],[[[]]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,2,2]
[[[],[],[]],[],[]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[5,1]
[[[],[[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,1,1]
[[[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,1,1]
[[[[],[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,1]
[[[[[]]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[3,1,1,1]
[[[],[],[]],[[]]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2]
[[[],[[]]],[[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,1]
[[[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[3,2,1]
[[[[],[]]],[[]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[3,2,1]
[[[[[]]]],[[]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,2,1,1]
[[[],[],[],[]],[]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1]
[[[],[],[[]]],[]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,1,1]
[[[],[[]],[]],[]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,1,1]
[[[],[[],[]]],[]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,1,1]
[[[],[[[]]]],[]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[3,1,1,1]
[[[[]],[],[]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[4,1,1]
[[[[]],[[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[3,2,1]
[[[[],[]],[]],[]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[4,1,1]
[[[[[]]],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[3,1,1,1]
[[[[],[],[]]],[]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[4,1,1]
[[[[],[[]]]],[]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[3,1,1,1]
[[[[[]],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[3,1,1,1]
[[[[[],[]]]],[]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[3,1,1,1]
[[[[[[]]]]],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,1,1,1,1]
[[[],[],[],[],[]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]
[[[],[],[],[[]]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[4,1,1]
[[[],[],[[]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[4,1,1]
[[[],[],[[],[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,1,1]
[[[],[],[[[]]]]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[3,1,1,1]
[[[],[[]],[],[]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,1,1]
[[[],[[]],[[]]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[3,2,1]
[[[],[[],[]],[]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,1,1]
[[[],[[[]]],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[3,1,1,1]
[[[],[[],[],[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,1,1]
[[[],[[],[[]]]]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,1,1,1]
[[[],[[[]],[]]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,1,1,1]
[[[],[[[],[]]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,1,1,1]
[[[],[[[[]]]]]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[[[[]],[],[],[]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[4,1,1]
[[[[]],[],[[]]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[3,2,1]
[[[[]],[[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[3,2,1]
[[[[]],[[],[]]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[3,2,1]
[[[[]],[[[]]]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[2,2,1,1]
[[[[],[]],[],[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[4,1,1]
[[[[[]]],[],[]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[3,1,1,1]
[[[[],[]],[[]]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[3,2,1]
[[[[[]]],[[]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[2,2,1,1]
[[[[],[],[]],[]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[4,1,1]
[[[[],[[]]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[3,1,1,1]
[[[[[]],[]],[]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[3,1,1,1]
[[[[[],[]]],[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[3,1,1,1]
[[[[[[]]]],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[2,1,1,1,1]
[[[[],[],[],[]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]
[[[[],[],[[]]]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[3,1,1,1]
[[[[],[[]],[]]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[3,1,1,1]
[[[[],[[],[]]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[3,1,1,1]
[[[[],[[[]]]]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[[[[[]],[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[3,1,1,1]
[[[[[]],[[]]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,2,1,1]
[[[[[],[]],[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[3,1,1,1]
[[[[[[]]],[]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,1,1,1,1]
[[[[[],[],[]]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]
[[[[[],[[]]]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[[[[[[]],[]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,1,1,1,1]
[[[[[[],[]]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[[[[[[[]]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[[],[],[],[],[],[],[]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7]
[[],[],[],[],[],[[]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[6,1]
[[],[],[],[],[[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1]
[[],[],[],[],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1]
[[],[],[],[],[[[]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[5,1,1]
[[],[],[],[[]],[],[]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[6,1]
[[],[],[],[[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[5,2]
[[],[],[],[[],[]],[]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[6,1]
[[],[],[],[[[]]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[5,1,1]
[[],[],[],[[],[],[]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[6,1]
[[],[],[],[[],[[]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[5,1,1]
[[],[],[],[[[]],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[5,1,1]
[[],[],[],[[[],[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[5,1,1]
[[],[],[],[[[[]]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[[],[],[[]],[],[],[]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[6,1]
[[],[],[[]],[],[[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[5,2]
[[],[],[[]],[[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[5,2]
[[],[],[[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[5,2]
[[],[],[[]],[[[]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,2,1]
[[],[],[[],[]],[],[]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[6,1]
[[],[],[[[]]],[],[]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,1,1]
[[],[],[[],[]],[[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[5,2]
[[],[],[[[]]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[4,2,1]
[[],[],[[],[],[]],[]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[6,1]
[[],[],[[],[[]]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[5,1,1]
[[],[],[[[]],[]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,1,1]
[[],[],[[[],[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,1,1]
[[],[],[[[[]]]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,1,1,1]
[[],[],[[],[],[],[]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[6,1]
[[],[],[[],[],[[]]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[5,1,1]
[[],[],[[],[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[5,1,1]
[[],[],[[],[[],[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[5,1,1]
[[],[],[[],[[[]]]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[[],[],[[[]],[],[]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,1,1]
[[],[],[[[]],[[]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,2,1]
[[],[],[[[],[]],[]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,1,1]
[[],[],[[[[]]],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,1,1,1]
[[],[],[[[],[],[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,1,1]
[[],[],[[[],[[]]]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[[],[],[[[[]],[]]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,1,1,1]
[[],[],[[[[],[]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[[],[],[[[[[]]]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[[],[[]],[],[],[],[]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[6,1]
[[],[[]],[],[],[[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[5,2]
[[],[[]],[],[[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[5,2]
[[],[[]],[],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[5,2]
[[],[[]],[],[[[]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[4,2,1]
[[],[[]],[[]],[],[]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,2]
[[],[[]],[[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[4,3]
[[],[[]],[[],[]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,2]
[[],[[]],[[[]]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,2,1]
[[],[[]],[[],[],[]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,2]
[[],[[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,2,1]
[[],[[]],[[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,2,1]
[[],[[]],[[[],[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,2,1]
[[],[[]],[[[[]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[3,2,1,1]
[[],[[],[]],[],[],[]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[6,1]
[[],[[[]]],[],[],[]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[5,1,1]
[[],[[],[]],[],[[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[5,2]
[[],[[[]]],[],[[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[4,2,1]
