Identifier
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1
[[]]=>[.,.]=>[1]=>[1]
[[],[]]=>[[.,.],.]=>[1,2]=>[2]
[[[]]]=>[.,[.,.]]=>[2,1]=>[1,1]
[[],[],[]]=>[[[.,.],.],.]=>[1,2,3]=>[3]
[[],[[]]]=>[[.,.],[.,.]]=>[1,3,2]=>[2,1]
[[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>[1,2]
[[[],[]]]=>[.,[[.,.],.]]=>[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]=>[2,2]
[[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1]
[[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,1,1]
[[[]],[],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[1,3]
[[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[1,2,1]
[[[],[]],[]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,2]
[[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[1,1,2]
[[[],[],[]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]
[[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[2,1,1]
[[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,2,1]
[[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[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]=>[3,2]
[[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1]
[[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,1,1]
[[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3]
[[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[2,2,1]
[[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,2]
[[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[2,1,2]
[[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[4,1]
[[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,1,1]
[[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,2,1]
[[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,1,1]
[[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,1,1,1]
[[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[1,4]
[[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[1,3,1]
[[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[1,2,2]
[[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[1,3,1]
[[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[1,2,1,1]
[[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3]
[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[1,1,3]
[[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[2,2,1]
[[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[1,1,2,1]
[[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[3,2]
[[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[2,1,2]
[[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[1,2,2]
[[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,1,2]
[[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[1,1,1,2]
[[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]
[[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[3,1,1]
[[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[2,2,1]
[[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,1,1]
[[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[2,1,1,1]
[[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,1]
[[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,2,1,1]
[[[[],[]],[]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[2,2,1]
[[[[[]]],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,1,2,1]
[[[[],[],[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[[[[],[[]]]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,1,1,1]
[[[[[]],[]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,1,1]
[[[[[],[]]]]]=>[.,[.,[.,[[.,.],.]]]]=>[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]=>[4,2]
[[],[],[],[[],[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1]
[[],[],[],[[[]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,1,1]
[[],[],[[]],[],[]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[3,3]
[[],[],[[]],[[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,2,1]
[[],[],[[],[]],[]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,2]
[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,1,2]
[[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[5,1]
[[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[4,1,1]
[[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,2,1]
[[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[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]=>[2,4]
[[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[2,3,1]
[[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[2,2,2]
[[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[2,3,1]
[[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[2,2,1,1]
[[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,3]
[[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[2,1,3]
[[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,2,1]
[[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[2,1,2,1]
[[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[4,2]
[[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,1,2]
[[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[2,2,2]
[[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,1,2]
[[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[2,1,1,2]
[[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[5,1]
[[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[4,1,1]
[[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,2,1]
[[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[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]=>[2,3,1]
[[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,2,1,1]
[[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,2,1]
[[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,1,2,1]
[[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[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]=>[2,2,1,1]
[[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[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]=>[1,5]
[[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[1,4,1]
[[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[1,3,2]
[[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[1,4,1]
[[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[1,3,1,1]
[[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[1,2,3]
[[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[1,2,2,1]
[[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[1,3,2]
[[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[1,2,1,2]
[[[]],[[],[],[]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[1,4,1]
[[[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[1,3,1,1]
[[[]],[[[]],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[1,2,2,1]
[[[]],[[[],[]]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[1,3,1,1]
[[[]],[[[[]]]]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[[[],[]],[],[],[]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,4]
[[[[]]],[],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[1,1,4]
[[[],[]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[2,3,1]
[[[[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[1,1,3,1]
[[[],[]],[[]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[2,2,2]
[[[[]]],[[]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[1,1,2,2]
[[[],[]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[2,3,1]
[[[],[]],[[[]]]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[2,2,1,1]
[[[[]]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[1,1,3,1]
[[[[]]],[[[]]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[[[],[],[]],[],[]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[3,3]
[[[],[[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[2,1,3]
[[[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[1,2,3]
[[[[],[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,1,3]
[[[[[]]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[1,1,1,3]
[[[],[],[]],[[]]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[3,2,1]
[[[],[[]]],[[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[2,1,2,1]
[[[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[1,2,2,1]
[[[[],[]]],[[]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,1,2,1]
[[[[[]]]],[[]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[[[],[],[],[]],[]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[4,2]
[[[],[],[[]]],[]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[3,1,2]
[[[],[[]],[]],[]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[2,2,2]
[[[],[[],[]]],[]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,1,2]
[[[],[[[]]]],[]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[2,1,1,2]
[[[[]],[],[]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[1,3,2]
[[[[]],[[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[1,2,1,2]
[[[[],[]],[]],[]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[2,2,2]
[[[[[]]],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[1,1,2,2]
[[[[],[],[]]],[]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,2]
[[[[],[[]]]],[]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,1,1,2]
[[[[[]],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[1,2,1,2]
[[[[[],[]]]],[]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,1,1,2]
[[[[[[]]]]],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[[[],[],[],[],[]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]
[[[],[],[],[[]]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[4,1,1]
[[[],[],[[]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[3,2,1]
[[[],[],[[],[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[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]=>[2,3,1]
[[[],[[]],[[]]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[2,2,1,1]
[[[],[[],[]],[]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[3,2,1]
[[[],[[[]]],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[2,1,2,1]
[[[],[[],[],[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[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]=>[2,2,1,1]
[[[],[[[],[]]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[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]=>[1,4,1]
[[[[]],[],[[]]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,3,1,1]
[[[[]],[[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,2,2,1]
[[[[]],[[],[]]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,3,1,1]
[[[[]],[[[]]]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,2,1,1,1]
[[[[],[]],[],[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[2,3,1]
[[[[[]]],[],[]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,1,3,1]
[[[[],[]],[[]]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[2,2,1,1]
[[[[[]]],[[]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,1,2,1,1]
[[[[],[],[]],[]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,2,1]
[[[[],[[]]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[2,1,2,1]
[[[[[]],[]],[]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,2,2,1]
[[[[[],[]]],[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[2,1,2,1]
[[[[[[]]]],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[[[[],[],[],[]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[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]=>[2,2,1,1]
[[[[],[[],[]]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[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]=>[1,3,1,1]
[[[[[]],[[]]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,1,1,1]
[[[[[],[]],[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,2,1,1]
[[[[[[]]],[]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[[[[[],[],[]]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[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]=>[1,2,1,1,1]
[[[[[[],[]]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[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]=>[5,2]
[[],[],[],[],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[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]=>[4,3]
[[],[],[],[[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[4,2,1]
[[],[],[],[[],[]],[]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,2]
[[],[],[],[[[]]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[4,1,2]
[[],[],[],[[],[],[]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[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]=>[4,2,1]
[[],[],[],[[[],[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[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]=>[3,4]
[[],[],[[]],[],[[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[3,3,1]
[[],[],[[]],[[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,2,2]
[[],[],[[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,3,1]
[[],[],[[]],[[[]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[3,2,1,1]
[[],[],[[],[]],[],[]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,3]
[[],[],[[[]]],[],[]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,1,3]
[[],[],[[],[]],[[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[4,2,1]
[[],[],[[[]]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[3,1,2,1]
[[],[],[[],[],[]],[]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[5,2]
[[],[],[[],[[]]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[4,1,2]
[[],[],[[[]],[]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,2,2]
[[],[],[[[],[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[4,1,2]
[[],[],[[[[]]]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[[],[],[[],[],[],[]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[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]=>[4,2,1]
[[],[],[[],[[],[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[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]=>[3,3,1]
[[],[],[[[]],[[]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,2,1,1]
[[],[],[[[],[]],[]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[4,2,1]
[[],[],[[[[]]],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,1,2,1]
[[],[],[[[],[],[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[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]=>[3,2,1,1]
[[],[],[[[[],[]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[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]=>[2,5]
[[],[[]],[],[],[[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[2,4,1]
[[],[[]],[],[[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[2,3,2]
[[],[[]],[],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[2,4,1]
[[],[[]],[],[[[]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[2,3,1,1]
[[],[[]],[[]],[],[]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[2,2,3]
[[],[[]],[[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[2,2,2,1]
