Identifier
Mp00139:
Ordered trees
—Zeilberger's Strahler bijection⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0002;cc-rep-3
[[]]=>[.,.]=>[1]=>[1]
[[],[]]=>[.,[.,.]]=>[2,1]=>[2]
[[[]]]=>[[.,.],.]=>[1,2]=>[1,1]
[[],[],[]]=>[.,[.,[.,.]]]=>[3,2,1]=>[3]
[[],[[]]]=>[.,[[.,.],.]]=>[2,3,1]=>[2,1]
[[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>[2,1]
[[[],[]]]=>[[.,.],[.,.]]=>[3,1,2]=>[2,1]
[[[[]]]]=>[[[.,.],.],.]=>[1,2,3]=>[1,1,1]
[[],[],[],[]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4]
[[],[],[[]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,1]
[[],[[]],[]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,1]
[[],[[],[]]]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,1]
[[],[[[]]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,1,1]
[[[]],[],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1]
[[[]],[[]]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,1,1]
[[[],[]],[]]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1]
[[[[]]],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,1]
[[[],[],[]]]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1]
[[[],[[]]]]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,1]
[[[[]],[]]]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,1,1]
[[[[],[]]]]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,1,1]
[[[[[]]]]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,1,1,1]
[[],[],[],[],[]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5]
[[],[],[],[[]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,1]
[[],[],[[]],[]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,1]
[[],[],[[],[]]]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[4,1]
[[],[],[[[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]
[[],[[]],[],[]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,1]
[[],[[]],[[]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,1,1]
[[],[[],[]],[]]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,1]
[[],[[[]]],[]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,1,1]
[[],[[],[],[]]]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[4,1]
[[],[[],[[]]]]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,1,1]
[[],[[[]],[]]]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[3,1,1]
[[],[[[],[]]]]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[3,1,1]
[[],[[[[]]]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,1,1,1]
[[[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1]
[[[]],[],[[]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,1,1]
[[[]],[[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,1,1]
[[[]],[[],[]]]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[3,1,1]
[[[]],[[[]]]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,1,1,1]
[[[],[]],[],[]]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,1]
[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,1]
[[[],[]],[[]]]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,1]
[[[[]]],[[]]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,1,1,1]
[[[],[],[]],[]]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1]
[[[],[[]]],[]]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,1,1]
[[[[]],[]],[]]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,1]
[[[[],[]]],[]]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,1]
[[[[[]]]],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,1,1]
[[[],[],[],[]]]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,1]
[[[],[],[[]]]]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,1]
[[[],[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[3,1,1]
[[[],[[],[]]]]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,1,1]
[[[],[[[]]]]]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,1,1]
[[[[]],[],[]]]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,1,1]
[[[[]],[[]]]]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,1,1,1]
[[[[],[]],[]]]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,1]
[[[[[]]],[]]]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,1,1,1]
[[[[],[],[]]]]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,1]
[[[[],[[]]]]]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,1,1,1]
[[[[[]],[]]]]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,1,1,1]
[[[[[],[]]]]]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,1,1,1]
[[[[[[]]]]]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,1,1,1,1]
[[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6]
[[],[],[],[],[[]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,1]
[[],[],[],[[]],[]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,1]
[[],[],[],[[],[]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[5,1]
[[],[],[],[[[]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,1,1]
[[],[],[[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,1]
[[],[],[[]],[[]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,1,1]
[[],[],[[],[]],[]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[5,1]
[[],[],[[[]]],[]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,1,1]
[[],[],[[],[],[]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[5,1]
[[],[],[[],[[]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[4,1,1]
[[],[],[[[]],[]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[4,1,1]
[[],[],[[[],[]]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[4,1,1]
[[],[],[[[[]]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,1,1,1]
[[],[[]],[],[],[]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,1]
[[],[[]],[],[[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,1,1]
[[],[[]],[[]],[]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,1,1]
[[],[[]],[[],[]]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[4,1,1]
[[],[[]],[[[]]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,1,1,1]
[[],[[],[]],[],[]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[5,1]
[[],[[[]]],[],[]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,1,1]
[[],[[],[]],[[]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,1,1]
[[],[[[]]],[[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,1,1,1]
[[],[[],[],[]],[]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,1]
[[],[[],[[]]],[]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[4,1,1]
[[],[[[]],[]],[]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[4,1,1]
[[],[[[],[]]],[]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[4,1,1]
[[],[[[[]]]],[]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,1,1,1]
[[],[[],[],[],[]]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[5,1]
[[],[[],[],[[]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[4,1,1]
[[],[[],[[]],[]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[4,1,1]
[[],[[],[[],[]]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[4,1,1]
[[],[[],[[[]]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,1,1,1]
[[],[[[]],[],[]]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,1,1]
[[],[[[]],[[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[3,1,1,1]
[[],[[[],[]],[]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[4,1,1]
[[],[[[[]]],[]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[3,1,1,1]
[[],[[[],[],[]]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[4,1,1]
[[],[[[],[[]]]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[3,1,1,1]
[[],[[[[]],[]]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[3,1,1,1]
[[],[[[[],[]]]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[3,1,1,1]
[[],[[[[[]]]]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,1,1,1,1]
[[[]],[],[],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1]
[[[]],[],[],[[]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,1,1]
[[[]],[],[[]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,1,1]
[[[]],[],[[],[]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[4,1,1]
[[[]],[],[[[]]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,1,1]
[[[]],[[]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,1,1]
[[[]],[[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,1,1,1]
[[[]],[[],[]],[]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[4,1,1]
[[[]],[[[]]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,1,1,1]
[[[]],[[],[],[]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,1]
[[[]],[[],[[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[3,1,1,1]
[[[]],[[[]],[]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,1,1,1]
[[[]],[[[],[]]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[3,1,1,1]
[[[]],[[[[]]]]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,1,1,1,1]
[[[],[]],[],[],[]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,1]
[[[[]]],[],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,1]
[[[],[]],[],[[]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[4,1,1]
[[[[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,1,1,1]
[[[],[]],[[]],[]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[4,1,1]
[[[[]]],[[]],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,1,1,1]
[[[],[]],[[],[]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[4,1,1]
[[[],[]],[[[]]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,1,1]
[[[[]]],[[],[]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,1,1,1]
[[[[]]],[[[]]]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,1,1,1,1]
[[[],[],[]],[],[]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,1]
[[[],[[]]],[],[]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,1]
[[[[]],[]],[],[]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,1,1]
[[[[],[]]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,1,1]
[[[[[]]]],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,1,1]
[[[],[],[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,1]
[[[],[[]]],[[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,1,1,1]
[[[[]],[]],[[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,1,1,1]
[[[[],[]]],[[]]]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,1,1,1]
[[[[[]]]],[[]]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,1,1,1,1]
[[[],[],[],[]],[]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1]
[[[],[],[[]]],[]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[4,1,1]
[[[],[[]],[]],[]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,1,1]
[[[],[[],[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,1,1]
[[[],[[[]]]],[]]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[3,1,1,1]
[[[[]],[],[]],[]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,1,1]
[[[[]],[[]]],[]]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,1,1,1]
[[[[],[]],[]],[]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,1,1]
[[[[[]]],[]],[]]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,1,1]
[[[[],[],[]]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,1,1]
[[[[],[[]]]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,1,1,1]
[[[[[]],[]]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,1,1]
[[[[[],[]]]],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,1,1]
[[[[[[]]]]],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,1,1,1]
[[[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,1]
[[[],[],[],[[]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[4,1,1]
[[[],[],[[]],[]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[4,1,1]
[[[],[],[[],[]]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[4,1,1]
[[[],[],[[[]]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,1,1]
[[[],[[]],[],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[4,1,1]
[[[],[[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[3,1,1,1]
[[[],[[],[]],[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[4,1,1]
[[[],[[[]]],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[3,1,1,1]
[[[],[[],[],[]]]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[4,1,1]
[[[],[[],[[]]]]]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,1,1,1]
[[[],[[[]],[]]]]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[3,1,1,1]
[[[],[[[],[]]]]]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[3,1,1,1]
[[[],[[[[]]]]]]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,1,1,1]
[[[[]],[],[],[]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,1]
[[[[]],[],[[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,1,1,1]
[[[[]],[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,1,1,1]
[[[[]],[[],[]]]]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[3,1,1,1]
[[[[]],[[[]]]]]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[2,1,1,1,1]
[[[[],[]],[],[]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,1,1]
[[[[[]]],[],[]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[3,1,1,1]
[[[[],[]],[[]]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,1,1]
[[[[[]]],[[]]]]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,1,1,1,1]
[[[[],[],[]],[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,1,1]
[[[[],[[]]],[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,1,1,1]
[[[[[]],[]],[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[3,1,1,1]
[[[[[],[]]],[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,1,1]
[[[[[[]]]],[]]]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,1,1,1,1]
[[[[],[],[],[]]]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[4,1,1]
[[[[],[],[[]]]]]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,1,1]
[[[[],[[]],[]]]]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[3,1,1,1]
[[[[],[[],[]]]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,1,1,1]
[[[[],[[[]]]]]]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[2,1,1,1,1]
[[[[[]],[],[]]]]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[3,1,1,1]
[[[[[]],[[]]]]]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,1,1,1,1]
[[[[[],[]],[]]]]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,1,1]
[[[[[[]]],[]]]]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,1,1,1,1]
[[[[[],[],[]]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,1,1]
[[[[[],[[]]]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,1,1,1,1]
[[[[[[]],[]]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,1,1,1,1]
[[[[[[],[]]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,1,1,1,1]
[[[[[[[]]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1]
[[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7]
[[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,1]
[[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,1]
[[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[6,1]
[[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,1,1]
[[],[],[],[[]],[],[]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,1]
[[],[],[],[[]],[[]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,1,1]
[[],[],[],[[],[]],[]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[6,1]
[[],[],[],[[[]]],[]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,1,1]
[[],[],[],[[],[],[]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[6,1]
[[],[],[],[[],[[]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[5,1,1]
[[],[],[],[[[]],[]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[5,1,1]
[[],[],[],[[[],[]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[5,1,1]