[[],[[],[]],[[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[5,2]
[[],[[[]]],[[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,2,1]
[[],[[],[]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[5,2]
[[],[[],[]],[[[]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,2,1]
[[],[[[]]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,2,1]
[[],[[[]]],[[[]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[3,2,2]
[[],[[],[],[]],[],[]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[6,1]
[[],[[],[[]]],[],[]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,1,1]
[[],[[[]],[]],[],[]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[5,1,1]
[[],[[[],[]]],[],[]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[5,1,1]
[[],[[[[]]]],[],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,1,1,1]
[[],[[],[],[]],[[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[5,2]
[[],[[],[[]]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[4,2,1]
[[],[[[]],[]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[4,2,1]
[[],[[[],[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[4,2,1]
[[],[[[[]]]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[3,2,1,1]
[[],[[],[],[],[]],[]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[6,1]
[[],[[],[],[[]]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[5,1,1]
[[],[[],[[]],[]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,1,1]
[[],[[],[[],[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,1,1]
[[],[[],[[[]]]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,1,1,1]
[[],[[[]],[],[]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[5,1,1]
[[],[[[]],[[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,2,1]
[[],[[[],[]],[]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[5,1,1]
[[],[[[[]]],[]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,1,1,1]
[[],[[[],[],[]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[5,1,1]
[[],[[[],[[]]]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,1,1,1]
[[],[[[[]],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,1,1,1]
[[],[[[[],[]]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,1,1,1]
[[],[[[[[]]]]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[3,1,1,1,1]
[[],[[],[],[],[],[]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[6,1]
[[],[[],[],[],[[]]]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[5,1,1]
[[],[[],[],[[]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[5,1,1]
[[],[[],[],[[],[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[5,1,1]
[[],[[],[],[[[]]]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[[],[[],[[]],[],[]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,1,1]
[[],[[],[[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,2,1]
[[],[[],[[],[]],[]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,1,1]
[[],[[],[[[]]],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,1,1,1]
[[],[[],[[],[],[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,1,1]
[[],[[],[[],[[]]]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[[],[[],[[[]],[]]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,1,1,1]
[[],[[],[[[],[]]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[[],[[],[[[[]]]]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[[],[[[]],[],[],[]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[5,1,1]
[[],[[[]],[],[[]]]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,2,1]
[[],[[[]],[[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,2,1]
[[],[[[]],[[],[]]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,2,1]
[[],[[[]],[[[]]]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[3,2,1,1]
[[],[[[],[]],[],[]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[5,1,1]
[[],[[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,1,1,1]
[[],[[[],[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,2,1]
[[],[[[[]]],[[]]]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[3,2,1,1]
[[],[[[],[],[]],[]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[5,1,1]
[[],[[[],[[]]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,1,1,1]
[[],[[[[]],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,1,1,1]
[[],[[[[],[]]],[]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,1,1,1]
[[],[[[[[]]]],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[3,1,1,1,1]
[[],[[[],[],[],[]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[5,1,1]
[[],[[[],[],[[]]]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[[],[[[],[[]],[]]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,1,1,1]
[[],[[[],[[],[]]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[[],[[[],[[[]]]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[[],[[[[]],[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,1,1,1]
[[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[3,2,1,1]
[[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,1,1,1]
[[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[3,1,1,1,1]
[[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[[],[[[[],[[]]]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[[],[[[[[]],[]]]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[3,1,1,1,1]
[[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[[],[[[[[[]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[[[]],[],[],[],[],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[6,1]
[[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[5,2]
[[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[5,2]
[[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[5,2]
[[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[4,2,1]
[[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2]
[[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[4,3]
[[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2]
[[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,2,1]
[[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2]
[[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,2,1]
[[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,2,1]
[[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,2,1]
[[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[3,2,1,1]
[[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[5,2]
[[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[4,3]
[[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3]
[[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3]
[[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[3,3,1]
[[[]],[[],[]],[],[]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[5,2]
[[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,2,1]
[[[]],[[],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[4,3]
[[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[3,3,1]
[[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[5,2]
[[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,2,1]
[[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,2,1]
[[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,2,1]
[[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[3,2,1,1]
[[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[5,2]
[[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,2,1]
[[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,2,1]
[[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,2,1]
[[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,2,1,1]
[[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,2,1]
[[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,3,1]
[[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,2,1]
[[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,2,1,1]
[[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,2,1]
[[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,2,1,1]
[[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,2,1,1]
[[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,2,1,1]
[[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,2,1,1,1]
[[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[6,1]
[[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[5,1,1]
[[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[5,2]
[[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,2,1]
[[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[5,2]
[[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,2,1]
[[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[5,2]
[[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[4,2,1]
[[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,2,1]
[[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,2,2]
[[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2]
[[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,2,1]
[[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[4,3]
[[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,3,1]
[[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2]
[[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[4,2,1]
[[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,2,1]
[[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,2,2]
[[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2]
[[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,2,1]
[[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,2,1]
[[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,2,1]
[[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,1]
[[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,2,1]