[[],[[]],[[],[]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[2,3,2]
[[],[[]],[[[]]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[2,2,1,2]
[[],[[]],[[],[],[]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[2,4,1]
[[],[[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[2,3,1,1]
[[],[[]],[[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[2,2,2,1]
[[],[[]],[[[],[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[2,3,1,1]
[[],[[]],[[[[]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[[],[[],[]],[],[],[]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,4]
[[],[[[]]],[],[],[]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[2,1,4]
[[],[[],[]],[],[[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[3,3,1]
[[],[[[]]],[],[[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[2,1,3,1]
[[],[[],[]],[[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,2,2]
[[],[[[]]],[[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[2,1,2,2]
[[],[[],[]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,3,1]
[[],[[],[]],[[[]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[3,2,1,1]
[[],[[[]]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[2,1,3,1]
[[],[[[]]],[[[]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[[],[[],[],[]],[],[]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[4,3]
[[],[[],[[]]],[],[]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,1,3]
[[],[[[]],[]],[],[]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[2,2,3]
[[],[[[],[]]],[],[]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,1,3]
[[],[[[[]]]],[],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[[],[[],[],[]],[[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[4,2,1]
[[],[[],[[]]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[3,1,2,1]
[[],[[[]],[]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[2,2,2,1]
[[],[[[],[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[3,1,2,1]
[[],[[[[]]]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[[],[[],[],[],[]],[]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[5,2]
[[],[[],[],[[]]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[4,1,2]
[[],[[],[[]],[]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,2,2]
[[],[[],[[],[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[4,1,2]
[[],[[],[[[]]]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[3,1,1,2]
[[],[[[]],[],[]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[2,3,2]
[[],[[[]],[[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[2,2,1,2]
[[],[[[],[]],[]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,2,2]
[[],[[[[]]],[]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[2,1,2,2]
[[],[[[],[],[]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,1,2]
[[],[[[],[[]]]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[3,1,1,2]
[[],[[[[]],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[2,2,1,2]
[[],[[[[],[]]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[3,1,1,2]
[[],[[[[[]]]]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[[],[[],[],[],[],[]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[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]=>[4,2,1]
[[],[[],[],[[],[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[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]=>[3,3,1]
[[],[[],[[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[3,2,1,1]
[[],[[],[[],[]],[]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[4,2,1]
[[],[[],[[[]]],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[3,1,2,1]
[[],[[],[[],[],[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[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]=>[3,2,1,1]
[[],[[],[[[],[]]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[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]=>[2,4,1]
[[],[[[]],[],[[]]]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,3,1,1]
[[],[[[]],[[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,2,2,1]
[[],[[[]],[[],[]]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,3,1,1]
[[],[[[]],[[[]]]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,2,1,1,1]
[[],[[[],[]],[],[]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,3,1]
[[],[[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,1,3,1]
[[],[[[],[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[3,2,1,1]
[[],[[[[]]],[[]]]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,1,2,1,1]
[[],[[[],[],[]],[]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,2,1]
[[],[[[],[[]]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[3,1,2,1]
[[],[[[[]],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,2,2,1]
[[],[[[[],[]]],[]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[3,1,2,1]
[[],[[[[[]]]],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[[],[[[],[],[],[]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[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]=>[3,2,1,1]
[[],[[[],[[],[]]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[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]=>[2,3,1,1]
[[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,2,1,1,1]
[[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[3,2,1,1]
[[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[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]=>[2,2,1,1,1]
[[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[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]=>[1,6]
[[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[1,5,1]
[[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[1,4,2]
[[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[1,5,1]
[[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[1,3,3]
[[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[1,4,2]
[[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[1,5,1]
[[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[1,4,1,1]
[[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[1,3,2,1]
[[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[1,4,1,1]
[[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[1,2,4]
[[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[1,2,3,1]
[[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[[[]],[[],[]],[],[]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[1,3,3]
[[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[[[]],[[],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[1,3,2,1]
[[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[1,4,2]
[[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[1,3,1,2]
[[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[1,2,2,2]
[[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[1,3,1,2]
[[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[1,5,1]
[[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[1,4,1,1]
[[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[1,3,2,1]
[[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[1,4,1,1]
[[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[1,3,1,1,1]
[[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[1,2,3,1]
[[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[1,2,2,1,1]
[[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[1,3,2,1]
[[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[1,2,1,2,1]
[[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[1,4,1,1]
[[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[1,3,1,1,1]
[[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[1,2,2,1,1]
[[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[1,3,1,1,1]
[[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,5]
[[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[1,1,5]
[[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[2,4,1]
[[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[2,3,2]
[[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[2,4,1]
[[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[2,3,1,1]
[[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[1,1,4,1]
[[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[2,2,3]
[[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[2,2,2,1]
[[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[2,3,2]
[[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[2,2,1,2]
[[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[1,1,3,2]
[[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[2,4,1]
[[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[2,3,1,1]
[[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[2,2,2,1]
[[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[2,3,1,1]
[[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[2,2,1,1,1]
[[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[1,1,4,1]
[[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[1,1,3,1,1]
[[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[1,1,2,2,1]
[[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[1,1,3,1,1]
[[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[3,4]
[[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[2,1,4]
[[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[1,2,4]
[[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,1,4]
[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[3,3,1]
[[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[2,1,3,1]
[[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[1,2,3,1]
[[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[2,1,3,1]
[[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[3,2,2]
[[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[2,1,2,2]
[[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[1,2,2,2]
[[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,1,2,2]
[[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[3,3,1]
[[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[3,2,1,1]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[2,1,3,1]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[2,1,2,1,1]
[[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[1,2,3,1]
[[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[1,2,2,1,1]
[[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,1,3,1]
[[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,1,2,1,1]
[[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[1,1,1,3,1]
[[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[4,3]
[[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[3,1,3]
[[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[2,2,3]
[[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,1,3]
[[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[2,1,1,3]
[[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[1,3,3]
[[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[1,2,1,3]
[[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[2,2,3]
[[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,3]
[[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,1,1,3]
[[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[4,2,1]
[[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[3,1,2,1]
[[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[2,2,2,1]
[[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[3,1,2,1]
[[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[2,1,1,2,1]
[[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[1,3,2,1]
[[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[1,2,1,2,1]
[[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[2,2,2,1]
[[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[1,1,2,2,1]
[[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[3,1,2,1]
[[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[2,1,1,2,1]
[[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[1,2,1,2,1]
[[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[2,1,1,2,1]
[[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[5,2]
[[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[4,1,2]
[[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[3,2,2]
[[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[4,1,2]
[[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[3,1,1,2]
[[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[2,3,2]
[[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[2,2,1,2]
[[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[3,2,2]
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[2,1,2,2]
[[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,1,2]
[[[],[[],[[]]]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[3,1,1,2]
[[[],[[[]],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[2,2,1,2]
[[[],[[[],[]]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[3,1,1,2]
[[[],[[[[]]]]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[[[[]],[],[],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[1,4,2]
[[[[]],[],[[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[1,3,1,2]
[[[[]],[[]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[1,2,2,2]
[[[[]],[[],[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[1,3,1,2]
[[[[]],[[[]]]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[1,2,1,1,2]
[[[[],[]],[],[]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[2,3,2]
[[[[[]]],[],[]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[[[[],[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[2,2,1,2]
[[[[[]]],[[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[1,1,2,1,2]
[[[[],[],[]],[]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,2,2]
[[[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[2,1,2,2]
[[[[[]],[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[[[[[],[]]],[]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[[[[[[]]]],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[[[[],[],[],[]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[4,1,2]
[[[[],[],[[]]]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[3,1,1,2]
[[[[],[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[2,2,1,2]
[[[[],[[],[]]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[3,1,1,2]
[[[[],[[[]]]]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[[[[[]],[],[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[[[[[]],[[]]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[1,2,1,1,2]