[[],[],[],[[[[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[[],[],[[]],[],[],[]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,1]
[[],[],[[]],[],[[]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,1,1]
[[],[],[[]],[[]],[]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,1,1]
[[],[],[[]],[[],[]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[5,1,1]
[[],[],[[]],[[[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,1,1,1]
[[],[],[[],[]],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[6,1]
[[],[],[[[]]],[],[]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,1,1]
[[],[],[[],[]],[[]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[5,1,1]
[[],[],[[[]]],[[]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,1,1,1]
[[],[],[[],[],[]],[]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[6,1]
[[],[],[[],[[]]],[]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[5,1,1]
[[],[],[[[]],[]],[]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[5,1,1]
[[],[],[[[],[]]],[]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[5,1,1]
[[],[],[[[[]]]],[]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,1,1,1]
[[],[],[[],[],[],[]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[6,1]
[[],[],[[],[],[[]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[5,1,1]
[[],[],[[],[[]],[]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[5,1,1]
[[],[],[[],[[],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[5,1,1]
[[],[],[[],[[[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[4,1,1,1]
[[],[],[[[]],[],[]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[5,1,1]
[[],[],[[[]],[[]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[4,1,1,1]
[[],[],[[[],[]],[]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[5,1,1]
[[],[],[[[[]]],[]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[4,1,1,1]
[[],[],[[[],[],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[5,1,1]
[[],[],[[[],[[]]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[4,1,1,1]
[[],[],[[[[]],[]]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[4,1,1,1]
[[],[],[[[[],[]]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[4,1,1,1]
[[],[],[[[[[]]]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,1,1,1,1]
[[],[[]],[],[],[],[]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,1]
[[],[[]],[],[],[[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,1,1]
[[],[[]],[],[[]],[]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,1,1]
[[],[[]],[],[[],[]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[5,1,1]
[[],[[]],[],[[[]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,1,1,1]
[[],[[]],[[]],[],[]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,1,1]
[[],[[]],[[]],[[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,1,1,1]
[[],[[]],[[],[]],[]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[5,1,1]
[[],[[]],[[[]]],[]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,1,1,1]
[[],[[]],[[],[],[]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[5,1,1]
[[],[[]],[[],[[]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[4,1,1,1]
[[],[[]],[[[]],[]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[4,1,1,1]
[[],[[]],[[[],[]]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[4,1,1,1]
[[],[[]],[[[[]]]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,1,1,1,1]
[[],[[],[]],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[6,1]
[[],[[[]]],[],[],[]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,1,1]
[[],[[],[]],[],[[]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[5,1,1]
[[],[[[]]],[],[[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,1,1,1]
[[],[[],[]],[[]],[]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[5,1,1]
[[],[[[]]],[[]],[]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,1,1,1]
[[],[[],[]],[[],[]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[5,1,1]
[[],[[],[]],[[[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,1,1,1]
[[],[[[]]],[[],[]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,1,1,1]
[[],[[[]]],[[[]]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,1,1,1,1]
[[],[[],[],[]],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[6,1]
[[],[[],[[]]],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,1,1]
[[],[[[]],[]],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,1,1]
[[],[[[],[]]],[],[]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[5,1,1]
[[],[[[[]]]],[],[]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,1,1,1]
[[],[[],[],[]],[[]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,1,1]
[[],[[],[[]]],[[]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[4,1,1,1]
[[],[[[]],[]],[[]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[4,1,1,1]
[[],[[[],[]]],[[]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[4,1,1,1]
[[],[[[[]]]],[[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,1,1,1,1]
[[],[[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,1]
[[],[[],[],[[]]],[]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[5,1,1]
[[],[[],[[]],[]],[]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[5,1,1]
[[],[[],[[],[]]],[]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[5,1,1]
[[],[[],[[[]]]],[]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[4,1,1,1]
[[],[[[]],[],[]],[]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[5,1,1]
[[],[[[]],[[]]],[]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[4,1,1,1]
[[],[[[],[]],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[5,1,1]
[[],[[[[]]],[]],[]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[4,1,1,1]
[[],[[[],[],[]]],[]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[5,1,1]
[[],[[[],[[]]]],[]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[4,1,1,1]
[[],[[[[]],[]]],[]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[4,1,1,1]
[[],[[[[],[]]]],[]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[4,1,1,1]
[[],[[[[[]]]]],[]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,1,1,1,1]
[[],[[],[],[],[],[]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[6,1]
[[],[[],[],[],[[]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[5,1,1]
[[],[[],[],[[]],[]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[5,1,1]
[[],[[],[],[[],[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[5,1,1]
[[],[[],[],[[[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[4,1,1,1]
[[],[[],[[]],[],[]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[5,1,1]
[[],[[],[[]],[[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[4,1,1,1]
[[],[[],[[],[]],[]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[5,1,1]
[[],[[],[[[]]],[]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[4,1,1,1]
[[],[[],[[],[],[]]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[5,1,1]
[[],[[],[[],[[]]]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[4,1,1,1]
[[],[[],[[[]],[]]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[4,1,1,1]
[[],[[],[[[],[]]]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[4,1,1,1]
[[],[[],[[[[]]]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,1,1,1,1]
[[],[[[]],[],[],[]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[5,1,1]
[[],[[[]],[],[[]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,1,1,1]
[[],[[[]],[[]],[]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,1,1,1]
[[],[[[]],[[],[]]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[4,1,1,1]
[[],[[[]],[[[]]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,1,1,1,1]
[[],[[[],[]],[],[]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,1,1]
[[],[[[[]]],[],[]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[4,1,1,1]
[[],[[[],[]],[[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[4,1,1,1]
[[],[[[[]]],[[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[3,1,1,1,1]
[[],[[[],[],[]],[]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[5,1,1]
[[],[[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[4,1,1,1]
[[],[[[[]],[]],[]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[4,1,1,1]
[[],[[[[],[]]],[]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[4,1,1,1]
[[],[[[[[]]]],[]]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[3,1,1,1,1]
[[],[[[],[],[],[]]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[5,1,1]
[[],[[[],[],[[]]]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[4,1,1,1]
[[],[[[],[[]],[]]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[4,1,1,1]
[[],[[[],[[],[]]]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[4,1,1,1]
[[],[[[],[[[]]]]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[3,1,1,1,1]
[[],[[[[]],[],[]]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[4,1,1,1]
[[],[[[[]],[[]]]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[3,1,1,1,1]
[[],[[[[],[]],[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[4,1,1,1]
[[],[[[[[]]],[]]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[3,1,1,1,1]
[[],[[[[],[],[]]]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[4,1,1,1]
[[],[[[[],[[]]]]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[3,1,1,1,1]
[[],[[[[[]],[]]]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[3,1,1,1,1]
[[],[[[[[],[]]]]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[3,1,1,1,1]
[[],[[[[[[]]]]]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,1,1,1,1,1]
[[[]],[],[],[],[],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1]
[[[]],[],[],[],[[]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,1,1]
[[[]],[],[],[[]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,1,1]
[[[]],[],[],[[],[]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[5,1,1]
[[[]],[],[],[[[]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,1,1,1]
[[[]],[],[[]],[],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,1,1]
[[[]],[],[[]],[[]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,1,1,1]
[[[]],[],[[],[]],[]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[5,1,1]
[[[]],[],[[[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,1,1,1]
[[[]],[],[[],[],[]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[5,1,1]
[[[]],[],[[],[[]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[4,1,1,1]
[[[]],[],[[[]],[]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[4,1,1,1]
[[[]],[],[[[],[]]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[4,1,1,1]
[[[]],[],[[[[]]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,1,1,1,1]
[[[]],[[]],[],[],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,1,1]
[[[]],[[]],[],[[]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,1,1,1]
[[[]],[[]],[[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,1,1,1]
[[[]],[[]],[[],[]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,1,1]
[[[]],[[]],[[[]]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,1,1,1,1]
[[[]],[[],[]],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,1]
[[[]],[[[]]],[],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,1,1,1]
[[[]],[[],[]],[[]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[4,1,1,1]
[[[]],[[[]]],[[]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,1,1,1,1]
[[[]],[[],[],[]],[]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[5,1,1]
[[[]],[[],[[]]],[]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[4,1,1,1]
[[[]],[[[]],[]],[]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[4,1,1,1]
[[[]],[[[],[]]],[]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[4,1,1,1]
[[[]],[[[[]]]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,1,1,1,1]
[[[]],[[],[],[],[]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[5,1,1]
[[[]],[[],[],[[]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,1,1]
[[[]],[[],[[]],[]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,1,1]
[[[]],[[],[[],[]]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[4,1,1,1]
[[[]],[[],[[[]]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,1,1,1,1]
[[[]],[[[]],[],[]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[4,1,1,1]
[[[]],[[[]],[[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[3,1,1,1,1]
[[[]],[[[],[]],[]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[4,1,1,1]
[[[]],[[[[]]],[]]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[3,1,1,1,1]
[[[]],[[[],[],[]]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[4,1,1,1]
[[[]],[[[],[[]]]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[3,1,1,1,1]
[[[]],[[[[]],[]]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[3,1,1,1,1]
[[[]],[[[[],[]]]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[3,1,1,1,1]
[[[]],[[[[[]]]]]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,1,1,1,1,1]
[[[],[]],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,1]
[[[[]]],[],[],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,1]
[[[],[]],[],[],[[]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[5,1,1]
[[[[]]],[],[],[[]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,1,1,1]
[[[],[]],[],[[]],[]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[5,1,1]
[[[[]]],[],[[]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,1,1,1]
[[[],[]],[],[[],[]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[5,1,1]
[[[],[]],[],[[[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[4,1,1,1]
[[[[]]],[],[[],[]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,1,1]
[[[[]]],[],[[[]]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,1,1,1]
[[[],[]],[[]],[],[]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[5,1,1]
[[[[]]],[[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,1,1,1]
[[[],[]],[[]],[[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[4,1,1,1]
[[[[]]],[[]],[[]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,1,1,1,1]
[[[],[]],[[],[]],[]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[5,1,1]
[[[],[]],[[[]]],[]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[4,1,1,1]
[[[[]]],[[],[]],[]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[4,1,1,1]
[[[[]]],[[[]]],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,1,1,1,1]
[[[],[]],[[],[],[]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[5,1,1]
[[[],[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[4,1,1,1]
[[[],[]],[[[]],[]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[4,1,1,1]
[[[],[]],[[[],[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[4,1,1,1]
[[[],[]],[[[[]]]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,1,1,1]
[[[[]]],[[],[],[]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[4,1,1,1]
[[[[]]],[[],[[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,1,1,1,1]
[[[[]]],[[[]],[]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,1,1,1,1]
[[[[]]],[[[],[]]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,1,1,1,1]
[[[[]]],[[[[]]]]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,1,1,1,1,1]
[[[],[],[]],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,1]
[[[],[[]]],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[5,1,1]
[[[[]],[]],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,1,1]
[[[[],[]]],[],[],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,1,1]