[[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,2]
[[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,2]
[[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,2]
[[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,2,2,1]
[[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[6,1]
[[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[5,1,1]
[[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,1,1]
[[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,1,1]
[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,1,1]
[[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2]
[[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,2,1]
[[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,2,1]
[[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,2,1]
[[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[3,2,1,1]
[[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2]
[[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,2,1]
[[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,2,1]
[[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,2,1]
[[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[3,2,1,1]
[[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2]
[[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,1]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,2,1]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,2]
[[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,2,1]
[[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[3,2,2]
[[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,2,1]
[[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[3,2,2]
[[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[3,2,1,1]
[[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,2,2,1]
[[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,1]
[[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,1,1]
[[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,1,1]
[[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,1,1]
[[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[4,1,1,1]
[[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,1,1]
[[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[4,2,1]
[[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,1,1]
[[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,1,1,1]
[[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,1]
[[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[4,1,1,1]
[[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,1,1,1]
[[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,1,1,1]
[[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[3,1,1,1,1]
[[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2]
[[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[4,2,1]
[[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[4,2,1]
[[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[4,2,1]
[[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[3,2,1,1]
[[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[4,2,1]
[[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[3,3,1]
[[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[4,2,1]
[[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[3,2,1,1]
[[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[4,2,1]
[[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[3,2,1,1]
[[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[3,2,1,1]
[[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[3,2,1,1]
[[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[2,2,1,1,1]
[[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1]
[[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[5,1,1]
[[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,1,1]
[[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[5,1,1]
[[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[4,1,1,1]
[[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[5,1,1]
[[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[4,2,1]
[[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[5,1,1]
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[4,1,1,1]
[[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[5,1,1]
[[[],[[],[[]]]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[4,1,1,1]
[[[],[[[]],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[4,1,1,1]
[[[],[[[],[]]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[4,1,1,1]
[[[],[[[[]]]]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[3,1,1,1,1]
[[[[]],[],[],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[5,1,1]
[[[[]],[],[[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[4,2,1]
[[[[]],[[]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[4,2,1]
[[[[]],[[],[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[4,2,1]
[[[[]],[[[]]]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[3,2,1,1]
[[[[],[]],[],[]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[5,1,1]
[[[[[]]],[],[]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,1,1,1]
[[[[],[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[4,2,1]
[[[[[]]],[[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[3,2,1,1]
[[[[],[],[]],[]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[5,1,1]
[[[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[4,1,1,1]
[[[[[]],[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,1,1,1]
[[[[[],[]]],[]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,1,1,1]
[[[[[[]]]],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[3,1,1,1,1]
[[[[],[],[],[]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[5,1,1]
[[[[],[],[[]]]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[4,1,1,1]
[[[[],[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[4,1,1,1]
[[[[],[[],[]]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[4,1,1,1]
[[[[],[[[]]]]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[3,1,1,1,1]
[[[[[]],[],[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,1,1,1]
[[[[[]],[[]]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[3,2,1,1]
[[[[[],[]],[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,1,1,1]
[[[[[[]]],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[3,1,1,1,1]
[[[[[],[],[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,1,1,1]
[[[[[],[[]]]]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[3,1,1,1,1]
[[[[[[]],[]]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[3,1,1,1,1]
[[[[[[],[]]]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[3,1,1,1,1]
[[[[[[[]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,1,1,1,1,1]
[[[],[],[],[],[],[]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]
[[[],[],[],[],[[]]]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[5,1,1]
[[[],[],[],[[]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[5,1,1]
[[[],[],[],[[],[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,1,1]
[[[],[],[],[[[]]]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[[[],[],[[]],[],[]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[5,1,1]
[[[],[],[[]],[[]]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[4,2,1]
[[[],[],[[],[]],[]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[5,1,1]
[[[],[],[[[]]],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[4,1,1,1]
[[[],[],[[],[],[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[5,1,1]
[[[],[],[[],[[]]]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[[[],[],[[[]],[]]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[4,1,1,1]
[[[],[],[[[],[]]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[[[],[],[[[[]]]]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[[[],[[]],[],[],[]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[5,1,1]
[[[],[[]],[],[[]]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[4,2,1]
[[[],[[]],[[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[4,2,1]
[[[],[[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[4,2,1]
[[[],[[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[3,2,1,1]
[[[],[[],[]],[],[]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[5,1,1]
[[[],[[[]]],[],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[4,1,1,1]
[[[],[[],[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[4,2,1]
[[[],[[[]]],[[]]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[3,2,1,1]
[[[],[[],[],[]],[]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[5,1,1]
[[[],[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[4,1,1,1]
[[[],[[[]],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[4,1,1,1]
[[[],[[[],[]]],[]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[4,1,1,1]
[[[],[[[[]]]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[3,1,1,1,1]
[[[],[[],[],[],[]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[5,1,1]
[[[],[[],[],[[]]]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[[[],[[],[[]],[]]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[4,1,1,1]
[[[],[[],[[],[]]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[[[],[[],[[[]]]]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[[[],[[[]],[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[4,1,1,1]
[[[],[[[]],[[]]]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[3,2,1,1]
[[[],[[[],[]],[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[4,1,1,1]
[[[],[[[[]]],[]]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[3,1,1,1,1]