[[[[[],[]],[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[[[[[[]]],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[[[[[],[],[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[[[[[],[[]]]]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[[[[[[]],[]]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[[[[[[],[]]]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[[[[[[[]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[[[],[],[],[],[],[]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[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]=>[4,2,1]
[[[],[],[],[[],[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[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]=>[3,3,1]
[[[],[],[[]],[[]]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[3,2,1,1]
[[[],[],[[],[]],[]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[4,2,1]
[[[],[],[[[]]],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[3,1,2,1]
[[[],[],[[],[],[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[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]=>[3,2,1,1]
[[[],[],[[[],[]]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[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]=>[2,4,1]
[[[],[[]],[],[[]]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[2,3,1,1]
[[[],[[]],[[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[2,2,2,1]
[[[],[[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[2,3,1,1]
[[[],[[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[2,2,1,1,1]
[[[],[[],[]],[],[]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[3,3,1]
[[[],[[[]]],[],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[2,1,3,1]
[[[],[[],[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[3,2,1,1]
[[[],[[[]]],[[]]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[2,1,2,1,1]
[[[],[[],[],[]],[]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[4,2,1]
[[[],[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[3,1,2,1]
[[[],[[[]],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[2,2,2,1]
[[[],[[[],[]]],[]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[3,1,2,1]
[[[],[[[[]]]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[[[],[[],[],[],[]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[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]=>[3,2,1,1]
[[[],[[],[[],[]]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[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]=>[2,3,1,1]
[[[],[[[]],[[]]]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[2,2,1,1,1]
[[[],[[[],[]],[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,1,1]
[[[],[[[[]]],[]]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[[[],[[[],[],[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[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]=>[2,2,1,1,1]
[[[],[[[[],[]]]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[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]=>[1,5,1]
[[[[]],[],[],[[]]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,4,1,1]
[[[[]],[],[[]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,3,2,1]
[[[[]],[],[[],[]]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,4,1,1]
[[[[]],[],[[[]]]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,3,1,1,1]
[[[[]],[[]],[],[]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,2,3,1]
[[[[]],[[]],[[]]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,2,2,1,1]
[[[[]],[[],[]],[]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,3,2,1]
[[[[]],[[[]]],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,2,1,2,1]
[[[[]],[[],[],[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,1,1]
[[[[]],[[],[[]]]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,3,1,1,1]
[[[[]],[[[]],[]]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,2,2,1,1]
[[[[]],[[[],[]]]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,3,1,1,1]
[[[[]],[[[[]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]
[[[[],[]],[],[],[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[2,4,1]
[[[[[]]],[],[],[]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[[[[],[]],[],[[]]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[2,3,1,1]
[[[[[]]],[],[[]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,1,3,1,1]
[[[[],[]],[[]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[2,2,2,1]
[[[[[]]],[[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,1,2,2,1]
[[[[],[]],[[],[]]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[2,3,1,1]
[[[[],[]],[[[]]]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[2,2,1,1,1]
[[[[[]]],[[],[]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,1,3,1,1]
[[[[[]]],[[[]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]
[[[[],[],[]],[],[]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,3,1]
[[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[2,1,3,1]
[[[[[]],[]],[],[]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[[[[[],[]]],[],[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[[[[[[]]]],[],[]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[[[[],[],[]],[[]]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[3,2,1,1]
[[[[],[[]]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[2,1,2,1,1]
[[[[[]],[]],[[]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,2,2,1,1]
[[[[[],[]]],[[]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[2,1,2,1,1]
[[[[[[]]]],[[]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]
[[[[],[],[],[]],[]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[4,2,1]
[[[[],[],[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[3,1,2,1]
[[[[],[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[2,2,2,1]
[[[[],[[],[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[3,1,2,1]
[[[[],[[[]]]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[[[[[]],[],[]],[]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[[[[[]],[[]]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,2,1,2,1]
[[[[[],[]],[]],[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[[[[[[]]],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[[[[[],[],[]]],[]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[[[[[],[[]]]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[[[[[[]],[]]],[]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[[[[[[],[]]]],[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[[[[[[[]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[[[[],[],[],[],[]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[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]=>[3,2,1,1]
[[[[],[],[[],[]]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[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]=>[2,3,1,1]
[[[[],[[]],[[]]]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,2,1,1,1]
[[[[],[[],[]],[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[3,2,1,1]
[[[[],[[[]]],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[[[[],[[],[],[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[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]=>[2,2,1,1,1]
[[[[],[[[],[]]]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[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]=>[1,4,1,1]
[[[[[]],[],[[]]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,3,1,1,1]
[[[[[]],[[]],[]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,2,1,1]
[[[[[]],[[],[]]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,3,1,1,1]
[[[[[]],[[[]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]
[[[[[],[]],[],[]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[[[[[[]]],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[[[[[],[]],[[]]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,2,1,1,1]
[[[[[[]]],[[]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]
[[[[[],[],[]],[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[[[[[],[[]]],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[[[[[[]],[]],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[[[[[[],[]]],[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[[[[[[[]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[[[[[],[],[],[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[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]=>[2,2,1,1,1]
[[[[[],[[],[]]]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[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]=>[1,3,1,1,1]
[[[[[[]],[[]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]
[[[[[[],[]],[]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[[[[[[[]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[[[[[[],[],[]]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[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]=>[1,2,1,1,1,1]
[[[[[[[],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[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]=>[6,2]
[[],[],[],[],[],[[],[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[7,1]
[[],[],[],[],[],[[[]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[[],[],[],[],[[]],[],[]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[5,3]
[[],[],[],[],[[]],[[]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[5,2,1]
[[],[],[],[],[[],[]],[]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[6,2]
[[],[],[],[],[[[]]],[]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[[],[],[],[],[[],[],[]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[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]=>[5,2,1]
[[],[],[],[],[[[],[]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[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]=>[4,4]
[[],[],[],[[]],[],[[]]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[[],[],[],[[]],[[]],[]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[[],[],[],[[]],[[],[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[4,3,1]
[[],[],[],[[]],[[[]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[[],[],[],[[],[]],[],[]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[5,3]
[[],[],[],[[[]]],[],[]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[[],[],[],[[],[]],[[]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[5,2,1]
[[],[],[],[[[]]],[[]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[[],[],[],[[],[],[]],[]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[6,2]
[[],[],[],[[],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[5,1,2]
[[],[],[],[[[]],[]],[]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[4,2,2]
[[],[],[],[[[],[]]],[]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[5,1,2]
[[],[],[],[[[[]]]],[]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[[],[],[],[[],[],[],[]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[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]=>[5,2,1]
[[],[],[],[[],[[],[]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[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]=>[4,3,1]
[[],[],[],[[[]],[[]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[4,2,1,1]
[[],[],[],[[[],[]],[]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[5,2,1]
[[],[],[],[[[[]]],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[[],[],[],[[[],[],[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[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]=>[4,2,1,1]
[[],[],[],[[[[],[]]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[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]=>[3,5]
[[],[],[[]],[],[],[[]]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[3,4,1]
[[],[],[[]],[],[[],[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[3,4,1]
[[],[],[[]],[[]],[],[]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[[],[],[[]],[[]],[[]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[[],[],[[]],[[],[]],[]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[3,3,2]
[[],[],[[]],[[[]]],[]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[[],[],[[]],[[],[],[]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[3,4,1]
[[],[],[[]],[[],[[]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[3,3,1,1]
[[],[],[[]],[[[]],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[3,2,2,1]
[[],[],[[]],[[[],[]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[3,3,1,1]
[[],[],[[]],[[[[]]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[[],[],[[],[]],[],[],[]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[4,4]
[[],[],[[[]]],[],[],[]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[[],[],[[],[]],[],[[]]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[4,3,1]
[[],[],[[[]]],[],[[]]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[[],[],[[[]]],[[]],[]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[[],[],[[],[]],[[],[]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[4,3,1]
[[],[],[[],[]],[[[]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[4,2,1,1]
[[],[],[[[]]],[[],[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[3,1,3,1]
[[],[],[[[]]],[[[]]]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[[],[],[[],[],[]],[],[]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[5,3]
[[],[],[[],[[]]],[],[]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[4,1,3]
[[],[],[[[],[]]],[],[]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[4,1,3]
[[],[],[[[[]]]],[],[]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[[],[],[[],[],[]],[[]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[5,2,1]
[[],[],[[[],[]]],[[]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,2,5,6,4,3,8,7]=>[4,1,2,1]
[[],[],[[[[]]]],[[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[[],[],[[],[],[],[]],[]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[6,2]
[[],[],[[],[],[[]]],[]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,2,4,5,7,6,3,8]=>[5,1,2]
[[],[],[[],[[],[]]],[]]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[5,1,2]
[[],[],[[],[[[]]]],[]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[[],[],[[[]],[],[]],[]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[3,3,2]
[[],[],[[[],[]],[]],[]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[4,2,2]
[[],[],[[[],[],[]]],[]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[5,1,2]
[[],[],[[[],[[]]]],[]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[[],[],[[[[[]]]]],[]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[[],[],[[],[],[],[],[]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[7,1]
[[],[],[[],[],[],[[]]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[[],[],[[],[],[[],[]]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[[],[],[[],[],[[[]]]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[[],[],[[],[[]],[],[]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[4,3,1]