[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,1,1]
[[[],[],[]],[],[[]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[5,1,1]
[[[],[[]]],[],[[]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,1,1]
[[[[]],[]],[],[[]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,1,1,1]
[[[[],[]]],[],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[4,1,1,1]
[[[[[]]]],[],[[]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,1,1,1,1]
[[[],[],[]],[[]],[]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[5,1,1]
[[[],[[]]],[[]],[]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,1,1]
[[[[]],[]],[[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,1,1,1]
[[[[],[]]],[[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[4,1,1,1]
[[[[[]]]],[[]],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,1,1,1,1]
[[[],[],[]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[5,1,1]
[[[],[],[]],[[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,1,1]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,1,1]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,1,1,1,1]
[[[[]],[]],[[],[]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,1,1,1]
[[[[]],[]],[[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,1,1,1]
[[[[],[]]],[[],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[4,1,1,1]
[[[[],[]]],[[[]]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,1,1,1]
[[[[[]]]],[[],[]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[3,1,1,1,1]
[[[[[]]]],[[[]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,1,1,1,1,1]
[[[],[],[],[]],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,1]
[[[],[],[[]]],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,1]
[[[],[[]],[]],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,1]
[[[],[[],[]]],[],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[5,1,1]
[[[],[[[]]]],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,1,1,1]
[[[[]],[],[]],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,1,1]
[[[[]],[[]]],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,1,1,1]
[[[[],[]],[]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,1,1]
[[[[[]]],[]],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,1,1,1]
[[[[],[],[]]],[],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,1,1]
[[[[],[[]]]],[],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[4,1,1,1]
[[[[[]],[]]],[],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,1,1,1]
[[[[[],[]]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,1,1,1]
[[[[[[]]]]],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,1,1,1]
[[[],[],[],[]],[[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,1]
[[[],[],[[]]],[[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[4,1,1,1]
[[[],[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,1,1,1]
[[[],[[],[]]],[[]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,1,1,1]
[[[],[[[]]]],[[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[3,1,1,1,1]
[[[[]],[],[]],[[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[4,1,1,1]
[[[[]],[[]]],[[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,1,1,1,1]
[[[[],[]],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[4,1,1,1]
[[[[[]]],[]],[[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[3,1,1,1,1]
[[[[],[],[]]],[[]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[4,1,1,1]
[[[[],[[]]]],[[]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,1,1,1,1]
[[[[[]],[]]],[[]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,1,1,1,1]
[[[[[],[]]]],[[]]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[3,1,1,1,1]
[[[[[[]]]]],[[]]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,1,1,1,1,1]
[[[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1]
[[[],[],[],[[]]],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[5,1,1]
[[[],[],[[]],[]],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[5,1,1]
[[[],[],[[],[]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[5,1,1]
[[[],[],[[[]]]],[]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[4,1,1,1]
[[[],[[]],[],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,1,1]
[[[],[[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[4,1,1,1]
[[[],[[],[]],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[5,1,1]
[[[],[[[]]],[]],[]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[4,1,1,1]
[[[],[[],[],[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,1,1]
[[[],[[],[[]]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[4,1,1,1]
[[[],[[[]],[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[4,1,1,1]
[[[],[[[],[]]]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[4,1,1,1]
[[[],[[[[]]]]],[]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[3,1,1,1,1]
[[[[]],[],[],[]],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,1,1]
[[[[]],[],[[]]],[]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[4,1,1,1]
[[[[]],[[]],[]],[]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,1,1,1]
[[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[4,1,1,1]
[[[[]],[[[]]]],[]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[3,1,1,1,1]
[[[[],[]],[],[]],[]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,1,1]
[[[[[]]],[],[]],[]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,1,1,1]
[[[[],[]],[[]]],[]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[4,1,1,1]
[[[[[]]],[[]]],[]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,1,1,1,1]
[[[[],[],[]],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,1,1]
[[[[],[[]]],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[4,1,1,1]
[[[[[]],[]],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,1,1,1]
[[[[[],[]]],[]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,1,1,1]
[[[[[[]]]],[]],[]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,1,1,1]
[[[[],[],[],[]]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,1,1]
[[[[],[],[[]]]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[4,1,1,1]
[[[[],[[]],[]]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,1,1,1]
[[[[],[[],[]]]],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,1,1,1]
[[[[],[[[]]]]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[3,1,1,1,1]
[[[[[]],[],[]]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,1,1,1]
[[[[[]],[[]]]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,1,1,1,1]
[[[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,1,1,1]
[[[[[[]]],[]]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,1,1,1]
[[[[[],[],[]]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,1,1,1]
[[[[[],[[]]]]],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,1,1,1,1]
[[[[[[]],[]]]],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,1,1,1]
[[[[[[],[]]]]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,1,1,1]
[[[[[[[]]]]]],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1]
[[[],[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,1]
[[[],[],[],[],[[]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[5,1,1]
[[[],[],[],[[]],[]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[5,1,1]
[[[],[],[],[[],[]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[5,1,1]
[[[],[],[],[[[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[4,1,1,1]
[[[],[],[[]],[],[]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[5,1,1]
[[[],[],[[]],[[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[4,1,1,1]
[[[],[],[[],[]],[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[5,1,1]
[[[],[],[[[]]],[]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[4,1,1,1]
[[[],[],[[],[],[]]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[5,1,1]
[[[],[],[[],[[]]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[4,1,1,1]
[[[],[],[[[]],[]]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[4,1,1,1]
[[[],[],[[[],[]]]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[4,1,1,1]
[[[],[],[[[[]]]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,1,1,1]
[[[],[[]],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[5,1,1]
[[[],[[]],[],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[4,1,1,1]
[[[],[[]],[[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[4,1,1,1]
[[[],[[]],[[],[]]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[4,1,1,1]
[[[],[[]],[[[]]]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[3,1,1,1,1]
[[[],[[],[]],[],[]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,1]
[[[],[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[4,1,1,1]
[[[],[[],[]],[[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[4,1,1,1]
[[[],[[[]]],[[]]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[3,1,1,1,1]
[[[],[[],[],[]],[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[5,1,1]
[[[],[[],[[]]],[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[4,1,1,1]
[[[],[[[]],[]],[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,1,1,1]
[[[],[[[],[]]],[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[4,1,1,1]
[[[],[[[[]]]],[]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[3,1,1,1,1]
[[[],[[],[],[],[]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[5,1,1]
[[[],[[],[],[[]]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[4,1,1,1]
[[[],[[],[[]],[]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[4,1,1,1]
[[[],[[],[[],[]]]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[4,1,1,1]
[[[],[[],[[[]]]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,1,1,1,1]
[[[],[[[]],[],[]]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,1,1,1]
[[[],[[[]],[[]]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[3,1,1,1,1]
[[[],[[[],[]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[4,1,1,1]
[[[],[[[[]]],[]]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[3,1,1,1,1]
[[[],[[[],[],[]]]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[4,1,1,1]
[[[],[[[],[[]]]]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[3,1,1,1,1]
[[[],[[[[]],[]]]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[3,1,1,1,1]
[[[],[[[[],[]]]]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[3,1,1,1,1]
[[[],[[[[[]]]]]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,1,1,1,1]
[[[[]],[],[],[],[]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[5,1,1]
[[[[]],[],[],[[]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,1,1]
[[[[]],[],[[]],[]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,1,1]
[[[[]],[],[[],[]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[4,1,1,1]
[[[[]],[],[[[]]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,1,1,1]
[[[[]],[[]],[],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[4,1,1,1]
[[[[]],[[]],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,1,1,1,1]
[[[[]],[[],[]],[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,1,1]
[[[[]],[[[]]],[]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,1,1,1,1]
[[[[]],[[],[],[]]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,1,1]
[[[[]],[[],[[]]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[3,1,1,1,1]
[[[[]],[[[]],[]]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[3,1,1,1,1]
[[[[]],[[[],[]]]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[3,1,1,1,1]
[[[[]],[[[[]]]]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[2,1,1,1,1,1]
[[[[],[]],[],[],[]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[5,1,1]
[[[[[]]],[],[],[]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,1,1,1]
[[[[],[]],[],[[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,1,1,1]
[[[[[]]],[],[[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[3,1,1,1,1]
[[[[],[]],[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,1,1,1]
[[[[[]]],[[]],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[3,1,1,1,1]
[[[[],[]],[[],[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,1,1,1]
[[[[],[]],[[[]]]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,1,1,1]
[[[[[]]],[[],[]]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[3,1,1,1,1]
[[[[[]]],[[[]]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[2,1,1,1,1,1]
[[[[],[],[]],[],[]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,1,1]
[[[[],[[]]],[],[]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,1,1]
[[[[[]],[]],[],[]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,1,1]
[[[[[],[]]],[],[]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[4,1,1,1]
[[[[[[]]]],[],[]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[3,1,1,1,1]
[[[[],[],[]],[[]]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[4,1,1,1]
[[[[],[[]]],[[]]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[3,1,1,1,1]
[[[[[]],[]],[[]]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[3,1,1,1,1]
[[[[[],[]]],[[]]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,1,1,1]
[[[[[[]]]],[[]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,1,1,1,1,1]
[[[[],[],[],[]],[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,1,1]
[[[[],[],[[]]],[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[4,1,1,1]
[[[[],[[]],[]],[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[4,1,1,1]
[[[[],[[],[]]],[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[4,1,1,1]
[[[[],[[[]]]],[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[3,1,1,1,1]
[[[[[]],[],[]],[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,1,1]
[[[[[]],[[]]],[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[3,1,1,1,1]
[[[[[],[]],[]],[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[4,1,1,1]
[[[[[[]]],[]],[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[3,1,1,1,1]
[[[[[],[],[]]],[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,1,1,1]
[[[[[],[[]]]],[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[3,1,1,1,1]
[[[[[[]],[]]],[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[3,1,1,1,1]
[[[[[[],[]]]],[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,1,1,1]
[[[[[[[]]]]],[]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,1,1,1,1,1]
[[[[],[],[],[],[]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[5,1,1]
[[[[],[],[],[[]]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[4,1,1,1]
[[[[],[],[[]],[]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[4,1,1,1]
[[[[],[],[[],[]]]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[4,1,1,1]
[[[[],[],[[[]]]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,1,1,1]
[[[[],[[]],[],[]]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[4,1,1,1]
[[[[],[[]],[[]]]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[3,1,1,1,1]
[[[[],[[],[]],[]]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[4,1,1,1]
[[[[],[[[]]],[]]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[3,1,1,1,1]
[[[[],[[],[],[]]]]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[4,1,1,1]
[[[[],[[],[[]]]]]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,1,1,1,1]
[[[[],[[[]],[]]]]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[3,1,1,1,1]
[[[[],[[[],[]]]]]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[3,1,1,1,1]
[[[[],[[[[]]]]]]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[2,1,1,1,1,1]
[[[[[]],[],[],[]]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,1,1]