[[[],[[[],[],[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[[[],[[[],[[]]]]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[[[],[[[[]],[]]]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[3,1,1,1,1]
[[[],[[[[],[]]]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[[[],[[[[[]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[[[[]],[],[],[],[]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[5,1,1]
[[[[]],[],[],[[]]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[4,2,1]
[[[[]],[],[[]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[4,2,1]
[[[[]],[],[[],[]]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[4,2,1]
[[[[]],[],[[[]]]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[3,2,1,1]
[[[[]],[[]],[],[]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[4,2,1]
[[[[]],[[]],[[]]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[3,3,1]
[[[[]],[[],[]],[]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[4,2,1]
[[[[]],[[[]]],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[3,2,1,1]
[[[[]],[[],[],[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[4,2,1]
[[[[]],[[],[[]]]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[3,2,1,1]
[[[[]],[[[]],[]]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[3,2,1,1]
[[[[]],[[[],[]]]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[3,2,1,1]
[[[[]],[[[[]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[2,2,1,1,1]
[[[[],[]],[],[],[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[5,1,1]
[[[[[]]],[],[],[]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,1,1,1]
[[[[],[]],[],[[]]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[4,2,1]
[[[[[]]],[],[[]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[3,2,1,1]
[[[[],[]],[[]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[4,2,1]
[[[[[]]],[[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[3,2,1,1]
[[[[],[]],[[],[]]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[4,2,1]
[[[[],[]],[[[]]]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[3,2,1,1]
[[[[[]]],[[],[]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[3,2,1,1]
[[[[[]]],[[[]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[2,2,2,1]
[[[[],[],[]],[],[]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[5,1,1]
[[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[4,1,1,1]
[[[[[]],[]],[],[]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,1,1,1]
[[[[[],[]]],[],[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,1,1,1]
[[[[[[]]]],[],[]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[3,1,1,1,1]
[[[[],[],[]],[[]]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[4,2,1]
[[[[],[[]]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[3,2,1,1]
[[[[[]],[]],[[]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[3,2,1,1]
[[[[[],[]]],[[]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[3,2,1,1]
[[[[[[]]]],[[]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[2,2,1,1,1]
[[[[],[],[],[]],[]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[5,1,1]
[[[[],[],[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[4,1,1,1]
[[[[],[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[4,1,1,1]
[[[[],[[],[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[4,1,1,1]
[[[[],[[[]]]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[3,1,1,1,1]
[[[[[]],[],[]],[]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,1,1,1]
[[[[[]],[[]]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[3,2,1,1]
[[[[[],[]],[]],[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,1,1,1]
[[[[[[]]],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[3,1,1,1,1]
[[[[[],[],[]]],[]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,1,1,1]
[[[[[],[[]]]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[3,1,1,1,1]
[[[[[[]],[]]],[]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[3,1,1,1,1]
[[[[[[],[]]]],[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[3,1,1,1,1]
[[[[[[[]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[2,1,1,1,1,1]
[[[[],[],[],[],[]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]
[[[[],[],[],[[]]]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[[[[],[],[[]],[]]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[4,1,1,1]
[[[[],[],[[],[]]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[[[[],[],[[[]]]]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[[[[],[[]],[],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[4,1,1,1]
[[[[],[[]],[[]]]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[3,2,1,1]
[[[[],[[],[]],[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[4,1,1,1]
[[[[],[[[]]],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[3,1,1,1,1]
[[[[],[[],[],[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[[[[],[[],[[]]]]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[[[[],[[[]],[]]]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[3,1,1,1,1]
[[[[],[[[],[]]]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[[[[],[[[[]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[[[[[]],[],[],[]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,1,1,1]
[[[[[]],[],[[]]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[3,2,1,1]
[[[[[]],[[]],[]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[3,2,1,1]
[[[[[]],[[],[]]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[3,2,1,1]
[[[[[]],[[[]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[2,2,1,1,1]
[[[[[],[]],[],[]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,1,1,1]
[[[[[[]]],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[3,1,1,1,1]
[[[[[],[]],[[]]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[3,2,1,1]
[[[[[[]]],[[]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[2,2,1,1,1]
[[[[[],[],[]],[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,1,1,1]
[[[[[],[[]]],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[3,1,1,1,1]
[[[[[[]],[]],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[3,1,1,1,1]
[[[[[[],[]]],[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[3,1,1,1,1]
[[[[[[[]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,1,1,1,1,1]
[[[[[],[],[],[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[[[[],[],[[]]]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[[[[[],[[]],[]]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[3,1,1,1,1]
[[[[[],[[],[]]]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[[[[[],[[[]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[[[[[[]],[],[]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[3,1,1,1,1]
[[[[[[]],[[]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[2,2,1,1,1]
[[[[[[],[]],[]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[3,1,1,1,1]
[[[[[[[]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,1,1,1,1,1]
[[[[[[],[],[]]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[[[[[[],[[]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[[]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[[],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[[[[[[[[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]
[[],[],[],[],[],[],[[]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[7,1]
[[],[],[],[],[],[[]],[]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[7,1]
[[],[],[],[],[],[[],[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,1]
[[],[],[],[],[[]],[],[]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[7,1]
[[],[],[],[],[[],[],[]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[7,1]
[[],[],[],[],[[],[[]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[6,1,1]
[[],[],[],[],[[[]],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[6,1,1]
[[],[],[],[],[[[],[]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[6,1,1]
[[],[],[],[],[[[[]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[[],[],[],[[]],[],[],[]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[7,1]
[[],[],[],[[]],[[]],[]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[6,2]
[[],[],[],[[]],[[],[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[6,2]
[[],[],[],[[]],[[[]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[5,2,1]
[[],[],[],[[],[]],[],[]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[7,1]
[[],[],[],[[],[]],[[]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[6,2]
[[],[],[],[[[]]],[[]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[5,2,1]
[[],[],[],[[],[],[]],[]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[7,1]
[[],[],[],[[],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[6,1,1]
[[],[],[],[[[]],[]],[]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[6,1,1]
[[],[],[],[[[],[]]],[]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[6,1,1]
[[],[],[],[[[[]]]],[]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[5,1,1,1]
[[],[],[],[[],[],[],[]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[7,1]
[[],[],[],[[],[],[[]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[[],[],[],[[],[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[6,1,1]
[[],[],[],[[],[[],[]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[[],[],[],[[],[[[]]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[[],[],[],[[[]],[],[]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[6,1,1]
[[],[],[],[[[]],[[]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[5,2,1]
[[],[],[],[[[],[]],[]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[6,1,1]