[[],[],[[],[[]],[[]]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[4,2,1,1]
[[],[],[[],[[],[]],[]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[5,2,1]
[[],[],[[],[[[]]],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[4,1,2,1]
[[],[],[[],[[],[],[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[[],[],[[],[[],[[]]]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[[],[],[[],[[[],[]]]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[[],[],[[],[[[[]]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[[],[],[[[]],[],[],[]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,4,1]
[[],[],[[[]],[],[[]]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>[3,3,1,1]
[[],[],[[[]],[[[]]]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]
[[],[],[[[],[]],[],[]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[4,3,1]
[[],[],[[[[]]],[],[]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[[],[],[[[],[]],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,2,5,6,4,8,7,3]=>[4,2,1,1]
[[],[],[[[[]]],[[]]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[3,1,2,1,1]
[[],[],[[[],[],[]],[]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[5,2,1]
[[],[],[[[],[[]]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[[],[],[[[],[],[],[]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[6,1,1]
[[],[],[[[],[],[[]]]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[[],[],[[[],[[]],[]]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[4,2,1,1]
[[],[],[[[],[[],[]]]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[5,1,1,1]
[[],[],[[[],[[[]]]]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[[],[],[[[[]],[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[3,3,1,1]
[[],[],[[[[]],[[]]]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]
[[],[],[[[[],[]],[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[4,2,1,1]
[[],[],[[[[[]]],[]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[[],[],[[[[],[],[]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[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]=>[2,6]
[[],[[]],[],[],[[]],[]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[[],[[]],[],[],[[],[]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[2,5,1]
[[],[[]],[],[],[[[]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[2,4,1,1]
[[],[[]],[],[[]],[],[]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[2,3,3]
[[],[[]],[],[[]],[[]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[[],[[]],[],[[[]]],[]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[[],[[]],[],[[],[],[]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[2,5,1]
[[],[[]],[],[[],[[]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[2,4,1,1]
[[],[[]],[],[[[]],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[2,3,2,1]
[[],[[]],[],[[[[]]]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[[],[[]],[[]],[],[],[]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[[],[[]],[[]],[[]],[]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[[],[[]],[[]],[[],[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[2,2,3,1]
[[],[[]],[[]],[[[]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[[],[[]],[[],[]],[],[]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[2,3,3]
[[],[[]],[[[]]],[],[]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[2,2,1,3]
[[],[[]],[[[]]],[[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]
[[],[[]],[[],[],[]],[]]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[2,4,2]
[[],[[]],[[],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[2,3,1,2]
[[],[[]],[[[]],[]],[]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[2,2,2,2]
[[],[[]],[[[],[]]],[]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[2,3,1,2]
[[],[[]],[[[[]]]],[]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[[],[[]],[[],[],[],[]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[2,5,1]
[[],[[]],[[],[[]],[]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[2,3,2,1]
[[],[[]],[[],[[],[]]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[2,4,1,1]
[[],[[]],[[],[[[]]]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]
[[],[[]],[[[]],[],[]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[2,2,3,1]
[[],[[]],[[[]],[[]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[2,2,2,1,1]
[[],[[]],[[[],[]],[]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[2,3,2,1]
[[],[[]],[[[[]]],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[2,2,1,2,1]
[[],[[]],[[[],[],[]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>[2,4,1,1]
[[],[[]],[[[],[[]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[2,3,1,1,1]
[[],[[]],[[[[],[]]]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]
[[],[[]],[[[[[]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[[],[[],[]],[],[],[],[]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[3,5]
[[],[[[]]],[],[],[],[]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[[],[[],[]],[],[],[[]]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[3,4,1]
[[],[[[]]],[],[],[[]]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[2,1,4,1]
[[],[[],[]],[],[[]],[]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[3,3,2]
[[],[[[]]],[],[[]],[]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[2,1,3,2]
[[],[[],[]],[],[[],[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[3,4,1]
[[],[[],[]],[],[[[]]]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[3,3,1,1]
[[],[[[]]],[],[[],[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[2,1,4,1]
[[],[[[]]],[],[[[]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[[],[[[]]],[[]],[],[]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[[],[[],[]],[[]],[[]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[3,2,2,1]
[[],[[[]]],[[]],[[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[[],[[],[]],[[],[]],[]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,3,2]
[[],[[],[]],[[[]]],[]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[3,2,1,2]
[[],[[[]]],[[],[]],[]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[2,1,3,2]
[[],[[[]]],[[[]]],[]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[[],[[],[]],[[],[],[]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,4,1]
[[],[[],[]],[[],[[]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[3,3,1,1]
[[],[[],[]],[[[]],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[3,2,2,1]
[[],[[],[]],[[[],[]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[3,3,1,1]
[[],[[],[]],[[[[]]]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]
[[],[[[]]],[[],[],[]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[2,1,4,1]
[[],[[[]]],[[],[[]]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[2,1,3,1,1]
[[],[[[]]],[[[]],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[2,1,2,2,1]
[[],[[[]]],[[[[]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[[],[[],[],[]],[],[],[]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[4,4]
[[],[[],[[]]],[],[],[]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[3,1,4]
[[],[[[[]]]],[],[],[]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[[],[[],[],[]],[],[[]]]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>[4,3,1]
[[],[[],[[]]],[],[[]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[3,1,3,1]
[[],[[[[]]]],[],[[]]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[[],[[],[],[]],[[]],[]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[4,2,2]
[[],[[],[[]]],[[]],[]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[3,1,2,2]
[[],[[[]],[]],[[]],[]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[2,2,2,2]
[[],[[[],[]]],[[]],[]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[3,1,2,2]
[[],[[[[]]]],[[]],[]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]
[[],[[],[],[]],[[],[]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[4,3,1]
[[],[[],[],[]],[[[]]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[4,2,1,1]
[[],[[],[[]]],[[],[]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[3,1,3,1]
[[],[[[]],[]],[[],[]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>[2,2,3,1]
[[],[[[]],[]],[[[]]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]
[[],[[[[]]]],[[],[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[2,1,1,3,1]
[[],[[[[]]]],[[[]]]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[[],[[],[[],[]]],[],[]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[4,1,3]
[[],[[],[[[]]]],[],[]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[3,1,1,3]
[[],[[[]],[[]]],[],[]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[2,2,1,3]
[[],[[[[]]],[]],[],[]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[[],[[[],[],[]]],[],[]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[4,1,3]
[[],[[[],[[]]]],[],[]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[3,1,1,3]
[[],[[[[]],[]]],[],[]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[[],[[[[],[]]]],[],[]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[3,1,1,3]
[[],[[],[],[],[]],[[]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>[5,2,1]
[[],[[],[[[]]]],[[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>[3,1,1,2,1]
[[],[[[],[],[]]],[[]]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,4,5,6,3,2,8,7]=>[4,1,2,1]
[[],[[[[]],[]]],[[]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]
[[],[[],[],[],[],[]],[]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[6,2]
[[],[[],[[]],[[]]],[]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[3,2,1,2]
[[],[[],[[[]]],[]],[]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[3,1,2,2]
[[],[[],[[],[],[]]],[]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[5,1,2]
[[],[[],[[],[[]]]],[]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[4,1,1,2]
[[],[[],[[[],[]]]],[]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[4,1,1,2]
[[],[[[]],[],[[]]],[]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[2,3,1,2]
[[],[[[]],[[]],[]],[]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[2,2,2,2]
[[],[[[],[]],[],[]],[]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>[3,3,2]
[[],[[[[]]],[],[]],[]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[2,1,3,2]
[[],[[[],[]],[[]]],[]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[3,2,1,2]
[[],[[[[]],[]],[]],[]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[[],[[[[[]]]],[]],[]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[[],[[[],[],[],[]]],[]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[5,1,2]
[[],[[[],[],[[]]]],[]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[4,1,1,2]
[[],[[[],[[]],[]]],[]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[3,2,1,2]
[[],[[[[],[],[]]]],[]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[[],[[],[],[],[],[],[]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[7,1]
[[],[[],[],[],[],[[]]]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[6,1,1]
[[],[[],[],[],[[[]]]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[[],[[],[],[[]],[],[]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[4,3,1]
[[],[[],[],[[],[]],[]]]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[5,2,1]
[[],[[],[],[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[4,1,2,1]
[[],[[],[],[[],[],[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[[],[[],[],[[],[[]]]]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[[],[[],[],[[[]],[]]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[[],[[],[],[[[],[]]]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[5,1,1,1]
[[],[[],[],[[[[]]]]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[[],[[],[[]],[],[],[]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[3,4,1]
[[],[[],[[]],[[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[3,2,2,1]
[[],[[],[[]],[[],[]]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[3,3,1,1]
[[],[[],[[]],[[[]]]]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[3,2,1,1,1]
[[],[[],[[],[]],[],[]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[4,3,1]
[[],[[],[[[]]],[[]]]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]
[[],[[],[[],[],[]],[]]]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[5,2,1]
[[],[[],[[],[[]]],[]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[4,1,2,1]
[[],[[],[[],[],[],[]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[[],[[],[[],[],[[]]]]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[[],[[],[[],[[]],[]]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[[],[[],[[],[[],[]]]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[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]
[[],[[],[[[]],[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[[],[[],[[[]],[[]]]]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]
[[],[[],[[[],[]],[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[[],[[],[[[],[],[]]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[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]
[[],[[],[[[[]],[]]]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[[],[[],[[[[[]]]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[[],[[[]],[],[[]],[]]]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[2,3,2,1]
[[],[[[]],[],[[],[]]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[2,4,1,1]
[[],[[[]],[],[[[]]]]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]
[[],[[[]],[[]],[],[]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[2,2,3,1]
[[],[[[]],[[]],[[]]]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]
[[],[[[]],[[],[]],[]]]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[2,3,2,1]
[[],[[[]],[[],[],[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[2,4,1,1]
[[],[[[]],[[],[[]]]]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]
[[],[[[]],[[[]],[]]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,2,2,1,1]
[[],[[[]],[[[],[]]]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]
[[],[[[]],[[[[]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]
[[],[[[],[]],[],[],[]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[3,4,1]
[[],[[[[]]],[],[],[]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[[],[[[],[]],[],[[]]]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[3,3,1,1]
[[],[[[[]]],[],[[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[2,1,3,1,1]
[[],[[[[]]],[[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,5,4,3,7,6,8,2]=>[2,1,2,2,1]
[[],[[[],[]],[[[]]]]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]
[[],[[[[]]],[[],[]]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[2,1,3,1,1]