[[[[[]],[],[[]]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[3,1,1,1,1]
[[[[[]],[[]],[]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[3,1,1,1,1]
[[[[[]],[[],[]]]]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[3,1,1,1,1]
[[[[[]],[[[]]]]]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[2,1,1,1,1,1]
[[[[[],[]],[],[]]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[4,1,1,1]
[[[[[[]]],[],[]]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[3,1,1,1,1]
[[[[[],[]],[[]]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,1,1,1]
[[[[[[]]],[[]]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,1,1,1,1,1]
[[[[[],[],[]],[]]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[4,1,1,1]
[[[[[],[[]]],[]]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[3,1,1,1,1]
[[[[[[]],[]],[]]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[3,1,1,1,1]
[[[[[[],[]]],[]]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,1,1,1]
[[[[[[[]]]],[]]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,1,1,1,1,1]
[[[[[],[],[],[]]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[4,1,1,1]
[[[[[],[],[[]]]]]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,1,1,1]
[[[[[],[[]],[]]]]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[3,1,1,1,1]
[[[[[],[[],[]]]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,1,1,1,1]
[[[[[],[[[]]]]]]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[2,1,1,1,1,1]
[[[[[[]],[],[]]]]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,1,1,1,1]
[[[[[[]],[[]]]]]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,1,1,1,1,1]
[[[[[[],[]],[]]]]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,1,1,1]
[[[[[[[]]],[]]]]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,1,1,1,1,1]
[[[[[[],[],[]]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,1,1,1]
[[[[[[],[[]]]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,1,1,1,1,1]
[[[[[[[]],[]]]]]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,1,1,1,1,1]
[[[[[[[],[]]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,1,1,1,1,1]
[[[[[[[[]]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8]
[[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[7,1]
[[],[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,1]
[[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[7,1]
[[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[]],[],[]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,1]
[[],[],[],[],[[]],[[]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[],[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[7,1]
[[],[],[],[],[[[]]],[]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[],[],[]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[7,1]
[[],[],[],[],[[],[[]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[[],[]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[6,1,1]
[[],[],[],[],[[[[]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,1,1,1]
[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,1]
[[],[],[],[[]],[],[[]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,1,1]
[[],[],[],[[]],[[]],[]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,1,1]
[[],[],[],[[]],[[],[]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[6,1,1]
[[],[],[],[[]],[[[]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[],[]],[],[]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[7,1]
[[],[],[],[[[]]],[],[]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,1,1]
[[],[],[],[[[]]],[[]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[],[],[]],[]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[7,1]
[[],[],[],[[],[[]]],[]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[6,1,1]
[[],[],[],[[[]],[]],[]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[6,1,1]
[[],[],[],[[[],[]]],[]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[6,1,1]
[[],[],[],[[[[]]]],[]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[],[],[],[]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[7,1]
[[],[],[],[[],[],[[]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[6,1,1]
[[],[],[],[[],[[]],[]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[6,1,1]
[[],[],[],[[],[[],[]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[6,1,1]
[[],[],[],[[],[[[]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[5,1,1,1]
[[],[],[],[[[]],[],[]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[6,1,1]
[[],[],[],[[[],[]],[]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[6,1,1]
[[],[],[],[[[[]]],[]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[5,1,1,1]
[[],[],[],[[[],[],[]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[6,1,1]
[[],[],[],[[[],[[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[[[]],[]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[[[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[5,1,1,1]
[[],[],[],[[[[[]]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,1,1,1,1]
[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,1]
[[],[],[[]],[],[],[[]]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[6,1,1]
[[],[],[[]],[],[[],[]]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[6,1,1]
[[],[],[[]],[],[[[]]]]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[5,1,1,1]
[[],[],[[]],[[]],[],[]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[6,1,1]
[[],[],[[]],[[[]]],[]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,1,1,1]
[[],[],[[]],[[],[],[]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[6,1,1]
[[],[],[[]],[[],[[]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[5,1,1,1]
[[],[],[[]],[[[]],[]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[5,1,1,1]
[[],[],[[]],[[[[]]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,1,1,1,1]
[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[7,1]
[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,1,1]
[[],[],[[],[]],[],[[]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[6,1,1]
[[],[],[[],[]],[[]],[]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[6,1,1]
[[],[],[[],[]],[[],[]]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[6,1,1]
[[],[],[[],[]],[[[]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[5,1,1,1]
[[],[],[[[]]],[[],[]]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[5,1,1,1]
[[],[],[[],[],[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[7,1]
[[],[],[[],[[]]],[],[]]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[6,1,1]
[[],[],[[[]],[]],[],[]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[6,1,1]
[[],[],[[[],[]]],[],[]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[6,1,1]
[[],[],[[[[]]]],[],[]]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[5,1,1,1]
[[],[],[[],[],[]],[[]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[6,1,1]
[[],[],[[],[],[],[]],[]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[7,1]
[[],[],[[],[[],[]]],[]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[6,1,1]
[[],[],[[[]],[],[]],[]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[6,1,1]
[[],[],[[[],[]],[]],[]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[6,1,1]
[[],[],[[[[]]],[]],[]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[5,1,1,1]
[[],[],[[[],[],[]]],[]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[6,1,1]
[[],[],[[[[[]]]]],[]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,1,1,1,1]
[[],[],[[],[],[],[],[]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[7,1]
[[],[],[[],[],[],[[]]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[6,1,1]
[[],[],[[],[],[[]],[]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[6,1,1]
[[],[],[[],[],[[],[]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[6,1,1]
[[],[],[[],[[]],[],[]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[6,1,1]
[[],[],[[],[[],[]],[]]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[6,1,1]
[[],[],[[],[[[]]],[]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[5,1,1,1]
[[],[],[[],[[],[[]]]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[5,1,1,1]
[[],[],[[],[[[]],[]]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[5,1,1,1]
[[],[],[[],[[[],[]]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[5,1,1,1]
[[],[],[[],[[[[]]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,1,1,1,1]
[[],[],[[[]],[],[],[]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[6,1,1]
[[],[],[[[]],[],[[]]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[5,1,1,1]
[[],[],[[[]],[[]],[]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[5,1,1,1]
[[],[],[[[]],[[[]]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[4,1,1,1,1]
[[],[],[[[[]]],[],[]]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[5,1,1,1]
[[],[],[[[],[]],[[]]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[5,1,1,1]
[[],[],[[[[]]],[[]]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[4,1,1,1,1]
[[],[],[[[[],[]]],[]]]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[5,1,1,1]
[[],[],[[[[[]]]],[]]]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[4,1,1,1,1]
[[],[],[[[],[],[],[]]]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[6,1,1]
[[],[],[[[[]],[],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[5,1,1,1]
[[],[],[[[[],[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[5,1,1,1]
[[],[],[[[[[]]],[]]]]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[4,1,1,1,1]
[[],[],[[[[],[],[]]]]]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[5,1,1,1]
[[],[],[[[[[]],[]]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[4,1,1,1,1]
[[],[],[[[[[[]]]]]]]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[3,1,1,1,1,1]
[[],[[]],[],[],[],[],[]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,1]
[[],[[]],[],[],[],[[]]]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,1,1]
[[],[[]],[],[],[[]],[]]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,1,1]
[[],[[]],[],[],[[],[]]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[6,1,1]
[[],[[]],[],[[],[]],[]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[6,1,1]
[[],[[]],[],[[[]],[]]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[5,1,1,1]
[[],[[]],[],[[[],[]]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[5,1,1,1]
[[],[[]],[],[[[[]]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,1,1,1,1]
[[],[[]],[[]],[],[],[]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,1,1]
[[],[[]],[[]],[[]],[]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,1,1,1]
[[],[[]],[[]],[[],[]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[5,1,1,1]
[[],[[]],[[]],[[[]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[4,1,1,1,1]
[[],[[]],[[],[]],[],[]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[6,1,1]
[[],[[]],[[[]]],[],[]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[5,1,1,1]
[[],[[]],[[[]]],[[]]]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[4,1,1,1,1]
[[],[[]],[[],[],[]],[]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[6,1,1]
[[],[[]],[[],[[]]],[]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[5,1,1,1]
[[],[[]],[[],[],[],[]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[6,1,1]
[[],[[]],[[],[[]],[]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[5,1,1,1]
[[],[[]],[[],[[],[]]]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[5,1,1,1]
[[],[[]],[[],[[[]]]]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[4,1,1,1,1]
[[],[[]],[[[]],[],[]]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[5,1,1,1]
[[],[[]],[[[]],[[]]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[4,1,1,1,1]
[[],[[]],[[[],[]],[]]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[5,1,1,1]
[[],[[]],[[[[]]],[]]]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[4,1,1,1,1]
[[],[[]],[[[[[]]]]]]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[3,1,1,1,1,1]
[[],[[],[]],[],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[7,1]
[[],[[[]]],[],[],[],[]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,1,1]
[[],[[],[]],[],[],[[]]]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[6,1,1]
[[],[[],[]],[],[[]],[]]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[6,1,1]
[[],[[[]]],[],[[]],[]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,1,1,1]
[[],[[],[]],[],[[],[]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[6,1,1]
[[],[[],[]],[],[[[]]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[5,1,1,1]
[[],[[[]]],[],[[],[]]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[5,1,1,1]
[[],[[[]]],[],[[[]]]]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[4,1,1,1,1]
[[],[[],[]],[[]],[],[]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[6,1,1]
[[],[[[]]],[[]],[],[]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,1,1,1]
[[],[[],[]],[[],[]],[]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[6,1,1]
[[],[[[]]],[[],[]],[]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[5,1,1,1]
[[],[[[]]],[[[]]],[]]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[4,1,1,1,1]
[[],[[],[]],[[],[],[]]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[6,1,1]
[[],[[],[]],[[[]],[]]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[5,1,1,1]
[[],[[],[]],[[[[]]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,1,1,1,1]
[[],[[[]]],[[],[],[]]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[5,1,1,1]
[[],[[[]]],[[],[[]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[4,1,1,1,1]
[[],[[[]]],[[[]],[]]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[4,1,1,1,1]
[[],[[[]]],[[[[]]]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[3,1,1,1,1,1]
[[],[[],[],[]],[],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[7,1]
[[],[[],[[]]],[],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[6,1,1]
[[],[[[]],[]],[],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[6,1,1]
[[],[[[],[]]],[],[],[]]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[6,1,1]
[[],[[[[]]]],[],[],[]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,1,1,1]
[[],[[],[],[]],[],[[]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[6,1,1]
[[],[[],[[]]],[],[[]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[5,1,1,1]
[[],[[[]],[]],[],[[]]]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[5,1,1,1]
[[],[[[],[]]],[],[[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[5,1,1,1]
[[],[[[[]]]],[],[[]]]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[4,1,1,1,1]
[[],[[],[],[]],[[]],[]]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[6,1,1]
[[],[[],[[]]],[[]],[]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,1,1,1]
[[],[[[],[]]],[[]],[]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[5,1,1,1]
[[],[[[[]]]],[[]],[]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[4,1,1,1,1]
[[],[[],[],[]],[[],[]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[6,1,1]
[[],[[],[],[]],[[[]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,1,1,1]
[[],[[],[[]]],[[],[]]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,1,1,1]
[[],[[],[[]]],[[[]]]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[4,1,1,1,1]
[[],[[[]],[]],[[],[]]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[5,1,1,1]
[[],[[[]],[]],[[[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[4,1,1,1,1]