[[],[],[],[[[[]]],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[5,1,1,1]
[[],[],[],[[[],[],[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[[],[],[],[[[],[[]]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[[],[],[],[[[[]],[]]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[5,1,1,1]
[[],[],[],[[[[],[]]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[[],[],[],[[[[[]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[[],[],[[]],[],[],[],[]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[7,1]
[[],[],[[]],[],[],[[]]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[6,2]
[[],[],[[]],[],[[],[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[6,2]
[[],[],[[]],[[],[]],[]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[6,2]
[[],[],[[]],[[],[],[]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[6,2]
[[],[],[[]],[[[]],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[5,2,1]
[[],[],[[]],[[[],[]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[5,2,1]
[[],[],[[]],[[[[]]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[4,2,1,1]
[[],[],[[[]]],[],[[]]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[5,2,1]
[[],[],[[],[]],[[[]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[5,2,1]
[[],[],[[[]]],[[],[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[5,2,1]
[[],[],[[],[],[]],[],[]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[7,1]
[[],[],[[[]],[],[]],[]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[6,1,1]
[[],[],[[[],[]],[]],[]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[6,1,1]
[[],[],[[[],[],[]]],[]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[6,1,1]
[[],[],[[[],[[]]]],[]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>[5,1,1,1]
[[],[],[[],[],[[],[]]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[[],[],[[],[[[]]],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[5,1,1,1]
[[],[],[[],[[],[],[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[[],[],[[],[[],[[]]]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[[],[],[[],[[[[]]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[[],[],[[[]],[[[]]]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[4,2,1,1]
[[],[],[[[],[],[]],[]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[6,1,1]
[[],[],[[[],[[]]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[5,1,1,1]
[[],[],[[[],[],[],[]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[6,1,1]
[[],[],[[[],[[]],[]]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[5,1,1,1]
[[],[],[[[[]],[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[5,1,1,1]
[[],[],[[[[]],[[]]]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[4,2,1,1]
[[],[],[[[[[]]],[]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[4,1,1,1,1]
[[],[],[[[[],[],[]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[[],[],[[[[[[]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[[],[[]],[],[],[],[],[]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[7,1]
[[],[[]],[],[],[[]],[]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[6,2]
[[],[[]],[],[[]],[],[]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[6,2]
[[],[[]],[],[[]],[[]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[5,3]
[[],[[]],[],[[[]]],[]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[5,2,1]
[[],[[]],[],[[],[],[]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[6,2]
[[],[[]],[],[[],[[]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[5,2,1]
[[],[[]],[],[[[]],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[5,2,1]
[[],[[]],[],[[[[]]]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[4,2,1,1]
[[],[[]],[[]],[],[],[]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[6,2]
[[],[[]],[[]],[[]],[]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[5,3]
[[],[[]],[[]],[[],[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[5,3]
[[],[[]],[[[]],[],[]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[5,2,1]
[[],[[]],[[[]],[[]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[4,3,1]
[[],[[]],[[[[]]],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[4,2,1,1]
[[],[[]],[[[],[[]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[4,2,1,1]
[[],[[]],[[[[[]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[3,2,1,1,1]
[[],[[],[]],[],[],[],[]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[7,1]
[[],[[[]]],[],[],[[]]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[5,2,1]
[[],[[[]]],[],[[]],[]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[5,2,1]
[[],[[],[]],[],[[],[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[6,2]
[[],[[[]]],[],[[[]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[4,2,2]
[[],[[[]]],[[],[]],[]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[5,2,1]
[[],[[],[]],[[],[],[]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[6,2]
[[],[[],[]],[[],[[]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[5,2,1]
[[],[[],[]],[[[]],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[5,2,1]
[[],[[],[]],[[[],[]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[5,2,1]
[[],[[[]]],[[],[],[]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[5,2,1]
[[],[[[]]],[[[]],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[4,2,2]
[[],[[[]]],[[[[]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[3,2,2,1]
[[],[[],[[]]],[],[[]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[5,2,1]
[[],[[],[[],[]]],[],[]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[6,1,1]
[[],[[[]],[[]]],[],[]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[5,2,1]
[[],[[[[]]],[]],[],[]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[5,1,1,1]
[[],[[[],[],[]]],[],[]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[6,1,1]
[[],[[[],[[]]]],[],[]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[5,1,1,1]
[[],[[[[]],[]]],[],[]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[5,1,1,1]
[[],[[[[],[]]]],[],[]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[5,1,1,1]
[[],[[],[[[]]]],[[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>[4,2,1,1]
[[],[[[[]],[]]],[[]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[4,2,1,1]
[[],[[],[[]],[[]]],[]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[5,2,1]
[[],[[],[[[]]],[]],[]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[5,1,1,1]
[[],[[],[[],[],[]]],[]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[6,1,1]
[[],[[],[[],[[]]]],[]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[5,1,1,1]
[[],[[[[]]],[],[]],[]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[5,1,1,1]
[[],[[[[],[],[]]]],[]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[5,1,1,1]
[[],[[],[],[],[[[]]]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[[],[[],[],[[],[],[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[[],[[],[],[[[[]]]]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[[],[[],[[]],[[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[5,2,1]
[[],[[],[[],[],[],[]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[[],[[],[[],[[],[]]]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[[],[[],[[],[[[]]]]]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[[],[[],[[[],[],[]]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[[],[[],[[[],[[]]]]]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]
[[],[[],[[[[[]]]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[[],[[[]],[],[[],[]]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[5,2,1]
[[],[[[]],[[]],[],[]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[5,2,1]
[[],[[[]],[[]],[[]]]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[4,3,1]
[[],[[[]],[[],[[]]]]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[4,2,1,1]
[[],[[[]],[[[],[]]]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[4,2,1,1]
[[],[[[]],[[[[]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[3,2,1,1,1]
[[],[[[[]]],[],[[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[4,2,1,1]
[[],[[[[]]],[[[]]]]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[3,2,2,1]
[[],[[[],[[]]],[[]]]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[4,2,1,1]
[[],[[[[],[]]],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[4,2,1,1]
[[],[[[[[]]]],[[]]]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[3,2,1,1,1]
[[],[[[[[],[]]]],[]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[4,1,1,1,1]
[[],[[[],[[]],[[]]]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[4,2,1,1]
[[],[[[],[[[]]],[]]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[4,1,1,1,1]
[[],[[[],[[],[],[]]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[[],[[[],[[],[[]]]]]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[[],[[[],[[[],[]]]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[[],[[[[],[],[],[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[[],[[[[],[[]],[]]]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[4,1,1,1,1]
[[],[[[[[],[]],[]]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[4,1,1,1,1]
[[],[[[[[[]]],[]]]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[3,1,1,1,1,1]
[[],[[[[[],[],[]]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[[],[[[[[],[[]]]]]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[[],[[[[[[]],[]]]]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[3,1,1,1,1,1]