[[],[[[[]]],[[[]]]]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]
[[],[[[[]],[]],[],[]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[[],[[[[[]]]],[],[]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[[],[[[],[[]]],[[]]]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[3,1,2,1,1]
[[],[[[[],[]]],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]
[[],[[[[[]]]],[[]]]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]
[[],[[[],[],[],[]],[]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[5,2,1]
[[],[[[],[],[[]]],[]]]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[4,1,2,1]
[[],[[[],[[],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[4,1,2,1]
[[],[[[],[[[]]]],[]]]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]
[[],[[[[]],[],[]],[]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[[],[[[[]],[[]]],[]]]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[2,2,1,2,1]
[[],[[[[],[[]]]],[]]]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]
[[],[[[[[]],[]]],[]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[[],[[[[[],[]]]],[]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[3,1,1,2,1]
[[],[[[[[[]]]]],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[2,1,1,1,2,1]
[[],[[[],[],[],[],[]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[[],[[[],[],[[],[]]]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[[],[[[],[],[[[]]]]]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]
[[],[[[],[[]],[[]]]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]
[[],[[[],[[],[]],[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[4,2,1,1]
[[],[[[],[[[]]],[]]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[3,1,2,1,1]
[[],[[[],[[],[],[]]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[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]
[[],[[[],[[[]],[]]]]]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[3,2,1,1,1]
[[],[[[],[[[],[]]]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[[],[[[],[[[[]]]]]]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[[],[[[[[]]],[],[]]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[[],[[[[[]],[]],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]
[[],[[[[[[]]]],[]]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[[],[[[[],[],[],[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[[],[[[[],[],[[]]]]]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[[],[[[[],[[]],[]]]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]
[[],[[[[],[[],[]]]]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[[],[[[[],[[[]]]]]]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[[],[[[[[]],[],[]]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]
[[],[[[[[]],[[]]]]]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]
[[],[[[[[],[]],[]]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[[],[[[[[[]]],[]]]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[[],[[[[[],[],[]]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[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]=>[2,2,1,1,1,1]
[[],[[[[[[],[]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[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]
[[[]],[],[],[],[],[],[]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[1,7]
[[[]],[],[],[],[],[[]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[[[]],[],[],[[]],[],[]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[1,4,3]
[[[]],[],[],[[]],[[]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[1,4,2,1]
[[[]],[],[],[[],[],[]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[1,6,1]
[[[]],[],[],[[[]],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[1,4,2,1]
[[[]],[],[],[[[[]]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[[[]],[],[[]],[],[[]]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[[[]],[],[[]],[[[]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[[[]],[],[[],[]],[],[]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[2,1,3,5,6,4,7,8]=>[1,4,3]
[[[]],[],[[[]]],[],[]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[[[]],[],[[[],[]]],[]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>[1,4,1,2]
[[[]],[],[[[[]]]],[]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]
[[[]],[],[[],[],[],[]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[1,6,1]
[[[]],[],[[],[],[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[2,1,3,5,6,8,7,4]=>[1,5,1,1]
[[[]],[],[[],[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[1,4,2,1]
[[[]],[],[[],[[],[]]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[1,5,1,1]
[[[]],[],[[],[[[]]]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]
[[[]],[],[[[]],[],[]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[1,3,3,1]
[[[]],[],[[[]],[[]]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]
[[[]],[],[[[],[]],[]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[1,4,2,1]
[[[]],[],[[[[]]],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[1,3,1,2,1]
[[[]],[],[[[],[],[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[1,5,1,1]
[[[]],[],[[[],[[]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]
[[[]],[],[[[[]],[]]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]
[[[]],[],[[[[],[]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]
[[[]],[],[[[[[]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[[[]],[[]],[],[],[],[]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[[[]],[[]],[],[],[[]]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[[[]],[[]],[],[[],[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[1,2,4,1]
[[[]],[[]],[[]],[],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[[[]],[[]],[[]],[[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[[[]],[[]],[[],[],[]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[1,2,4,1]
[[[]],[[]],[[],[[]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]
[[[]],[[]],[[[]],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]
[[[]],[[]],[[[],[]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]
[[[]],[[]],[[[[]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[[[]],[[],[]],[],[],[]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[1,3,4]
[[[]],[[[]]],[],[],[]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[[[]],[[],[]],[],[[]]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[1,3,3,1]
[[[]],[[[]]],[],[[]]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[[[]],[[],[]],[[],[]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[2,1,4,5,3,7,8,6]=>[1,3,3,1]
[[[]],[[[]]],[[],[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]
[[[]],[[[]]],[[[]]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]
[[[]],[[],[],[]],[],[]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[2,1,4,5,6,3,7,8]=>[1,4,3]
[[[]],[[],[[]]],[],[]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[1,3,1,3]
[[[]],[[[],[]]],[],[]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[1,3,1,3]
[[[]],[[],[],[]],[[]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[1,4,2,1]
[[[]],[[],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]
[[[]],[[[]],[]],[[]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]
[[[]],[[[],[]]],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]
[[[]],[[[[]]]],[[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[[[]],[[],[[],[]]],[]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[1,4,1,2]
[[[]],[[],[[[]]]],[]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[1,3,1,1,2]
[[[]],[[[]],[],[]],[]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[1,2,3,2]
[[[]],[[[]],[[]]],[]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[2,1,5,4,7,6,3,8]=>[1,2,2,1,2]
[[[]],[[[],[],[]]],[]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>[1,4,1,2]
[[[]],[[],[],[],[],[]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[1,6,1]
[[[]],[[],[],[],[[]]]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[1,5,1,1]
[[[]],[[],[],[[],[]]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[1,5,1,1]
[[[]],[[],[],[[[]]]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]
[[[]],[[],[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]
[[[]],[[],[[],[]],[]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[1,4,2,1]
[[[]],[[],[[[]]],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[1,3,1,2,1]
[[[]],[[],[[],[],[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[1,5,1,1]
[[[]],[[],[[],[[]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]
[[[]],[[],[[[],[]]]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]
[[[]],[[],[[[[]]]]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[1,3,1,1,1,1]
[[[]],[[[]],[],[],[]]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[1,2,4,1]
[[[]],[[[]],[],[[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]
[[[]],[[[]],[[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]
[[[]],[[[]],[[],[]]]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]
[[[]],[[[]],[[[]]]]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[1,2,2,1,1,1]
[[[]],[[[],[]],[],[]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[1,3,3,1]
[[[]],[[[[]]],[],[]]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]
[[[]],[[[],[],[]],[]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[1,4,2,1]
[[[]],[[[],[[]]],[]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[1,3,1,2,1]
[[[]],[[[[]],[]],[]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]
[[[]],[[[],[],[],[]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[1,5,1,1]
[[[]],[[[],[],[[]]]]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]
[[[]],[[[],[[]],[]]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]
[[[]],[[[],[[],[]]]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]
[[[]],[[[],[[[]]]]]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[1,3,1,1,1,1]
[[[]],[[[[]],[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]
[[[]],[[[[]],[[]]]]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]
[[[]],[[[[],[]],[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]
[[[]],[[[[[]]],[]]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]
[[[]],[[[[],[],[]]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]
[[[]],[[[[],[[]]]]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[1,3,1,1,1,1]
[[[]],[[[[[]],[]]]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]
[[[]],[[[[[],[]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[1,3,1,1,1,1]
[[[]],[[[[[[]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[[[],[]],[],[],[],[],[]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,6]
[[[[]]],[],[],[],[],[]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[[[[]]],[],[],[],[[]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[[[[]]],[],[],[[]],[]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[1,1,4,2]
[[[],[]],[],[],[[],[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[2,5,1]
[[[],[]],[],[],[[[]]]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[2,4,1,1]
[[[[]]],[],[],[[],[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[1,1,5,1]
[[[[]]],[],[],[[[]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[[[[]]],[],[[]],[],[]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[[[[]]],[],[[]],[[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[[[],[]],[],[[],[]],[]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[2,4,2]
[[[[]]],[],[[],[]],[]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[1,1,4,2]
[[[[]]],[],[[[]]],[]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[[[],[]],[],[[],[],[]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[2,5,1]
[[[],[]],[],[[],[[]]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[2,4,1,1]
[[[],[]],[],[[[]],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[2,3,2,1]
[[[],[]],[],[[[],[]]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[2,4,1,1]
[[[],[]],[],[[[[]]]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]
[[[[]]],[],[[],[],[]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[1,1,5,1]
[[[[]]],[],[[],[[]]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[1,1,4,1,1]
[[[[]]],[],[[[]],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[1,1,3,2,1]
[[[[]]],[],[[[],[]]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[1,1,4,1,1]
[[[[]]],[],[[[[]]]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[[[],[]],[[]],[],[],[]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[2,2,4]
[[[[]]],[[]],[],[[]]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[[[],[]],[[]],[[]],[]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[2,2,2,2]
[[[[]]],[[]],[[]],[]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[[[[]]],[[]],[[],[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]
[[[[]]],[[]],[[[]]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[[[],[]],[[],[]],[],[]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[2,3,3]
[[[],[]],[[[]]],[],[]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[2,2,1,3]
[[[[]]],[[],[]],[],[]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[1,1,3,3]
[[[[]]],[[[]]],[],[]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[1,1,2,1,3]
[[[],[]],[[[]]],[[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]
[[[[]]],[[],[]],[[]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]
[[[[]]],[[[]]],[[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]
[[[],[]],[[],[],[]],[]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[2,4,2]
[[[],[]],[[[]],[]],[]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[2,2,2,2]
[[[],[]],[[[],[]]],[]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[2,3,1,2]
[[[],[]],[[[[]]]],[]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[2,3,1,7,6,5,4,8]=>[2,2,1,1,2]
[[[[]]],[[],[],[]],[]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[1,1,4,2]
[[[[]]],[[],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]
[[[[]]],[[[],[]]],[]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]
[[[[]]],[[[[]]]],[]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[[[],[]],[[],[],[],[]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[2,5,1]
[[[],[]],[[],[],[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[2,4,1,1]
[[[],[]],[[],[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[2,3,2,1]
[[[],[]],[[],[[],[]]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[2,4,1,1]
[[[],[]],[[],[[[]]]]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]
[[[],[]],[[[]],[],[]]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[2,2,3,1]
[[[],[]],[[[]],[[]]]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]