[[],[[[[]]]],[[],[]]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[4,1,1,1,1]
[[],[[[[]]]],[[[]]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[],[],[],[]],[],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[7,1]
[[],[[],[[]],[]],[],[]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[6,1,1]
[[],[[],[[],[]]],[],[]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[6,1,1]
[[],[[[]],[],[]],[],[]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[6,1,1]
[[],[[[],[]],[]],[],[]]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[6,1,1]
[[],[[[[]],[]]],[],[]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[5,1,1,1]
[[],[[[[],[]]]],[],[]]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[5,1,1,1]
[[],[[[[[]]]]],[],[]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,1,1,1,1]
[[],[[],[],[],[]],[[]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,1,1]
[[],[[[]],[],[]],[[]]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[5,1,1,1]
[[],[[[]],[[]]],[[]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[4,1,1,1,1]
[[],[[[[]]],[]],[[]]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[4,1,1,1,1]
[[],[[[],[],[]]],[[]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[5,1,1,1]
[[],[[[[]],[]]],[[]]]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[4,1,1,1,1]
[[],[[[[[]]]]],[[]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[],[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[7,1]
[[],[[],[],[],[[]]],[]]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[6,1,1]
[[],[[],[],[[]],[]],[]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[6,1,1]
[[],[[],[[]],[],[]],[]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[6,1,1]
[[],[[],[[]],[[]]],[]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[5,1,1,1]
[[],[[],[[],[]],[]],[]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[6,1,1]
[[],[[],[[[]]],[]],[]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[5,1,1,1]
[[],[[],[[],[],[]]],[]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[6,1,1]
[[],[[],[[],[[]]]],[]]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[5,1,1,1]
[[],[[],[[[],[]]]],[]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[5,1,1,1]
[[],[[],[[[[]]]]],[]]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[4,1,1,1,1]
[[],[[[]],[],[],[]],[]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[6,1,1]
[[],[[[]],[[],[]]],[]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[5,1,1,1]
[[],[[[]],[[[]]]],[]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[4,1,1,1,1]
[[],[[[],[]],[],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[6,1,1]
[[],[[[[]]],[],[]],[]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[5,1,1,1]
[[],[[[[]]],[[]]],[]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[4,1,1,1,1]
[[],[[[],[],[]],[]],[]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[6,1,1]
[[],[[[[[]]]],[]],[]]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[4,1,1,1,1]
[[],[[[],[],[],[]]],[]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[6,1,1]
[[],[[[],[[]],[]]],[]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[5,1,1,1]
[[],[[[[],[]],[]]],[]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[5,1,1,1]
[[],[[[[[]]],[]]],[]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[4,1,1,1,1]
[[],[[[[[],[]]]]],[]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[4,1,1,1,1]
[[],[[[[[[]]]]]],[]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[],[],[],[],[],[]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[7,1]
[[],[[],[],[],[],[[]]]]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[6,1,1]
[[],[[],[],[],[[]],[]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[6,1,1]
[[],[[],[],[],[[],[]]]]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[6,1,1]
[[],[[],[],[[]],[],[]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[6,1,1]
[[],[[],[],[[],[]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[6,1,1]
[[],[[],[],[[],[],[]]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[6,1,1]
[[],[[],[],[[],[[]]]]]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[6,7,4,5,3,2,8,1]=>[5,1,1,1]
[[],[[],[],[[[]],[]]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[5,1,1,1]
[[],[[],[],[[[],[]]]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[5,1,1,1]
[[],[[],[],[[[[]]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,1,1,1,1]
[[],[[],[[]],[],[],[]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[6,1,1]
[[],[[],[[]],[[]],[]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[5,1,1,1]
[[],[[],[[]],[[],[]]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[5,1,1,1]
[[],[[],[[],[]],[],[]]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,1,1]
[[],[[],[[],[]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[5,1,1,1]
[[],[[],[[],[],[]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[6,1,1]
[[],[[],[[],[[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[5,1,1,1]
[[],[[],[[[]],[]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[5,1,1,1]
[[],[[],[[],[],[],[]]]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[6,1,1]
[[],[[],[[],[[]],[]]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[5,1,1,1]
[[],[[],[[],[[],[]]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[5,1,1,1]
[[],[[],[[[]],[],[]]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[5,1,1,1]
[[],[[],[[[],[]],[]]]]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[5,1,1,1]
[[],[[],[[[],[],[]]]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[5,1,1,1]
[[],[[],[[[],[[]]]]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[4,1,1,1,1]
[[],[[],[[[[]],[]]]]]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[4,1,1,1,1]
[[],[[],[[[[[]]]]]]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[3,1,1,1,1,1]
[[],[[[]],[],[],[],[]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[6,1,1]
[[],[[[]],[],[[]],[]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[5,1,1,1]
[[],[[[]],[],[[],[]]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[5,1,1,1]
[[],[[[]],[],[[[]]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,1,1,1,1]
[[],[[[]],[[]],[],[]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[5,1,1,1]
[[],[[[]],[[]],[[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[4,1,1,1,1]
[[],[[[]],[[],[]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[5,1,1,1]
[[],[[[]],[[[]]],[]]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[4,1,1,1,1]
[[],[[[]],[[],[],[]]]]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[5,1,1,1]
[[],[[[]],[[],[[]]]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[4,1,1,1,1]
[[],[[[]],[[[]],[]]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[4,1,1,1,1]
[[],[[[]],[[[],[]]]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[4,1,1,1,1]
[[],[[[]],[[[[]]]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[3,1,1,1,1,1]
[[],[[[],[]],[],[],[]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[6,1,1]
[[],[[[[]]],[],[],[]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[5,1,1,1]
[[],[[[[]]],[],[[]]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[4,1,1,1,1]
[[],[[[],[]],[[]],[]]]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[5,1,1,1]
[[],[[[[]]],[[]],[]]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[4,1,1,1,1]
[[],[[[],[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[5,1,1,1]
[[],[[[],[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[4,1,1,1,1]
[[],[[[[]]],[[],[]]]]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[4,1,1,1,1]
[[],[[[[]]],[[[]]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[3,1,1,1,1,1]
[[],[[[[[]]]],[],[]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[4,1,1,1,1]
[[],[[[[],[]]],[[]]]]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[4,1,1,1,1]
[[],[[[[[]]]],[[]]]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[3,1,1,1,1,1]
[[],[[[],[],[],[]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[6,1,1]
[[],[[[],[[],[]]],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[5,1,1,1]
[[],[[[[],[]],[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[5,1,1,1]
[[],[[[[[]]],[]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[4,1,1,1,1]
[[],[[[[],[],[]]],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[5,1,1,1]
[[],[[[[],[[]]]],[]]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[4,1,1,1,1]
[[],[[[[[]],[]]],[]]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[4,1,1,1,1]
[[],[[[[[],[]]]],[]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[4,1,1,1,1]
[[],[[[[[[]]]]],[]]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[3,1,1,1,1,1]
[[],[[[],[],[],[],[]]]]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[6,1,1]
[[],[[[],[],[],[[]]]]]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[5,1,1,1]
[[],[[[],[],[[]],[]]]]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[5,1,1,1]
[[],[[[],[],[[[]]]]]]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[4,1,1,1,1]
[[],[[[],[[]],[],[]]]]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[5,1,1,1]
[[],[[[],[[]],[[]]]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[4,1,1,1,1]
[[],[[[],[[[]]],[]]]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[4,1,1,1,1]
[[],[[[],[[],[],[]]]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[5,1,1,1]
[[],[[[],[[[[]]]]]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[3,1,1,1,1,1]
[[],[[[[]],[],[],[]]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[5,1,1,1]
[[],[[[[]],[[],[]]]]]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[4,1,1,1,1]
[[],[[[[]],[[[]]]]]]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[3,1,1,1,1,1]
[[],[[[[],[]],[],[]]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[5,1,1,1]
[[],[[[[[]]],[],[]]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[4,1,1,1,1]
[[],[[[[[]]],[[]]]]]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[3,1,1,1,1,1]
[[],[[[[],[],[]],[]]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[5,1,1,1]
[[],[[[[],[[]]],[]]]]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[4,1,1,1,1]
[[],[[[[[]],[]],[]]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[4,1,1,1,1]
[[],[[[[[],[]]],[]]]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[4,1,1,1,1]
[[],[[[[[[]]]],[]]]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[3,1,1,1,1,1]
[[],[[[[],[],[],[]]]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[5,1,1,1]
[[],[[[[],[[[]]]]]]]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[3,1,1,1,1,1]
[[],[[[[[]],[],[]]]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[4,1,1,1,1]
[[],[[[[[[]]],[]]]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[3,1,1,1,1,1]
[[],[[[[[],[],[]]]]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[4,1,1,1,1]
[[],[[[[[],[[]]]]]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[[[[[]],[]]]]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[[[[[],[]]]]]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[3,1,1,1,1,1]
[[],[[[[[[[]]]]]]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,1,1,1,1,1,1]
[[[]],[],[],[],[],[],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,1]
[[[]],[],[],[],[],[[]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,1,1]
[[[]],[],[],[],[[]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,1,1]
[[[]],[],[],[],[[],[]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[6,1,1]
[[[]],[],[],[],[[[]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,1,1,1]
[[[]],[],[],[[]],[],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,1,1]
[[[]],[],[],[[]],[[]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[5,1,1,1]
[[[]],[],[],[[],[]],[]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[6,1,1]
[[[]],[],[],[[[]]],[]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[5,1,1,1]
[[[]],[],[],[[],[],[]]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[6,1,1]
[[[]],[],[],[[],[[]]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[5,1,1,1]
[[[]],[],[],[[[],[]]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[5,1,1,1]
[[[]],[],[],[[[[]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,1,1,1,1]
[[[]],[],[[]],[],[],[]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[6,1,1]
[[[]],[],[[]],[],[[]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[5,1,1,1]
[[[]],[],[[]],[[]],[]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[5,1,1,1]
[[[]],[],[[]],[[],[]]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[5,1,1,1]
[[[]],[],[[],[]],[],[]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[6,1,1]
[[[]],[],[[[]]],[],[]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[5,1,1,1]
[[[]],[],[[],[[]]],[]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[5,1,1,1]
[[[]],[],[[[]],[]],[]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[5,1,1,1]
[[[]],[],[[],[],[],[]]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[6,1,1]
[[[]],[],[[],[],[[]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[5,1,1,1]
[[[]],[],[[],[[],[]]]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[5,1,1,1]
[[[]],[],[[],[[[]]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[4,1,1,1,1]
[[[]],[],[[[],[]],[]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[5,1,1,1]
[[[]],[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[5,1,1,1]
[[[]],[],[[[],[[]]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[4,1,1,1,1]
[[[]],[],[[[[[]]]]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[3,1,1,1,1,1]
[[[]],[[]],[],[],[],[]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[6,1,1]
[[[]],[[]],[],[],[[]]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[5,1,1,1]
[[[]],[[]],[],[[]],[]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[5,1,1,1]
[[[]],[[]],[[]],[],[]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[5,1,1,1]
[[[]],[[]],[[]],[[]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,1,1,1,1]
[[[]],[[]],[[],[]],[]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[5,1,1,1]
[[[]],[[]],[[[]]],[]]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[4,1,1,1,1]
[[[]],[[]],[[],[],[]]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[5,1,1,1]
[[[]],[[]],[[],[[]]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[]],[[[]],[]]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[]],[[[],[]]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[]],[[[[]]]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[3,1,1,1,1,1]
[[[]],[[[]]],[],[],[]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,1,1,1]
[[[]],[[],[]],[[[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[4,1,1,1,1]
[[[]],[[[]]],[[],[]]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[4,1,1,1,1]
[[[]],[[],[[]]],[],[]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[5,1,1,1]
[[[]],[[[]],[]],[],[]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[5,1,1,1]
[[[]],[[[],[]]],[],[]]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[5,1,1,1]
[[[]],[[[[]]]],[],[]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[4,1,1,1,1]
[[[]],[[],[],[]],[[]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[5,1,1,1]
[[[]],[[],[[]]],[[]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[4,1,1,1,1]