[[],[[[[[[],[]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[[],[[[[[[[]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[[[]],[],[],[[],[],[]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[6,2]
[[[]],[],[],[[[]],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[5,2,1]
[[[]],[],[],[[[[]]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[4,2,1,1]
[[[]],[],[[]],[[[]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[4,3,1]
[[[]],[],[[[],[]]],[]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>[5,2,1]
[[[]],[],[[[],[[]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[4,2,1,1]
[[[]],[],[[[[],[]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[4,2,1,1]
[[[]],[],[[[[[]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[3,2,1,1,1]
[[[]],[[]],[[]],[[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[4,4]
[[[]],[[]],[[],[],[]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[5,3]
[[[]],[[]],[[],[[]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[4,3,1]
[[[]],[[]],[[[]],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[4,3,1]
[[[]],[[]],[[[],[]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[4,3,1]
[[[]],[[]],[[[[]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[3,3,1,1]
[[[]],[[],[]],[],[[]]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[5,3]
[[[]],[[],[[]]],[],[]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[5,2,1]
[[[]],[[[],[]]],[],[]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[5,2,1]
[[[]],[[],[],[]],[[]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[5,3]
[[[]],[[],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[4,3,1]
[[[]],[[[]],[]],[[]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[4,3,1]
[[[]],[[[],[]]],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[4,3,1]
[[[]],[[[[]]]],[[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[3,3,1,1]
[[[]],[[],[],[],[],[]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[6,2]
[[[]],[[],[],[],[[]]]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[5,2,1]
[[[]],[[],[],[[],[]]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[5,2,1]
[[[]],[[],[],[[[]]]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[4,2,1,1]
[[[]],[[],[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[4,3,1]
[[[]],[[],[[],[]],[]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[5,2,1]
[[[]],[[],[[[]]],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[4,2,1,1]
[[[]],[[],[[],[],[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[5,2,1]
[[[]],[[],[[],[[]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[4,2,1,1]
[[[]],[[],[[[],[]]]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[4,2,1,1]
[[[]],[[],[[[[]]]]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[3,2,1,1,1]
[[[]],[[[]],[[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[4,3,1]
[[[]],[[[],[]],[],[]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[5,2,1]
[[[]],[[[],[],[]],[]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[5,2,1]
[[[]],[[[[]],[]],[]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[4,2,1,1]
[[[]],[[[],[],[],[]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[5,2,1]
[[[]],[[[],[[],[]]]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[4,2,1,1]
[[[]],[[[[]],[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[4,2,1,1]
[[[]],[[[[]],[[]]]]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[3,3,1,1]
[[[]],[[[[],[]],[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[4,2,1,1]
[[[]],[[[[[]]],[]]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[3,2,1,1,1]
[[[]],[[[[],[],[]]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[4,2,1,1]
[[[]],[[[[],[[]]]]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[3,2,1,1,1]
[[[]],[[[[[]],[]]]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[3,2,1,1,1]
[[[]],[[[[[],[]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[3,2,1,1,1]
[[[]],[[[[[[]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,2,1,1,1,1]
[[[[]]],[],[],[[],[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[5,2,1]
[[[],[]],[],[[],[]],[]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[6,2]
[[[],[]],[],[[],[],[]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[6,2]
[[[],[]],[],[[[]],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,2,1]
[[[],[]],[],[[[],[]]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[5,2,1]
[[[],[]],[],[[[[]]]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[4,2,1,1]
[[[[]]],[],[[],[],[]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[5,2,1]
[[[[]]],[],[[],[[]]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[4,2,2]
[[[[]]],[],[[[]],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[4,2,2]
[[[[]]],[],[[[],[]]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[4,2,2]
[[[[]]],[],[[[[]]]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,2,1]
[[[],[]],[[]],[[]],[]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[5,3]
[[[[]]],[[],[]],[],[]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[5,2,1]
[[[],[]],[[[]]],[[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[4,3,1]
[[[],[]],[[],[],[]],[]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[6,2]
[[[],[]],[[[],[]]],[]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[5,2,1]
[[[[]]],[[],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[4,2,2]
[[[],[]],[[],[],[],[]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[6,2]
[[[],[]],[[[]],[[]]]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[4,3,1]
[[[],[]],[[[],[],[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[5,2,1]
[[[],[]],[[[],[[]]]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[4,2,1,1]
[[[],[]],[[[[]],[]]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[4,2,1,1]
[[[],[]],[[[[[]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,2,1,1,1]
[[[[]]],[[],[],[],[]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[5,2,1]
[[[[]]],[[],[],[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[4,2,2]
[[[[]]],[[],[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[4,2,2]
[[[[]]],[[],[[],[]]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[4,2,2]
[[[[]]],[[],[[[]]]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[3,2,2,1]
[[[[]]],[[[]],[],[]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[4,2,2]
[[[[]]],[[[]],[[]]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,3,2]
[[[[]]],[[[],[]],[]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[4,2,2]
[[[[]]],[[[[]]],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,2,2,1]
[[[[]]],[[[],[],[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[4,2,2]
[[[[]]],[[[],[[]]]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[3,2,2,1]
[[[[]]],[[[[]],[]]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[3,2,2,1]
[[[[]]],[[[[],[]]]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[3,2,2,1]
[[[[]]],[[[[[]]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[2,2,2,1,1]
[[[],[],[]],[],[],[],[]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[7,1]
[[[[]],[]],[],[],[],[]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[6,1,1]
[[[[[]]]],[],[],[],[]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[5,1,1,1]
[[[],[],[]],[],[],[[]]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[6,2]
[[[[]],[]],[],[],[[]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[5,2,1]
[[[],[],[]],[],[[]],[]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[6,2]
[[[[]],[]],[],[[]],[]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[5,2,1]
[[[],[],[]],[],[[],[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[6,2]
[[[],[],[]],[],[[[]]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[5,2,1]
[[[[]],[]],[],[[],[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[5,2,1]
[[[[]],[]],[],[[[]]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,2,2]
[[[[[]]]],[],[[],[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,2,1,1]
[[[],[],[]],[[]],[],[]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[6,2]
[[[[]],[]],[[]],[],[]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[5,2,1]
[[[],[],[]],[[]],[[]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[5,3]
[[[],[[]]],[[]],[[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,3,1]
[[[[]],[]],[[]],[[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,1]
[[[[],[]]],[[]],[[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,3,1]
[[[[[]]]],[[]],[[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[3,3,1,1]
[[[],[],[]],[[],[]],[]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[6,2]
[[[],[],[]],[[[]]],[]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[5,2,1]
[[[[]],[]],[[],[]],[]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[5,2,1]
[[[[]],[]],[[[]]],[]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,2,2]
[[[],[],[]],[[],[],[]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[6,2]
[[[],[],[]],[[],[[]]]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[5,2,1]
[[[],[],[]],[[[]],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[5,2,1]
[[[],[],[]],[[[],[]]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[5,2,1]
[[[],[],[]],[[[[]]]]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,1,1]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[5,2,1]
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,2,2]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,2,2]
[[[[]],[]],[[],[],[]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,2,1]