[[[],[]],[[[],[]],[]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[2,3,2,1]
[[[],[]],[[[[]]],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]
[[[],[]],[[[],[],[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[2,4,1,1]
[[[],[]],[[[],[[]]]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]
[[[],[]],[[[[]],[]]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]
[[[],[]],[[[[],[]]]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]
[[[],[]],[[[[[]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]
[[[[]]],[[],[],[],[]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[1,1,5,1]
[[[[]]],[[],[],[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[1,1,4,1,1]
[[[[]]],[[],[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[1,1,3,2,1]
[[[[]]],[[],[[],[]]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[1,1,4,1,1]
[[[[]]],[[],[[[]]]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[1,1,3,1,1,1]
[[[[]]],[[[]],[],[]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[1,1,2,3,1]
[[[[]]],[[[]],[[]]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]
[[[[]]],[[[],[]],[]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]
[[[[]]],[[[[]]],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]
[[[[]]],[[[],[],[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[1,1,4,1,1]
[[[[]]],[[[],[[]]]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[1,1,3,1,1,1]
[[[[]]],[[[[]],[]]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[1,1,2,2,1,1]
[[[[]]],[[[[],[]]]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[1,1,3,1,1,1]
[[[[]]],[[[[[]]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[[[],[],[]],[],[],[],[]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[3,5]
[[[],[[]]],[],[],[],[]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[2,1,5]
[[[[]],[]],[],[],[],[]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[[[[],[]]],[],[],[],[]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[[[[[]]]],[],[],[],[]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[[[],[],[]],[],[],[[]]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[3,4,1]
[[[],[[]]],[],[],[[]]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[2,1,4,1]
[[[[]],[]],[],[],[[]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[1,2,4,1]
[[[[[]]]],[],[],[[]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[[[],[],[]],[],[[]],[]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[3,3,2]
[[[[]],[]],[],[[]],[]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[1,2,3,2]
[[[[[]]]],[],[[]],[]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[[[],[],[]],[],[[],[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[3,4,1]
[[[],[],[]],[],[[[]]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[3,3,1,1]
[[[],[[]]],[],[[],[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[2,1,4,1]
[[[[]],[]],[],[[],[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[1,2,4,1]
[[[[]],[]],[],[[[]]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[1,2,3,1,1]
[[[[],[]]],[],[[[]]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[2,1,3,1,1]
[[[[[]]]],[],[[],[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[1,1,1,4,1]
[[[[[]]]],[],[[[]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[[[],[],[]],[[]],[],[]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[3,2,3]
[[[[]],[]],[[]],[],[]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[1,2,2,3]
[[[[[]]]],[[]],[],[]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[[[],[],[]],[[]],[[]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[3,2,2,1]
[[[],[[]]],[[]],[[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]
[[[[]],[]],[[]],[[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]
[[[[],[]]],[[]],[[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]
[[[[[]]]],[[]],[[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[[[],[],[]],[[],[]],[]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[3,3,2]
[[[],[],[]],[[[]]],[]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[3,2,1,2]
[[[[]],[]],[[],[]],[]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[1,2,3,2]
[[[[]],[]],[[[]]],[]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]
[[[[[]]]],[[],[]],[]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]
[[[[[]]]],[[[]]],[]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[[[],[],[]],[[],[],[]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[3,4,1]
[[[],[],[]],[[],[[]]]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[3,3,1,1]
[[[],[],[]],[[[]],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[3,2,2,1]
[[[],[],[]],[[[],[]]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[3,3,1,1]
[[[],[],[]],[[[[]]]]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[2,1,4,1]
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]
[[[[]],[]],[[],[],[]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[1,2,4,1]
[[[[]],[]],[[],[[]]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[[[[]],[]],[[[]],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]
[[[[]],[]],[[[],[]]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]
[[[[]],[]],[[[[]]]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]
[[[[],[]]],[[],[],[]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[2,1,4,1]
[[[[],[]]],[[],[[]]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]
[[[[],[]]],[[[]],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[2,1,2,2,1]
[[[[],[]]],[[[],[]]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]
[[[[],[]]],[[[[]]]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]
[[[[[]]]],[[],[],[]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[1,1,1,4,1]
[[[[[]]]],[[],[[]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[1,1,1,3,1,1]
[[[[[]]]],[[[]],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]
[[[[[]]]],[[[],[]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[1,1,1,3,1,1]
[[[[[]]]],[[[[]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[[[],[],[],[]],[],[],[]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[4,4]
[[[],[],[[]]],[],[],[]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[3,1,4]
[[[],[[]],[]],[],[],[]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[2,2,4]
[[[],[[],[]]],[],[],[]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[3,1,4]
[[[],[[[]]]],[],[],[]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[[[[]],[],[]],[],[],[]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[[[[]],[[]]],[],[],[]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[1,2,1,4]
[[[[],[]],[]],[],[],[]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[[[[[]]],[]],[],[],[]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[[[[],[],[]]],[],[],[]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[[[[],[[]]]],[],[],[]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[[[[[]],[]]],[],[],[]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[[[[[[]]]]],[],[],[]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[[[],[],[],[]],[],[[]]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[4,3,1]
[[[],[[],[]]],[],[[]]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[3,1,3,1]
[[[],[[[]]]],[],[[]]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]
[[[[]],[[]]],[],[[]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]
[[[[],[]],[]],[],[[]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[2,2,3,1]
[[[[[]]],[]],[],[[]]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]
[[[[],[],[]]],[],[[]]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[3,1,3,1]
[[[[],[[]]]],[],[[]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[2,1,1,3,1]
[[[[[],[]]]],[],[[]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]
[[[[[[]]]]],[],[[]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[[[],[],[],[]],[[]],[]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[4,2,2]
[[[],[],[[]]],[[]],[]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[3,1,2,2]
[[[],[[]],[]],[[]],[]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[2,2,2,2]
[[[],[[],[]]],[[]],[]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[3,1,2,2]
[[[],[[[]]]],[[]],[]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[2,1,1,2,2]
[[[[]],[],[]],[[]],[]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[3,2,4,5,1,7,6,8]=>[1,3,2,2]
[[[[]],[[]]],[[]],[]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]
[[[[],[]],[]],[[]],[]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[2,2,2,2]
[[[[[]]],[]],[[]],[]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]
[[[[],[],[]]],[[]],[]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[3,1,2,2]
[[[[],[[]]]],[[]],[]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]
[[[[[]],[]]],[[]],[]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]
[[[[[],[]]]],[[]],[]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]
[[[[[[]]]]],[[]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[[[],[],[],[]],[[],[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[4,3,1]
[[[],[],[],[]],[[[]]]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[4,2,1,1]
[[[],[],[[]]],[[],[]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[3,1,3,1]
[[[],[],[[]]],[[[]]]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]
[[[],[[]],[]],[[],[]]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[2,2,3,1]
[[[],[[]],[]],[[[]]]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[2,2,2,1,1]
[[[],[[],[]]],[[],[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[3,1,3,1]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]
[[[],[[[]]]],[[],[]]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[2,1,1,3,1]
[[[],[[[]]]],[[[]]]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]
[[[[]],[],[]],[[],[]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[1,3,3,1]
[[[[]],[],[]],[[[]]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[1,3,2,1,1]
[[[[]],[[]]],[[],[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]
[[[[]],[[]]],[[[]]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]
[[[[],[]],[]],[[],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[2,2,3,1]
[[[[],[]],[]],[[[]]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]
[[[[[]]],[]],[[],[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]
[[[[[]]],[]],[[[]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]
[[[[],[],[]]],[[],[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[3,1,3,1]
[[[[],[],[]]],[[[]]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]
[[[[],[[]]]],[[],[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[2,1,1,3,1]
[[[[],[[]]]],[[[]]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]
[[[[[]],[]]],[[],[]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]
[[[[[]],[]]],[[[]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]
[[[[[],[]]]],[[],[]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[4,5,3,2,1,7,8,6]=>[2,1,1,3,1]
[[[[[],[]]]],[[[]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]
[[[[[[]]]]],[[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[1,1,1,1,3,1]
[[[[[[]]]]],[[[]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[[[],[],[],[],[]],[],[]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[5,3]
[[[],[],[[]],[]],[],[]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[3,2,3]
[[[],[[[]]],[]],[],[]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[[[],[[],[],[]]],[],[]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[4,1,3]
[[[],[[],[[]]]],[],[]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[[[],[[[]],[]]],[],[]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[2,2,1,3]
[[[[[]]],[],[]],[],[]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[[[[],[]],[[]]],[],[]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[2,2,1,3]
[[[[[]]],[[]]],[],[]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[1,1,2,1,3]
[[[[],[],[]],[]],[],[]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,2,3]
[[[[],[[]]],[]],[],[]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[2,1,2,3]
[[[[[]],[]],[]],[],[]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[[[[[],[]]],[]],[],[]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[[[[[[]]]],[]],[],[]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[[[[],[],[],[]]],[],[]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[[[[],[[],[]]]],[],[]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[[[[],[[[]]]]],[],[]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[[[[[]],[],[]]],[],[]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[[[[[]],[[]]]],[],[]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>[1,2,1,1,3]
[[[[[],[]],[]]],[],[]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[4,5,3,6,2,1,7,8]=>[2,2,1,3]
[[[[[[]]],[]]],[],[]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]
[[[[[],[],[]]]],[],[]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[[[[[[]],[]]]],[],[]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[1,2,1,1,3]
[[[[[[],[]]]]],[],[]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]
[[[[[[[]]]]]],[],[]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[[[],[],[],[],[]],[[]]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[5,2,1]
[[[],[],[[],[]]],[[]]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[4,1,2,1]
[[[],[],[[[]]]],[[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[3,1,1,2,1]
[[[],[[]],[[]]],[[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]
[[[],[[],[]],[]],[[]]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[3,2,2,1]
[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[2,1,2,2,1]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]
[[[],[[[],[]]]],[[]]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[3,1,1,2,1]
[[[],[[[[]]]]],[[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]
[[[[]],[[]],[]],[[]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]
[[[[]],[[],[]]],[[]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]
[[[[],[]],[],[]],[[]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[2,3,2,1]
[[[[[]]],[],[]],[[]]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[1,1,3,2,1]
[[[[],[]],[[]]],[[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]
[[[[],[],[]],[]],[[]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[3,2,2,1]
[[[[],[[]]],[]],[[]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]
[[[[[]],[]],[]],[[]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]
[[[[[],[]]],[]],[[]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]