[[[]],[[[]],[]],[[]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[4,1,1,1,1]
[[[]],[[[[]]]],[[]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[3,1,1,1,1,1]
[[[]],[[],[],[],[]],[]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[6,1,1]
[[[]],[[],[[]],[]],[]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[5,1,1,1]
[[[]],[[],[[],[]]],[]]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[5,1,1,1]
[[[]],[[[]],[],[]],[]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[5,1,1,1]
[[[]],[[[[]]],[]],[]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[4,1,1,1,1]
[[[]],[[[],[],[]]],[]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[5,1,1,1]
[[[]],[[[],[[]]]],[]]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[4,1,1,1,1]
[[[]],[[[[],[]]]],[]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[4,1,1,1,1]
[[[]],[[[[[]]]]],[]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[3,1,1,1,1,1]
[[[]],[[],[],[],[],[]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[6,1,1]
[[[]],[[],[],[],[[]]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[5,1,1,1]
[[[]],[[],[],[[]],[]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[5,1,1,1]
[[[]],[[],[],[[[]]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[],[[]],[],[]]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[5,1,1,1]
[[[]],[[],[[]],[[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[],[[[]]],[]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,1,1,1]
[[[]],[[],[[],[[]]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[4,1,1,1,1]
[[[]],[[],[[[[]]]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[3,1,1,1,1,1]
[[[]],[[[]],[],[],[]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[5,1,1,1]
[[[]],[[[]],[[],[]]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[4,1,1,1,1]
[[[]],[[[]],[[[]]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[]]],[],[]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[4,1,1,1,1]
[[[]],[[[],[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[4,1,1,1,1]
[[[]],[[[[]]],[[]]]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[],[]]],[]]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[4,1,1,1,1]
[[[]],[[[[[]]]],[]]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[3,1,1,1,1,1]
[[[]],[[[],[],[],[]]]]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[5,1,1,1]
[[[]],[[[[]],[],[]]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[4,1,1,1,1]
[[[]],[[[[],[]],[]]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[4,1,1,1,1]
[[[]],[[[[[]]],[]]]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[],[[]]]]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[[]],[]]]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[[],[]]]]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[3,1,1,1,1,1]
[[[]],[[[[[[]]]]]]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[2,1,1,1,1,1,1]
[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,1]
[[[[]]],[],[],[],[],[]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,1,1]
[[[],[]],[],[],[],[[]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[6,1,1]
[[[[]]],[],[],[],[[]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[5,1,1,1]
[[[],[]],[],[],[[]],[]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[6,1,1]
[[[[]]],[],[],[[]],[]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[5,1,1,1]
[[[],[]],[],[],[[],[]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[6,1,1]
[[[],[]],[],[],[[[]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[5,1,1,1]
[[[[]]],[],[],[[[]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[4,1,1,1,1]
[[[],[]],[],[[]],[],[]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[6,1,1]
[[[[]]],[],[[]],[],[]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[5,1,1,1]
[[[],[]],[],[[]],[[]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[5,1,1,1]
[[[],[]],[],[[],[]],[]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[6,1,1]
[[[],[]],[],[[[]]],[]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[5,1,1,1]
[[[[]]],[],[[],[]],[]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[5,1,1,1]
[[[],[]],[],[[],[],[]]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[6,1,1]
[[[],[]],[],[[],[[]]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[5,1,1,1]
[[[],[]],[],[[[],[]]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[5,1,1,1]
[[[],[]],[],[[[[]]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,1,1,1,1]
[[[[]]],[],[[],[[]]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,1,1,1]
[[[[]]],[],[[[]],[]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,1,1,1]
[[[[]]],[],[[[],[]]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,1,1,1]
[[[],[]],[[]],[],[],[]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[6,1,1]
[[[[]]],[[]],[],[],[]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,1,1,1]
[[[],[]],[[]],[],[[]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[5,1,1,1]
[[[[]]],[[]],[],[[]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,1,1,1,1]
[[[],[]],[[]],[[]],[]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[5,1,1,1]
[[[[]]],[[]],[[]],[]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[4,1,1,1,1]
[[[],[]],[[]],[[],[]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[5,1,1,1]
[[[],[]],[[]],[[[]]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[4,1,1,1,1]
[[[[]]],[[]],[[],[]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[]],[[[]]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[3,1,1,1,1,1]
[[[[]]],[[],[]],[],[]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[5,1,1,1]
[[[[]]],[[[]]],[],[]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[4,1,1,1,1]
[[[[]]],[[],[]],[[]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[]]],[[]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[3,1,1,1,1,1]
[[[],[]],[[],[],[]],[]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[6,1,1]
[[[],[]],[[[[]]]],[]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[4,1,1,1,1]
[[[[]]],[[],[],[]],[]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[5,1,1,1]
[[[[]]],[[],[[]]],[]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[]],[]],[]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[],[]]],[]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[[]]]],[]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[3,1,1,1,1,1]
[[[],[]],[[],[],[],[]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[6,1,1]
[[[],[]],[[],[[]],[]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[5,1,1,1]
[[[],[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[5,1,1,1]
[[[],[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[5,1,1,1]
[[[],[]],[[[],[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[5,1,1,1]
[[[],[]],[[[[]]],[]]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[4,1,1,1,1]
[[[],[]],[[[],[],[]]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[5,1,1,1]
[[[],[]],[[[[]],[]]]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[4,1,1,1,1]
[[[],[]],[[[[[]]]]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,1,1,1,1]
[[[[]]],[[],[],[],[]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[5,1,1,1]
[[[[]]],[[],[[[]]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[3,1,1,1,1,1]
[[[[]]],[[[]],[],[]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[]],[[]]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,1,1,1,1,1]
[[[[]]],[[[],[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[4,1,1,1,1]
[[[[]]],[[[[]]],[]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,1,1,1,1,1]
[[[[]]],[[[],[[]]]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,1,1,1,1,1]
[[[[]]],[[[[[]]]]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,1,1,1,1,1,1]
[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,1]
[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[6,1,1]
[[[[]],[]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[6,1,1]
[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[6,1,1]
[[[[[]]]],[],[],[],[]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,1,1,1]
[[[],[],[]],[],[],[[]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[6,1,1]
[[[],[[]]],[],[],[[]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[5,1,1,1]
[[[[]],[]],[],[],[[]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[5,1,1,1]
[[[[[]]]],[],[],[[]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[4,1,1,1,1]
[[[],[],[]],[],[[]],[]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[6,1,1]
[[[],[[]]],[],[[]],[]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[5,1,1,1]
[[[[]],[]],[],[[]],[]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[5,1,1,1]
[[[[],[]]],[],[[]],[]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[5,1,1,1]
[[[[[]]]],[],[[]],[]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,1,1,1,1]
[[[],[],[]],[],[[],[]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[6,1,1]
[[[],[],[]],[],[[[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[5,1,1,1]
[[[],[[]]],[],[[],[]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[5,1,1,1]
[[[[]],[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,1,1,1,1]
[[[[[]]]],[],[[],[]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,1,1,1,1]
[[[[[]]]],[],[[[]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[]],[[]],[],[]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[6,1,1]
[[[],[[]]],[[]],[],[]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[5,1,1,1]
[[[[]],[]],[[]],[],[]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[5,1,1,1]
[[[[[]]]],[[]],[],[]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,1,1,1,1]
[[[],[],[]],[[]],[[]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[5,1,1,1]
[[[],[[]]],[[]],[[]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,1,1,1]
[[[[]],[]],[[]],[[]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,1,1,1,1]
[[[[[]]]],[[]],[[]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[]],[[],[]],[]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[6,1,1]
[[[],[],[]],[[[]]],[]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[5,1,1,1]
[[[[]],[]],[[],[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[5,1,1,1]
[[[[]],[]],[[[]]],[]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,1,1,1,1]
[[[[],[]]],[[],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[5,1,1,1]
[[[[],[]]],[[[]]],[]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[4,1,1,1,1]
[[[[[]]]],[[],[]],[]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,1,1,1,1]
[[[[[]]]],[[[]]],[]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[]],[[],[],[]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[6,1,1]
[[[],[],[]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[5,1,1,1]
[[[],[],[]],[[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[5,1,1,1]
[[[],[],[]],[[[],[]]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[5,1,1,1]
[[[],[],[]],[[[[]]]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,1,1,1]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[5,1,1,1]
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,1,1,1]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[4,1,1,1,1]
[[[],[[]]],[[[],[]]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,1,1,1]
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,1,1,1,1,1]
[[[[]],[]],[[],[],[]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[5,1,1,1]
[[[[]],[]],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,1,1,1,1]
[[[[]],[]],[[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[4,1,1,1,1]
[[[[]],[]],[[[],[]]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,1,1,1,1]
[[[[]],[]],[[[[]]]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[3,1,1,1,1,1]
[[[[],[]]],[[],[],[]]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[5,1,1,1]
[[[[],[]]],[[[]],[]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[4,1,1,1,1]
[[[[],[]]],[[[[]]]]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[3,1,1,1,1,1]
[[[[[]]]],[[],[],[]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,1,1,1,1]
[[[[[]]]],[[],[[]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[3,1,1,1,1,1]
[[[[[]]]],[[[]],[]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[3,1,1,1,1,1]
[[[[[]]]],[[[],[]]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[3,1,1,1,1,1]
[[[[[]]]],[[[[]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,1]
[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[6,1,1]
[[[],[[]],[]],[],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[6,1,1]
[[[],[[],[]]],[],[],[]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[6,1,1]
[[[],[[[]]]],[],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,1,1]
[[[[]],[],[]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,1,1]
[[[[]],[[]]],[],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,1,1,1]
[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,1,1]
[[[[[]]],[]],[],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,1,1,1]
[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[6,1,1]
[[[[],[[]]]],[],[],[]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[5,1,1,1]
[[[[[]],[]]],[],[],[]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[5,1,1,1]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[5,1,1,1]
[[[[[[]]]]],[],[],[]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,1,1,1,1]
[[[],[],[],[]],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[6,1,1]
[[[],[],[[]]],[],[[]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,1,1]
[[[[]],[],[]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[5,1,1,1]
[[[[]],[[]]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[4,1,1,1,1]
[[[[],[]],[]],[],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[5,1,1,1]
[[[[],[[]]]],[],[[]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[4,1,1,1,1]
[[[[[]],[]]],[],[[]]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[4,1,1,1,1]
[[[[[],[]]]],[],[[]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[4,1,1,1,1]
[[[[[[]]]]],[],[[]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[],[]],[[]],[]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[6,1,1]
[[[],[[],[]]],[[]],[]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[5,1,1,1]
[[[],[[[]]]],[[]],[]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[4,1,1,1,1]
[[[[]],[],[]],[[]],[]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,1,1,1]
[[[[],[[]]]],[[]],[]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[4,1,1,1,1]
[[[[[[]]]]],[[]],[]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[],[]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[6,1,1]
[[[],[],[],[]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,1,1]
[[[],[],[[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[4,1,1,1,1]
[[[],[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[5,1,1,1]
[[[],[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,1,1,1,1]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,1,1,1,1]
[[[],[[[]]]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5]=>[4,1,1,1,1]
[[[],[[[]]]],[[[]]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[3,1,1,1,1,1]
[[[[]],[],[]],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[5,1,1,1]