[[[[]],[]],[[],[[]]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,2,2]
[[[[]],[]],[[[]],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,2,2]
[[[[]],[]],[[[],[]]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,2,2]
[[[[]],[]],[[[[]]]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[3,2,2,1]
[[[[],[]]],[[],[],[]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,2,1]
[[[[],[]]],[[[]],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,2,2]
[[[[],[]]],[[[],[]]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,2,2]
[[[[],[]]],[[[[]]]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[3,2,2,1]
[[[[[]]]],[[],[],[]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,2,1,1]
[[[[[]]]],[[[]],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[3,2,2,1]
[[[[[]]]],[[[],[]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[3,2,2,1]
[[[[[]]]],[[[[]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2]
[[[],[],[],[]],[],[],[]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[7,1]
[[[],[],[[]]],[],[],[]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[6,1,1]
[[[],[[]],[]],[],[],[]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[6,1,1]
[[[],[[],[]]],[],[],[]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[6,1,1]
[[[],[[[]]]],[],[],[]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,1,1,1]
[[[[]],[],[]],[],[],[]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[6,1,1]
[[[[]],[[]]],[],[],[]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,2,1]
[[[[],[]],[]],[],[],[]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[6,1,1]
[[[[[]]],[]],[],[],[]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,1,1,1]
[[[[],[],[]]],[],[],[]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[6,1,1]
[[[[],[[]]]],[],[],[]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,1,1,1]
[[[[[]],[]]],[],[],[]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,1,1,1]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,1,1]
[[[[[[]]]]],[],[],[]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[4,1,1,1,1]
[[[],[[],[]]],[],[[]]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[5,2,1]
[[[],[[[]]]],[],[[]]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[4,2,1,1]
[[[[]],[[]]],[],[[]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[4,3,1]
[[[[],[[]]]],[],[[]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[4,2,1,1]
[[[[[],[]]]],[],[[]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[4,2,1,1]
[[[[[[]]]]],[],[[]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[3,2,1,1,1]
[[[],[[],[]]],[[]],[]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[5,2,1]
[[[[]],[[]]],[[]],[]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[4,3,1]
[[[[],[[]]]],[[]],[]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[4,2,1,1]
[[[[[],[]]]],[[]],[]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[4,2,1,1]
[[[[[[]]]]],[[]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[3,2,1,1,1]
[[[],[],[],[]],[[[]]]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[5,2,1]
[[[],[],[[]]],[[[]]]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[4,2,2]
[[[],[[]],[]],[[[]]]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[4,2,2]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[4,2,2]
[[[],[[[]]]],[[[]]]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[3,2,2,1]
[[[[]],[],[]],[[[]]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[4,2,2]
[[[[]],[[]]],[[],[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[4,3,1]
[[[[]],[[]]],[[[]]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[3,3,2]
[[[[],[]],[]],[[],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,2,1]
[[[[],[]],[]],[[[]]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[4,2,2]
[[[[[]]],[]],[[[]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[3,2,2,1]
[[[[],[],[]]],[[[]]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[4,2,2]
[[[[],[[]]]],[[],[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[4,2,1,1]
[[[[],[[]]]],[[[]]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[3,2,2,1]
[[[[[]],[]]],[[[]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[3,2,2,1]
[[[[[],[]]]],[[[]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[3,2,2,1]
[[[[[[]]]]],[[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[3,2,1,1,1]
[[[[[[]]]]],[[[]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[2,2,2,1,1]
[[[],[[],[],[]]],[],[]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[6,1,1]
[[[],[[],[[]]]],[],[]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[5,1,1,1]
[[[[[]]],[[]]],[],[]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[4,2,1,1]
[[[[[[]]]],[]],[],[]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[4,1,1,1,1]
[[[[],[[[]]]]],[],[]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[4,1,1,1,1]
[[[[[]],[[]]]],[],[]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>[4,2,1,1]
[[[[[],[],[]]]],[],[]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[5,1,1,1]
[[[[[[],[]]]]],[],[]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[4,1,1,1,1]
[[[],[],[],[],[]],[[]]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[6,2]
[[[],[],[[],[]]],[[]]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[5,2,1]
[[[],[],[[[]]]],[[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[4,2,1,1]
[[[],[[],[]],[]],[[]]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[5,2,1]
[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[4,2,1,1]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[4,2,1,1]
[[[],[[[],[]]]],[[]]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[4,2,1,1]
[[[],[[[[]]]]],[[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[3,2,1,1,1]
[[[[]],[[]],[]],[[]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[4,3,1]
[[[[],[]],[],[]],[[]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[5,2,1]
[[[[],[],[]],[]],[[]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[5,2,1]
[[[[[]],[]],[]],[[]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[4,2,1,1]
[[[[[[]]]],[]],[[]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[3,2,1,1,1]
[[[[],[[],[]]]],[[]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[4,2,1,1]
[[[[[]],[[]]]],[[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[3,3,1,1]
[[[[[],[]],[]]],[[]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[4,2,1,1]
[[[[[[]]],[]]],[[]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[3,2,1,1,1]
[[[[[],[],[]]]],[[]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[4,2,1,1]
[[[[[],[[]]]]],[[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[3,2,1,1,1]
[[[[[[]],[]]]],[[]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[3,2,1,1,1]
[[[[[[],[]]]]],[[]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[3,2,1,1,1]
[[[[[[[]]]]]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[2,2,1,1,1,1]
[[[],[],[],[[[]]]],[]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[5,1,1,1]
[[[],[],[[],[],[]]],[]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[6,1,1]
[[[],[],[[],[[]]]],[]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>[5,1,1,1]
[[[],[],[[[]],[]]],[]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[5,1,1,1]
[[[],[],[[[],[]]]],[]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[5,1,1,1]
[[[],[],[[[[]]]]],[]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[4,1,1,1,1]
[[[],[[]],[[]],[]],[]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[5,2,1]
[[[],[[],[[],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[5,1,1,1]
[[[],[[[],[],[]]]],[]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[5,1,1,1]
[[[[]],[],[[],[]]],[]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[5,2,1]
[[[[]],[[]],[[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[4,3,1]
[[[[]],[[[]]],[]],[]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[4,2,1,1]
[[[[]],[[],[[]]]],[]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[4,2,1,1]
[[[[]],[[[],[]]]],[]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[4,2,1,1]
[[[[]],[[[[]]]]],[]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[3,2,1,1,1]
[[[[[]]],[],[[]]],[]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[4,2,1,1]
[[[[[[]]]],[],[]],[]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[4,1,1,1,1]
[[[[],[[]]],[[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[4,2,1,1]
[[[[[],[]]],[[]]],[]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[4,2,1,1]
[[[[[[]]]],[[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[3,2,1,1,1]
[[[[],[[]],[[]]]],[]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[4,2,1,1]
[[[[],[[],[],[]]]],[]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[5,1,1,1]
[[[[],[[],[[]]]]],[]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[4,1,1,1,1]
[[[[[[[]]]],[]]],[]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[3,1,1,1,1,1]
[[[[[],[],[],[]]]],[]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[5,1,1,1]
[[[[[],[],[[]]]]],[]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[4,1,1,1,1]
[[[[[[],[]],[]]]],[]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[4,1,1,1,1]
[[[[[[[]]],[]]]],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[3,1,1,1,1,1]
[[[[[[],[],[]]]]],[]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[4,1,1,1,1]
[[[[[[],[[]]]]]],[]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[[[[[]],[]]]]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[[[[[],[]]]]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[3,1,1,1,1,1]