[[[[[[]]]],[]],[[]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]
[[[[],[],[],[]]],[[]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[4,1,2,1]
[[[[],[[]],[]]],[[]]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[3,5,4,6,2,1,8,7]=>[2,2,1,2,1]
[[[[],[[],[]]]],[[]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]
[[[[],[[[]]]]],[[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]
[[[[[]],[],[]]],[[]]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]
[[[[[]],[[]]]],[[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]
[[[[[],[]],[]]],[[]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]
[[[[[[]]],[]]],[[]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[1,1,2,1,2,1]
[[[[[],[],[]]]],[[]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]
[[[[[],[[]]]]],[[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]
[[[[[[]],[]]]],[[]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]
[[[[[[],[]]]]],[[]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]
[[[[[[[]]]]]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[[[],[],[],[],[],[]],[]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[6,2]
[[[],[],[],[[[]]]],[]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[[[],[],[[]],[],[]],[]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[3,3,2]
[[[],[],[[],[]],[]],[]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[4,2,2]
[[[],[],[[],[],[]]],[]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[5,1,2]
[[[],[],[[],[[]]]],[]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[[[],[],[[[]],[]]],[]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[3,2,1,2]
[[[],[],[[[],[]]]],[]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[4,1,1,2]
[[[],[],[[[[]]]]],[]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[[[],[[]],[],[[]]],[]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[2,4,3,5,7,6,1,8]=>[2,3,1,2]
[[[],[[]],[[]],[]],[]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[2,2,2,2]
[[[],[[[]]],[],[]],[]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[[[],[[[[]]]],[]],[]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]
[[[],[[],[],[],[]]],[]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[5,1,2]
[[[],[[],[],[[]]]],[]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[[[],[[],[[],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[[[],[[],[[[]]]]],[]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[3,1,1,1,2]
[[[],[[[]],[[]]]],[]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[2,2,1,1,2]
[[[],[[[],[]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[3,2,1,2]
[[[],[[[],[],[]]]],[]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[4,1,1,2]
[[[],[[[[]],[]]]],[]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[2,6,5,7,4,3,1,8]=>[2,2,1,1,2]
[[[],[[[[[]]]]]],[]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[2,1,1,1,1,2]
[[[[]],[],[[],[]]],[]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[1,4,1,2]
[[[[]],[[]],[[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]
[[[[]],[[[]]],[]],[]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]
[[[[]],[[],[[]]]],[]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]
[[[[]],[[[],[]]]],[]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]
[[[[]],[[[[]]]]],[]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]
[[[[],[]],[],[],[]],[]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[[[[[]]],[],[[]]],[]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]
[[[[],[]],[[]],[]],[]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[2,2,2,2]
[[[[],[]],[[],[]]],[]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[2,3,1,2]
[[[[],[]],[[[]]]],[]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[2,2,1,1,2]
[[[[[]]],[[[]]]],[]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]
[[[[],[],[]],[],[]],[]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[3,3,2]
[[[[],[[]]],[],[]],[]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[[[[[],[]]],[],[]],[]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[[[[[[]]]],[],[]],[]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[[[[],[],[]],[[]]],[]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>[3,2,1,2]
[[[[],[[]]],[[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]
[[[[[],[]]],[[]]],[]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]
[[[[[[]]]],[[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]
[[[[],[],[],[]],[]],[]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[[[[],[],[[]]],[]],[]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[[[[],[[]],[]],[]],[]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[[[[],[[[]]]],[]],[]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[[[[[]],[[]]],[]],[]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]
[[[[[],[]],[]],[]],[]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[[[[[[]]],[]],[]],[]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[[[[[[]],[]]],[]],[]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]
[[[[[[[]]]]],[]],[]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[[[[],[],[[[]]]]],[]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[3,1,1,1,2]
[[[[],[[]],[[]]]],[]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[2,2,1,1,2]
[[[[],[[],[]],[]]],[]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[3,2,1,2]
[[[[],[[],[],[]]]],[]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[4,1,1,2]
[[[[],[[],[[]]]]],[]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[3,1,1,1,2]
[[[[[]],[],[[]]]],[]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]
[[[[[]],[[[]]]]],[]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]
[[[[[[]]],[],[]]],[]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[[[[[],[]],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[2,2,1,1,2]
[[[[[],[],[]],[]]],[]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[[[[[],[[]]],[]]],[]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]
[[[[[[]],[]],[]]],[]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[[[[[[],[]]],[]]],[]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[[[[[[[]]]],[]]],[]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]
[[[[[],[],[],[]]]],[]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[[[[[],[],[[]]]]],[]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[3,1,1,1,2]
[[[[[],[[]],[]]]],[]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]
[[[[[],[[],[]]]]],[]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[3,1,1,1,2]
[[[[[],[[[]]]]]],[]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[]],[],[]]]],[]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[[[[[[]],[[]]]]],[]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]
[[[[[[],[]],[]]]],[]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[[[[[[[]]],[]]]],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[[[[[[],[],[]]]]],[]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[[[[[[],[[]]]]]],[]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[[]],[]]]]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[[[[[[[],[]]]]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[[[[[[[[]]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[[[],[],[],[],[],[],[]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[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]=>[5,2,1]
[[[],[],[],[],[[],[]]]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[6,1,1]
[[[],[],[],[],[[[]]]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[[[],[],[],[[]],[],[]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[4,3,1]
[[[],[],[],[[]],[[]]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[4,2,1,1]
[[[],[],[],[[[]]],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[[[],[],[],[[],[],[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[[[],[],[],[[],[[]]]]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[[[],[],[],[[[],[]]]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[[[],[],[],[[[[]]]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[[[],[],[[]],[],[],[]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[3,4,1]
[[[],[],[[]],[[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[3,2,2,1]
[[[],[],[[]],[[[]]]]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[3,2,1,1,1]
[[[],[],[[],[]],[],[]]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[4,3,1]
[[[],[],[[[]]],[],[]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[[[],[],[[],[[]]],[]]]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[[[],[],[[[],[]]],[]]]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[[[],[],[[[[]]]],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]
[[[],[],[[],[],[],[]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[6,1,1]
[[[],[],[[],[],[[]]]]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[[[],[],[[],[[]],[]]]]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[4,2,1,1]
[[[],[],[[],[[],[]]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[[[],[],[[[]],[[]]]]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[3,2,1,1,1]
[[[],[],[[[],[]],[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[4,2,1,1]
[[[],[],[[[[]]],[]]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]
[[[],[],[[[],[],[]]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[[[],[],[[[],[[]]]]]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]
[[[],[],[[[[]],[]]]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]
[[[],[],[[[[[]]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[[[],[[]],[],[],[],[]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[2,5,1]
[[[],[[]],[],[],[[]]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[2,4,1,1]
[[[],[[]],[],[[]],[]]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[2,3,2,1]
[[[],[[]],[],[[[]]]]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[2,3,1,1,1]
[[[],[[]],[[]],[],[]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[2,2,3,1]
[[[],[[]],[[]],[[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]
[[[],[[]],[[[]]],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[2,2,1,2,1]
[[[],[[]],[[],[],[]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[2,4,1,1]
[[[],[[]],[[],[[]]]]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]
[[[],[[]],[[[[]]]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[2,2,1,1,1,1]
[[[],[[],[]],[],[],[]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[3,4,1]
[[[],[[[]]],[],[],[]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[[[],[[[]]],[],[[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[2,1,3,1,1]
[[[],[[[]]],[[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[2,1,2,2,1]
[[[],[[],[]],[[[]]]]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]
[[[],[[[]]],[[],[]]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[2,1,3,1,1]
[[[],[[[]]],[[[]]]]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]
[[[],[[[]],[]],[],[]]]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[2,2,3,1]
[[[],[[[[]]]],[],[]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[[[],[[],[[]]],[[]]]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[3,1,2,1,1]
[[[],[[[[]]]],[[]]]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[2,1,1,2,1,1]
[[[],[[],[],[],[]],[]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[5,2,1]
[[[],[[],[],[[]]],[]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[[[],[[],[[]],[]],[]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[[[],[[],[[],[]]],[]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[4,1,2,1]
[[[],[[[]],[],[]],[]]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[2,3,2,1]
[[[],[[[]],[[]]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]
[[[],[[[],[]],[]],[]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[[[],[[[],[[]]]],[]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[3,1,1,2,1]
[[[],[[[[[]]]]],[]]]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[2,1,1,1,2,1]
[[[],[[],[],[],[],[]]]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[6,1,1]
[[[],[[],[],[[],[]]]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[[[],[[],[[]],[[]]]]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]
[[[],[[],[[[]]],[]]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]
[[[],[[],[[],[],[]]]]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[[[],[[],[[],[[]]]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[[[],[[],[[[],[]]]]]]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[[[],[[],[[[[]]]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[[[],[[[]],[[[]]]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]
[[[],[[[[]]],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]
[[[],[[[],[]],[[]]]]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]
[[[],[[[[]],[]],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]
[[[],[[[[],[]]],[]]]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]
[[[],[[[[[]]]],[]]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[2,1,1,2,1,1]
[[[],[[[],[],[],[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[[[],[[[],[],[[]]]]]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[[[],[[[],[[]],[]]]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]
[[[],[[[],[[],[]]]]]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[[[],[[[[]],[],[]]]]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]
[[[],[[[[]],[[]]]]]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]
[[[],[[[[],[]],[]]]]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]
[[[],[[[[[]]],[]]]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[2,1,2,1,1,1]
[[[],[[[[],[],[]]]]]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[[[],[[[[],[[]]]]]]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[[[],[[[[[]],[]]]]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]
[[[],[[[[[[]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[[[[]],[],[],[],[],[]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,6,1]
[[[[]],[],[],[[]],[]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[1,4,2,1]
[[[[]],[],[[[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[1,3,1,2,1]
[[[[]],[],[[],[],[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[3,2,4,6,7,8,5,1]=>[1,5,1,1]
[[[[]],[],[[[[]]]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,3,1,1,1,1]
[[[[]],[[]],[],[],[]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[1,2,4,1]
[[[[]],[[]],[[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]
[[[[]],[[],[],[]],[]]]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,4,2,1]