[[[[]],[],[]],[[[]]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[4,1,1,1,1]
[[[[]],[[]]],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[4,1,1,1,1]
[[[[]],[[]]],[[[]]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,1,1,1,1,1]
[[[[],[]],[]],[[],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[5,1,1,1]
[[[[],[]],[]],[[[]]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[4,1,1,1,1]
[[[[[]]],[]],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[4,1,1,1,1]
[[[[[]]],[]],[[[]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,1,1,1,1,1]
[[[[],[[]]]],[[],[]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[4,1,1,1,1]
[[[[],[[]]]],[[[]]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,1,1,1,1,1]
[[[[[]],[]]],[[],[]]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[4,1,1,1,1]
[[[[[]],[]]],[[[]]]]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[3,1,1,1,1,1]
[[[[[],[]]]],[[],[]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[4,1,1,1,1]
[[[[[[]]]]],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[3,1,1,1,1,1]
[[[[[[]]]]],[[[]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,1]
[[[],[],[],[[]]],[],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,1]
[[[],[],[[],[]]],[],[]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[6,1,1]
[[[],[],[[[]]]],[],[]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[5,1,1,1]
[[[],[[]],[],[]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[6,1,1]
[[[],[[]],[[]]],[],[]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[5,1,1,1]
[[[],[[],[]],[]],[],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[6,1,1]
[[[],[[],[],[]]],[],[]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[6,1,1]
[[[],[[[]],[]]],[],[]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[5,1,1,1]
[[[],[[[],[]]]],[],[]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[5,1,1,1]
[[[],[[[[]]]]],[],[]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[4,1,1,1,1]
[[[[]],[],[],[]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,1,1]
[[[[]],[],[[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[5,1,1,1]
[[[[]],[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[5,1,1,1]
[[[[]],[[[]]]],[],[]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[4,1,1,1,1]
[[[[[]]],[],[]],[],[]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[5,1,1,1]
[[[[],[]],[[]]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[5,1,1,1]
[[[[[]]],[[]]],[],[]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[4,1,1,1,1]
[[[[],[],[]],[]],[],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[6,1,1]
[[[[],[[]]],[]],[],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[5,1,1,1]
[[[[[]],[]],[]],[],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[5,1,1,1]
[[[[[],[]]],[]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,1,1,1]
[[[[[[]]]],[]],[],[]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[4,1,1,1,1]
[[[[],[],[],[]]],[],[]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[6,1,1]
[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[5,1,1,1]
[[[[],[[]],[]]],[],[]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[5,1,1,1]
[[[[],[[[]]]]],[],[]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[4,1,1,1,1]
[[[[[]],[],[]]],[],[]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[5,1,1,1]
[[[[[]],[[]]]],[],[]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[4,1,1,1,1]
[[[[[],[],[]]]],[],[]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[5,1,1,1]
[[[[[[],[]]]]],[],[]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[4,1,1,1,1]
[[[[[[[]]]]]],[],[]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,1,1,1,1,1]
[[[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,1]
[[[],[],[],[[]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[5,1,1,1]
[[[],[],[[],[]]],[[]]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[5,1,1,1]
[[[],[],[[[]]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[4,1,1,1,1]
[[[],[[]],[],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[5,1,1,1]
[[[],[[]],[[]]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[4,1,1,1,1]
[[[],[[],[],[]]],[[]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[5,1,1,1]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[4,1,1,1,1]
[[[],[[[]],[]]],[[]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[4,1,1,1,1]
[[[],[[[[]]]]],[[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[3,1,1,1,1,1]
[[[[]],[],[],[]],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[5,1,1,1]
[[[[]],[],[[]]],[[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[4,1,1,1,1]
[[[[]],[[]],[]],[[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,1,1,1,1]
[[[[]],[[[]]]],[[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[3,1,1,1,1,1]
[[[[[]]],[],[]],[[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[4,1,1,1,1]
[[[[[]]],[[]]],[[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,1,1,1,1,1]
[[[[],[],[]],[]],[[]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[5,1,1,1]
[[[[],[[]]],[]],[[]]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[4,1,1,1,1]
[[[[[]],[]],[]],[[]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[4,1,1,1,1]
[[[[[[]]]],[]],[[]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[3,1,1,1,1,1]
[[[[],[],[],[]]],[[]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[5,1,1,1]
[[[[],[],[[]]]],[[]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[4,1,1,1,1]
[[[[],[[]],[]]],[[]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[4,1,1,1,1]
[[[[],[[],[]]]],[[]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,1,1,1,1]
[[[[],[[[]]]]],[[]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[3,1,1,1,1,1]
[[[[[]],[],[]]],[[]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[4,1,1,1,1]
[[[[[]],[[]]]],[[]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[3,1,1,1,1,1]
[[[[[],[]],[]]],[[]]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[4,1,1,1,1]
[[[[[],[],[]]]],[[]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[4,1,1,1,1]
[[[[[[]],[]]]],[[]]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[3,1,1,1,1,1]
[[[[[[],[]]]]],[[]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[]]]]]],[[]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1]
[[[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[6,1,1]
[[[],[],[],[[],[]]],[]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[6,1,1]
[[[],[],[],[[[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[5,1,1,1]
[[[],[],[[]],[[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[5,1,1,1]
[[[],[],[[],[]],[]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[6,1,1]
[[[],[],[[[]]],[]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[5,1,1,1]
[[[],[],[[],[],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[6,1,1]
[[[],[],[[],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[5,1,1,1]
[[[],[],[[[[]]]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[4,1,1,1,1]
[[[],[[]],[],[],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,1,1]
[[[],[[]],[[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[5,1,1,1]
[[[],[[]],[[],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,2,3,1,8]=>[5,1,1,1]
[[[],[[],[]],[],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,1]
[[[],[[[]]],[[]]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[4,1,1,1,1]
[[[],[[],[],[]],[]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[6,1,1]
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,1,1,1]
[[[],[[[],[]]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[5,1,1,1]
[[[],[[[[]]]],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[4,1,1,1,1]
[[[],[[],[],[],[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[6,1,1]
[[[],[[],[],[[]]]],[]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[5,1,1,1]
[[[],[[],[[]],[]]],[]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[5,1,1,1]
[[[],[[[],[]],[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[5,1,1,1]
[[[],[[[[]],[]]]],[]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[4,1,1,1,1]
[[[],[[[[[]]]]]],[]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[3,1,1,1,1,1]
[[[[]],[],[],[],[]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,1,1]
[[[[]],[],[],[[]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[5,1,1,1]
[[[[]],[],[[]],[]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[5,1,1,1]
[[[[]],[],[[[]]]],[]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[4,1,1,1,1]
[[[[]],[[[],[]]]],[]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[4,1,1,1,1]
[[[[]],[[[[]]]]],[]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[3,1,1,1,1,1]
[[[[],[]],[],[],[]],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,1,1]
[[[[[]]],[],[],[]],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,1,1,1]
[[[[],[]],[],[[]]],[]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,1,1,1]
[[[[[]]],[],[[]]],[]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[4,1,1,1,1]
[[[[],[]],[[],[]]],[]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[5,1,1,1]
[[[[],[]],[[[]]]],[]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[4,1,1,1,1]
[[[[[]]],[[],[]]],[]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[4,1,1,1,1]
[[[[[]]],[[[]]]],[]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[3,1,1,1,1,1]
[[[[],[],[]],[],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,1,1]
[[[[],[[]]],[],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[5,1,1,1]
[[[[[]],[]],[],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,1,1,1]
[[[[[],[]]],[],[]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[5,1,1,1]
[[[[[[]]]],[],[]],[]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,1,1,1,1]
[[[[],[],[]],[[]]],[]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[5,1,1,1]
[[[[[]],[]],[[]]],[]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[4,1,1,1,1]
[[[[[],[]]],[[]]],[]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[4,1,1,1,1]
[[[[[[]]]],[[]]],[]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[3,1,1,1,1,1]
[[[[],[],[],[]],[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,1,1]
[[[[],[],[[]]],[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[5,1,1,1]
[[[[],[[]],[]],[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[5,1,1,1]
[[[[],[[[]]]],[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[4,1,1,1,1]
[[[[[]],[],[]],[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[5,1,1,1]
[[[[[],[]],[]],[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,1,1,1]
[[[[[],[],[]]],[]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,1,1,1]
[[[[[[]],[]]],[]],[]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[4,1,1,1,1]
[[[[[[],[]]]],[]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[4,1,1,1,1]
[[[[[[[]]]]],[]],[]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,1,1,1,1,1]
[[[[],[],[],[],[]]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[6,1,1]
[[[[],[],[],[[]]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[5,1,1,1]
[[[[],[],[[]],[]]],[]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[5,1,1,1]
[[[[],[],[[[]]]]],[]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[4,1,1,1,1]
[[[[],[[],[]],[]]],[]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[5,1,1,1]
[[[[],[[],[],[]]]],[]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[5,1,1,1]
[[[[],[[[],[]]]]],[]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[4,1,1,1,1]
[[[[],[[[[]]]]]],[]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[3,1,1,1,1,1]
[[[[[]],[],[],[]]],[]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,1,1,1]
[[[[[]],[[[]]]]],[]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[3,1,1,1,1,1]
[[[[[],[]],[],[]]],[]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[5,1,1,1]
[[[[[[]]],[],[]]],[]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[4,1,1,1,1]
[[[[[[]]],[[]]]],[]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[3,1,1,1,1,1]
[[[[[],[],[]],[]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[5,1,1,1]
[[[[[],[[]]],[]]],[]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[4,1,1,1,1]
[[[[[[[]]]],[]]],[]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[3,1,1,1,1,1]
[[[[[],[],[],[]]]],[]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,1,1,1]
[[[[[],[],[[]]]]],[]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[4,1,1,1,1]
[[[[[],[[],[]]]]],[]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,1,1,1,1]
[[[[[[]],[],[]]]],[]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,1,1,1,1]
[[[[[[]],[[]]]]],[]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[3,1,1,1,1,1]
[[[[[[],[]],[]]]],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[4,1,1,1,1]
[[[[[[[]]],[]]]],[]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[3,1,1,1,1,1]
[[[[[[],[],[]]]]],[]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,1,1,1,1]
[[[[[[],[[]]]]]],[]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[]],[]]]]],[]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[],[]]]]]],[]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[[]]]]]]],[]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[],[],[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,1]
[[[],[],[],[],[],[[]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[6,1,1]
[[[],[],[],[],[[]],[]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[6,1,1]
[[[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[6,1,1]
[[[],[],[],[],[[[]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[5,1,1,1]
[[[],[],[],[[]],[],[]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[6,1,1]
[[[],[],[],[[]],[[]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[5,1,1,1]
[[[],[],[],[[],[]],[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[6,1,1]
[[[],[],[],[[[]]],[]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[5,1,1,1]
[[[],[],[],[[],[],[]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[6,1,1]
[[[],[],[],[[],[[]]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[5,1,1,1]
[[[],[],[],[[[]],[]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[5,1,1,1]
[[[],[],[],[[[[]]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[4,1,1,1,1]
[[[],[],[[]],[],[],[]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[6,1,1]
[[[],[],[[]],[[]],[]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[5,1,1,1]
[[[],[],[[]],[[],[]]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[5,1,1,1]
[[[],[],[[],[]],[],[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,1]
[[[],[],[[[]]],[],[]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[5,1,1,1]
[[[],[],[[[]]],[[]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[4,1,1,1,1]
[[[],[],[[],[],[]],[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[6,1,1]
[[[],[],[[],[[]]],[]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[5,1,1,1]
[[[],[],[[[[]]]],[]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[4,1,1,1,1]
[[[],[],[[],[],[],[]]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[6,1,1]
[[[],[],[[],[],[[]]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[5,1,1,1]
[[[],[],[[],[[]],[]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[5,1,1,1]