[[[[[[[[]]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[],[],[]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]
[[[],[],[],[],[],[[]]]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[[[],[],[],[],[[]],[]]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[6,1,1]
[[[],[],[],[],[[[]]]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[[[],[],[],[[]],[],[]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[6,1,1]
[[[],[],[],[[]],[[]]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[5,2,1]
[[[],[],[],[[[]]],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[5,1,1,1]
[[[],[],[],[[],[],[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[[[],[],[],[[[[]]]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[[[],[],[[]],[],[],[]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[6,1,1]
[[[],[],[[]],[[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[5,2,1]
[[[],[],[[],[]],[],[]]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[6,1,1]
[[[],[],[[[[]]]],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[4,1,1,1,1]
[[[],[],[[],[],[],[]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[[[],[],[[],[[],[]]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[[[],[],[[[[]]],[]]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[4,1,1,1,1]
[[[],[],[[[[[]]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[[[],[[]],[],[],[],[]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[6,1,1]
[[[],[[]],[],[],[[]]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[5,2,1]
[[[],[[]],[[]],[],[]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[5,2,1]
[[[],[[]],[[]],[[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[4,3,1]
[[[],[[]],[[[[]]]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[3,2,1,1,1]
[[[],[[],[]],[],[],[]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[6,1,1]
[[[],[[[]]],[[],[]]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[4,2,1,1]
[[[],[[],[],[],[]],[]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[6,1,1]
[[[],[[],[[],[[]]]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[[[],[[[]],[[[]]]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[3,2,1,1,1]
[[[],[[[[]]],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[4,1,1,1,1]
[[[],[[[[[]]]],[]]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[3,1,1,1,1,1]
[[[],[[[],[],[],[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[[[],[[[[[]],[]]]]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[3,1,1,1,1,1]
[[[],[[[[[[]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[[[[]],[],[],[],[],[]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[6,1,1]
[[[[]],[],[],[[]],[]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[5,2,1]
[[[[]],[],[[[[]]]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[3,2,1,1,1]
[[[[]],[[]],[],[],[]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[5,2,1]
[[[[]],[[]],[[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[4,3,1]
[[[[]],[[[]],[]],[]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[4,2,1,1]
[[[[]],[[[],[]]],[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[4,2,1,1]
[[[[]],[[],[],[],[]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[5,2,1]
[[[[]],[[[],[[]]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[3,2,1,1,1]
[[[[]],[[[[[]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[2,2,1,1,1,1]
[[[[],[]],[],[],[],[]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[6,1,1]
[[[[],[]],[],[],[[]]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[5,2,1]
[[[[[]]],[],[],[[]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[4,2,1,1]
[[[[[]]],[],[[[]]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[3,2,2,1]
[[[[],[]],[[]],[],[]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[5,2,1]
[[[[[]]],[[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[3,3,1,1]
[[[[],[]],[[[],[]]]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[4,2,1,1]
[[[[],[]],[[[[]]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[3,2,1,1,1]
[[[[[]]],[[[[]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[2,2,2,1,1]
[[[[],[[]]],[],[],[]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[5,1,1,1]
[[[[[]],[]],[],[],[]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[5,1,1,1]
[[[[[[]]]],[],[],[]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[4,1,1,1,1]
[[[[[[]]]],[],[[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[3,2,1,1,1]
[[[[[]],[]],[[]],[]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[4,2,1,1]
[[[[[[]]]],[[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[3,2,1,1,1]
[[[[[[]]]],[[],[]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[3,2,1,1,1]
[[[[[[]]]],[[[]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[2,2,2,1,1]
[[[[[[]]],[]],[],[]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[4,1,1,1,1]
[[[[[[[]]]]],[],[]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[3,1,1,1,1,1]
[[[[],[[],[]]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[4,2,1,1]
[[[[[]],[[]]],[[]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[3,3,1,1]
[[[[[[]]],[]],[[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[3,2,1,1,1]
[[[[[],[[]]]],[[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[3,2,1,1,1]
[[[[[[]],[]]],[[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[3,2,1,1,1]
[[[[[[[]]]]],[[]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[2,2,1,1,1,1]
[[[[],[],[[[]]]],[]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[4,1,1,1,1]
[[[[],[[]],[],[]],[]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[5,1,1,1]
[[[[],[[],[]],[]],[]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[5,1,1,1]
[[[[],[[[]]],[]],[]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[4,1,1,1,1]
[[[[],[[],[],[]]],[]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[5,1,1,1]
[[[[],[[],[[]]]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[4,1,1,1,1]
[[[[[]],[[]],[]],[]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[4,2,1,1]
[[[[[]],[[[]]]],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[3,2,1,1,1]
[[[[[[]]],[[]]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[3,2,1,1,1]
[[[[[],[],[]],[]],[]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[5,1,1,1]
[[[[[],[[]]],[]],[]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[4,1,1,1,1]
[[[[[[]],[]],[]],[]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[4,1,1,1,1]
[[[[[[[]]]],[]],[]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[3,1,1,1,1,1]
[[[[[],[],[],[]]],[]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[5,1,1,1]
[[[[[],[[]],[]]],[]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[4,1,1,1,1]
[[[[[],[[[]]]]],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[3,1,1,1,1,1]
[[[[],[],[[[]]],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[4,1,1,1,1]
[[[[],[[],[],[],[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[[[[],[[],[[],[]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[[[[],[[],[[[]]]]]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[[[[],[[[[]]],[]]]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[3,1,1,1,1,1]
[[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[[[[[]],[[]],[[]]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[3,3,1,1]
[[[[[],[]],[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[4,2,1,1]
[[[[[[]]],[[],[]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[3,2,1,1,1]
[[[[[[[]]]],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[3,1,1,1,1,1]
[[[[[],[],[],[]],[]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[5,1,1,1]
[[[[[[]],[],[]],[]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[4,1,1,1,1]
[[[[[[],[[]]]],[]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[3,1,1,1,1,1]
[[[[[[[[]]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[2,1,1,1,1,1,1]
[[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[[[[[],[],[],[[]]]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[[[[[],[],[[]],[]]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[4,1,1,1,1]
[[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[4,1,1,1,1]
[[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[4,1,1,1,1]
[[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[3,1,1,1,1,1]
[[[[[],[[[[]]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[]],[],[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[4,1,1,1,1]
[[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[3,2,1,1,1]
[[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[4,1,1,1,1]
[[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[3,1,1,1,1,1]
[[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[4,1,1,1,1]
[[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[[[[[[],[],[[]]]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[],[[]],[]]]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[],[[],[]]]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[],[[[]]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[]],[],[]]]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[],[],[]]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[[[[[[[],[[]]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[[]],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[[],[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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.