[[[[]],[[[]],[]],[]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[1,2,2,2,1]
[[[[]],[[[],[]]],[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,3,1,2,1]
[[[[]],[[],[],[],[]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[1,5,1,1]
[[[[]],[[],[],[[]]]]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[1,4,1,1,1]
[[[[]],[[],[[]],[]]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>[1,3,2,1,1]
[[[[]],[[],[[[]]]]]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[1,3,1,1,1,1]
[[[[]],[[[]],[],[]]]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[3,2,6,5,7,8,4,1]=>[1,2,3,1,1]
[[[[]],[[[]],[[]]]]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[1,2,2,1,1,1]
[[[[]],[[[],[]],[]]]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]
[[[[]],[[[[]]],[]]]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]
[[[[]],[[[],[[]]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[1,3,1,1,1,1]
[[[[]],[[[[[]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]
[[[[],[]],[],[],[],[]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[2,5,1]
[[[[[]]],[],[],[],[]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[[[[],[]],[],[],[[]]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[2,4,1,1]
[[[[[]]],[],[],[[]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[1,1,4,1,1]
[[[[[]]],[],[[]],[]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,1,3,2,1]
[[[[],[]],[],[[],[]]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[2,4,1,1]
[[[[],[]],[],[[[]]]]]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]
[[[[[]]],[],[[[]]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[1,1,3,1,1,1]
[[[[],[]],[[]],[],[]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[2,2,3,1]
[[[[[]]],[[]],[],[]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>[1,1,2,3,1]
[[[[[]]],[[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]
[[[[],[]],[[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[2,2,1,2,1]
[[[[[]]],[[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[1,1,3,2,1]
[[[[[]]],[[[]]],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[1,1,2,1,2,1]
[[[[],[]],[[],[],[]]]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[2,4,1,1]
[[[[],[]],[[],[[]]]]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[2,3,1,1,1]
[[[[],[]],[[[]],[]]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[3,4,2,7,6,8,5,1]=>[2,2,2,1,1]
[[[[],[]],[[[],[]]]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[2,3,1,1,1]
[[[[],[]],[[[[]]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]
[[[[[]]],[[],[],[]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,1,4,1,1]
[[[[[]]],[[],[[]]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[1,1,3,1,1,1]
[[[[[]]],[[[[]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]
[[[[],[],[]],[],[],[]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,1]
[[[[],[[]]],[],[],[]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[2,1,4,1]
[[[[[]],[]],[],[],[]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,2,4,1]
[[[[[],[]]],[],[],[]]]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[2,1,4,1]
[[[[[[]]]],[],[],[]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[[[[],[],[]],[],[[]]]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[3,3,1,1]
[[[[[[]]]],[],[[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[1,1,1,3,1,1]
[[[[],[],[]],[[]],[]]]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[3,2,2,1]
[[[[[]],[]],[[]],[]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]
[[[[[],[]]],[[]],[]]]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[4,5,3,2,7,6,8,1]=>[2,1,2,2,1]
[[[[[[]]]],[[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]
[[[[],[],[]],[[],[]]]]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[3,3,1,1]
[[[[],[],[]],[[[]]]]]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[3,4,5,2,8,7,6,1]=>[3,2,1,1,1]
[[[[[],[]]],[[],[]]]]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[2,1,3,1,1]
[[[[[],[]]],[[[]]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]
[[[[[[]]]],[[],[]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[1,1,1,3,1,1]
[[[[[[]]]],[[[]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]
[[[[],[],[],[]],[],[]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[[[[],[[]],[]],[],[]]]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[2,2,3,1]
[[[[],[[],[]]],[],[]]]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[[[[],[[[]]]],[],[]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]
[[[[[[]]],[]],[],[]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]
[[[[[[]],[]]],[],[]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]
[[[[[[[]]]]],[],[]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[[[[],[[],[]]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]
[[[[],[[[]]]],[[]]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]
[[[[[]],[[]]],[[]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]
[[[[[[]]],[]],[[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]
[[[[[],[],[]]],[[]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]
[[[[[],[[]]]],[[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]
[[[[[[]],[]]],[[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]
[[[[[[[]]]]],[[]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]
[[[[],[],[[]],[]],[]]]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[3,2,2,1]
[[[[],[],[[],[]]],[]]]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[4,1,2,1]
[[[[],[],[[[]]]],[]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[3,1,1,2,1]
[[[[],[[]],[],[]],[]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[[[[],[[]],[[]]],[]]]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]
[[[[],[[],[]],[]],[]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[[[[],[[[]]],[]],[]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]
[[[[],[[],[],[]]],[]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[4,1,2,1]
[[[[],[[],[[]]]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[[[[],[[[]],[]]],[]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]
[[[[],[[[[]]]]],[]]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]
[[[[[]],[[]],[]],[]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]
[[[[[]],[[],[]]],[]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]
[[[[[]],[[[]]]],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]
[[[[[[]]],[],[]],[]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]
[[[[[[]]],[[]]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[1,1,2,1,2,1]
[[[[[],[],[]],[]],[]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[[[[[],[[]]],[]],[]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[[[[[[]],[]],[]],[]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[[[[[[],[]]],[]],[]]]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[2,1,2,2,1]
[[[[[[[]]]],[]],[]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[[[[[],[],[],[]]],[]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[[[[[],[],[[]]]],[]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]
[[[[[],[[]],[]]],[]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]
[[[[[],[[[]]]]],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[[]],[],[]]],[]]]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[[[[[[]],[[]]]],[]]]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[[],[]],[]]],[]]]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]
[[[[[[],[],[]]]],[]]]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[[[[[[],[[]]]]],[]]]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[[[]],[]]]],[]]]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[[[[[[[],[]]]]],[]]]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]
[[[[[[[[]]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[[[[],[],[],[[],[]]]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[[[[],[],[],[[[]]]]]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[[[[],[],[[]],[],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[[[[],[],[[[]]],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]
[[[[],[],[[],[],[]]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[[[[],[],[[[]],[]]]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[3,2,1,1,1]
[[[[],[],[[[[]]]]]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[[[[],[[]],[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[2,2,2,1,1]
[[[[],[[],[]],[],[]]]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[3,3,1,1]
[[[[],[[],[[]]],[]]]]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]
[[[[],[[[]],[]],[]]]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]
[[[[],[[[],[]]],[]]]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[3,1,2,1,1]
[[[[],[[[[]]]],[]]]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[2,1,1,2,1,1]
[[[[],[[],[],[],[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[[[[],[[],[],[[]]]]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[[[[],[[],[[],[]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[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]
[[[[],[[[]],[],[]]]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[3,6,5,7,8,4,2,1]=>[2,3,1,1,1]
[[[[],[[[]],[[]]]]]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]
[[[[],[[[],[]],[]]]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[3,2,1,1,1]
[[[[],[[[[]]],[]]]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]
[[[[],[[[[]],[]]]]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[2,2,1,1,1,1]
[[[[],[[[[],[]]]]]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]
[[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[[[[[]],[],[],[],[]]]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[[[[[]],[],[[]],[]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[1,3,2,1,1]
[[[[[]],[],[[],[]]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]
[[[[[]],[[]],[[]]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]
[[[[[]],[[[]]],[]]]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]
[[[[[]],[[],[],[]]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]
[[[[[]],[[],[[]]]]]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[1,3,1,1,1,1]
[[[[[]],[[[]],[]]]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]
[[[[[]],[[[],[]]]]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,3,1,1,1,1]
[[[[[]],[[[[]]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]
[[[[[],[]],[],[],[]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[[[[[],[]],[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]
[[[[[[]]],[],[[]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,1,3,1,1,1]
[[[[[],[]],[[]],[]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[2,2,2,1,1]
[[[[[[]]],[[]],[]]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]
[[[[[[]]],[[],[]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,1,3,1,1,1]
[[[[[[]]],[[[]]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]
[[[[[],[[]]],[],[]]]]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]
[[[[[[[]]]],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]
[[[[[],[],[]],[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]
[[[[[],[[]]],[[]]]]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]
[[[[[[]],[]],[[]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]
[[[[[[],[]]],[[]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]
[[[[[[[]]]],[[]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]
[[[[[],[],[],[]],[]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[[[[[],[],[[]]],[]]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[4,5,7,6,3,8,2,1]=>[3,1,2,1,1]
[[[[[],[[]],[]],[]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[4,6,5,7,3,8,2,1]=>[2,2,2,1,1]
[[[[[],[[[]]]],[]]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[[]],[],[]],[]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[[[[[[]],[[]]],[]]]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]
[[[[[[],[]],[]],[]]]]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[[[[[[[]]],[]],[]]]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[[[[[[],[[]]]],[]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[[[]],[]]],[]]]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[[[[[[[],[]]]],[]]]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]
[[[[[[[[]]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[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]=>[3,2,1,1,1]
[[[[[],[],[[],[]]]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]
[[[[[],[],[[[]]]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]
[[[[[],[[]],[[]]]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[2,2,1,1,1,1]
[[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]
[[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]
[[[[[],[[],[],[]]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]
[[[[[],[[],[[]]]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[[[[[],[[[]],[]]]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]
[[[[[],[[[],[]]]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[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]=>[1,4,1,1,1]
[[[[[[]],[],[[]]]]]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[1,3,1,1,1,1]
[[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[[]],[[],[]]]]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[1,3,1,1,1,1]
[[[[[[]],[[[]]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]
[[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]
[[[[[[],[]],[[]]]]]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[2,2,1,1,1,1]
[[[[[[[]]],[[]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]
[[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]
[[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[2,1,2,1,1,1]
[[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]
[[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[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]=>[2,2,1,1,1,1]
[[[[[[],[[],[]]]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[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]=>[1,3,1,1,1,1]
[[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]
[[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[[[[[[[],[],[]]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[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]=>[1,2,1,1,1,1,1]
[[[[[[[[],[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[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
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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