[[[],[],[[],[[[]]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[4,1,1,1,1]
[[[],[],[[[]],[],[]]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[5,1,1,1]
[[[],[],[[[[]]],[]]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[4,1,1,1,1]
[[[],[],[[[[[]]]]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,1,1,1,1]
[[[],[[]],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[6,1,1]
[[[],[[]],[],[[]],[]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[5,1,1,1]
[[[],[[]],[],[[],[]]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[5,1,1,1]
[[[],[[]],[],[[[]]]]]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[4,1,1,1,1]
[[[],[[]],[[]],[],[]]]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[5,1,1,1]
[[[],[[]],[[]],[[]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[4,1,1,1,1]
[[[],[[]],[[],[]],[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[5,1,1,1]
[[[],[[]],[[[]]],[]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[4,1,1,1,1]
[[[],[[]],[[],[],[]]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[5,1,1,1]
[[[],[[]],[[],[[]]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[4,1,1,1,1]
[[[],[[]],[[[]],[]]]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[4,1,1,1,1]
[[[],[[]],[[[[]]]]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[3,1,1,1,1,1]
[[[],[[],[]],[],[],[]]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[6,1,1]
[[[],[[[]]],[],[],[]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[5,1,1,1]
[[[],[[],[]],[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,1,1]
[[[],[[[]]],[[]],[]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[4,1,1,1,1]
[[[],[[],[]],[[],[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,1,1]
[[[],[[],[]],[[[]]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[4,1,1,1,1]
[[[],[[[]]],[[],[]]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,1,1,1,1]
[[[],[[[]]],[[[]]]]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[3,1,1,1,1,1]
[[[],[[],[[]]],[],[]]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[5,1,1,1]
[[[],[[[[]]]],[],[]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[4,1,1,1,1]
[[[],[[],[[]]],[[]]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[4,1,1,1,1]
[[[],[[[]],[]],[[]]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,1,1,1,1]
[[[],[[[[]]]],[[]]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[3,1,1,1,1,1]
[[[],[[],[],[],[]],[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[6,1,1]
[[[],[[],[],[[]]],[]]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[5,1,1,1]
[[[],[[],[[[]]]],[]]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[4,1,1,1,1]
[[[],[[[]],[],[]],[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[5,1,1,1]
[[[],[[[]],[[]]],[]]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[4,1,1,1,1]
[[[],[[[],[]],[]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[5,1,1,1]
[[[],[[[],[],[]]],[]]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>[5,1,1,1]
[[[],[[[],[[]]]],[]]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[4,1,1,1,1]
[[[],[[[[]],[]]],[]]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[4,1,1,1,1]
[[[],[[[[[]]]]],[]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[3,1,1,1,1,1]
[[[],[[],[],[],[],[]]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[6,1,1]
[[[],[[],[],[],[[]]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[5,1,1,1]
[[[],[[],[],[[[]]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[4,1,1,1,1]
[[[],[[],[[]],[],[]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[5,1,1,1]
[[[],[[],[[]],[[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[4,1,1,1,1]
[[[],[[],[[],[]],[]]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[5,1,1,1]
[[[],[[],[[[]]],[]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[4,1,1,1,1]
[[[],[[],[[],[[]]]]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[4,1,1,1,1]
[[[],[[],[[[]],[]]]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[4,1,1,1,1]
[[[],[[],[[[],[]]]]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[4,1,1,1,1]
[[[],[[],[[[[]]]]]]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[3,1,1,1,1,1]
[[[],[[[]],[],[],[]]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[5,1,1,1]
[[[],[[[]],[],[[]]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,1,1,1,1]
[[[],[[[]],[[]],[]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,1,1,1,1]
[[[],[[[]],[[[]]]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[3,1,1,1,1,1]
[[[],[[[],[]],[],[]]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[5,1,1,1]
[[[],[[[[]]],[],[]]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[4,1,1,1,1]
[[[],[[[],[]],[[]]]]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[4,1,1,1,1]
[[[],[[[[]]],[[]]]]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[3,1,1,1,1,1]
[[[],[[[],[[]]],[]]]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[4,1,1,1,1]
[[[],[[[[],[]]],[]]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[4,1,1,1,1]
[[[],[[[[[]]]],[]]]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[3,1,1,1,1,1]
[[[],[[[],[[]],[]]]]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[4,1,1,1,1]
[[[],[[[[],[]],[]]]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[4,1,1,1,1]
[[[],[[[[[]]],[]]]]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[3,1,1,1,1,1]
[[[],[[[[],[],[]]]]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[4,1,1,1,1]
[[[],[[[[],[[]]]]]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[3,1,1,1,1,1]
[[[],[[[[[]],[]]]]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[3,1,1,1,1,1]
[[[],[[[[[],[]]]]]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[3,1,1,1,1,1]
[[[],[[[[[[]]]]]]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,1,1,1,1,1]
[[[[]],[],[],[],[],[]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[6,1,1]
[[[[]],[],[],[],[[]]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[5,1,1,1]
[[[[]],[],[],[[]],[]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[5,1,1,1]
[[[[]],[],[],[[],[]]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[5,1,1,1]
[[[[]],[],[],[[[]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[4,1,1,1,1]
[[[[]],[],[[]],[],[]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[5,1,1,1]
[[[[]],[],[[]],[[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,1,1,1]
[[[[]],[],[[],[]],[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[5,1,1,1]
[[[[]],[],[[[]]],[]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[4,1,1,1,1]
[[[[]],[],[[],[],[]]]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,3,1,2,8]=>[5,1,1,1]
[[[[]],[],[[[]],[]]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[4,1,1,1,1]
[[[[]],[],[[[[]]]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,1,1,1,1,1]
[[[[]],[[]],[],[],[]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[5,1,1,1]
[[[[]],[[]],[],[[]]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[4,1,1,1,1]
[[[[]],[[]],[[]],[]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[4,1,1,1,1]
[[[[]],[[]],[[],[]]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[4,1,1,1,1]
[[[[]],[[]],[[[]]]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,1,1,1,1,1]
[[[[]],[[],[]],[],[]]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[5,1,1,1]
[[[[]],[[[]]],[],[]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[4,1,1,1,1]
[[[[]],[[],[]],[[]]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,1,1,1]
[[[[]],[[[]]],[[]]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,1,1,1,1,1]
[[[[]],[[],[],[]],[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[5,1,1,1]
[[[[]],[[],[[]]],[]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[4,1,1,1,1]
[[[[]],[[[]],[]],[]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[4,1,1,1,1]
[[[[]],[[[],[]]],[]]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[4,1,1,1,1]
[[[[]],[[[[]]]],[]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,1,1,1,1,1]
[[[[]],[[],[],[],[]]]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[5,1,1,1]
[[[[]],[[],[[],[]]]]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[4,1,1,1,1]
[[[[]],[[[]],[[]]]]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[3,1,1,1,1,1]
[[[[]],[[[],[]],[]]]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[4,1,1,1,1]
[[[[]],[[[[]],[]]]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[3,1,1,1,1,1]
[[[[]],[[[[[]]]]]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[2,1,1,1,1,1,1]
[[[[],[]],[],[],[],[]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[6,1,1]
[[[[[]]],[],[],[],[]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,1,1]
[[[[],[]],[],[],[[]]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[5,1,1,1]
[[[[[]]],[],[],[[]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,1,1,1,1]
[[[[],[]],[],[[]],[]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[5,1,1,1]
[[[[[]]],[],[[]],[]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,1,1,1,1]
[[[[],[]],[],[[],[]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,1,1,1]
[[[[[]]],[],[[],[]]]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[4,1,1,1,1]
[[[[[]]],[],[[[]]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[3,1,1,1,1,1]
[[[[],[]],[[]],[],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[5,1,1,1]
[[[[[]]],[[]],[],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,1,1,1,1]
[[[[],[]],[[]],[[]]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,1,1,1,1]
[[[[[]]],[[]],[[]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[3,1,1,1,1,1]
[[[[],[]],[[[]]],[]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,1,1,1,1]
[[[[[]]],[[],[]],[]]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[4,1,1,1,1]
[[[[[]]],[[[]]],[]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[3,1,1,1,1,1]
[[[[],[]],[[],[],[]]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[5,1,1,1]
[[[[],[]],[[],[[]]]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,1,1,1,1]
[[[[],[]],[[[],[]]]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,1,1,1,1]
[[[[],[]],[[[[]]]]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,1,1,1,1]
[[[[[]]],[[],[],[]]]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[4,1,1,1,1]
[[[[[]]],[[[]],[]]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[3,1,1,1,1,1]
[[[[[]]],[[[[]]]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[2,1,1,1,1,1,1]
[[[[],[],[]],[],[],[]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[6,1,1]
[[[[],[[]]],[],[],[]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,1,1,1]
[[[[[]],[]],[],[],[]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,1,1,1]
[[[[[],[]]],[],[],[]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,1,1,1]
[[[[[[]]]],[],[],[]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[4,1,1,1,1]
[[[[],[[]]],[],[[]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[4,1,1,1,1]
[[[[[]],[]],[],[[]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,1,1,1]
[[[[[],[]]],[],[[]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[4,1,1,1,1]
[[[[[[]]]],[],[[]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[3,1,1,1,1,1]
[[[[[]],[]],[[]],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[4,1,1,1,1]
[[[[[],[]]],[[]],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[4,1,1,1,1]
[[[[[[]]]],[[]],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[3,1,1,1,1,1]
[[[[],[],[]],[[[]]]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[4,1,1,1,1]
[[[[],[[]]],[[],[]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[4,1,1,1,1]
[[[[],[[]]],[[[]]]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[3,1,1,1,1,1]
[[[[[]],[]],[[[]]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[3,1,1,1,1,1]
[[[[[],[]]],[[],[]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[4,1,1,1,1]
[[[[[],[]]],[[[]]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[3,1,1,1,1,1]
[[[[[[]]]],[[],[]]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[3,1,1,1,1,1]
[[[[[[]]]],[[[]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[2,1,1,1,1,1,1]
[[[[],[],[],[]],[],[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,1,1]
[[[[],[[[]]]],[],[]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[4,1,1,1,1]
[[[[[]],[],[]],[],[]]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[5,1,1,1]
[[[[[]],[[]]],[],[]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[4,1,1,1,1]
[[[[[],[]],[]],[],[]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[5,1,1,1]
[[[[[[]]],[]],[],[]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[4,1,1,1,1]
[[[[[],[[]]]],[],[]]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[4,1,1,1,1]
[[[[[[]],[]]],[],[]]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,1,1,1]
[[[[[[[]]]]],[],[]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[3,1,1,1,1,1]
[[[[],[],[],[]],[[]]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[5,1,1,1]
[[[[],[[],[]]],[[]]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[4,1,1,1,1]
[[[[],[[[]]]],[[]]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[3,1,1,1,1,1]
[[[[[]],[],[]],[[]]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,1,1,1]
[[[[[]],[[]]],[[]]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[3,1,1,1,1,1]
[[[[[],[]],[]],[[]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[4,1,1,1,1]
[[[[[[]]],[]],[[]]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[3,1,1,1,1,1]
[[[[[],[],[]]],[[]]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[4,1,1,1,1]
[[[[[],[[]]]],[[]]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[3,1,1,1,1,1]
[[[[[[]],[]]],[[]]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[3,1,1,1,1,1]
[[[[[[],[]]]],[[]]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[3,1,1,1,1,1]
[[[[[[[]]]]],[[]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,1,1,1,1,1,1]
[[[[],[],[],[],[]],[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[6,1,1]
[[[[],[[]],[],[]],[]]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[5,1,1,1]
[[[[],[[]],[[]]],[]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[4,1,1,1,1]
[[[[],[[],[]],[]],[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[5,1,1,1]
[[[[],[[[]]],[]],[]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,1,1,1,1]
[[[[],[[],[[]]]],[]]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[4,1,1,1,1]
[[[[],[[[]],[]]],[]]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,1,1,1,1]
[[[[],[[[],[]]]],[]]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[4,1,1,1,1]
[[[[],[[[[]]]]],[]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[3,1,1,1,1,1]
[[[[[]],[],[],[]],[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[5,1,1,1]
[[[[[]],[],[[]]],[]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[4,1,1,1,1]
[[[[[]],[[],[]]],[]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[4,1,1,1,1]
[[[[[]],[[[]]]],[]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[3,1,1,1,1,1]
[[[[[[]]],[],[]],[]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[4,1,1,1,1]
[[[[[],[]],[[]]],[]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[4,1,1,1,1]
[[[[[[]]],[[]]],[]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[3,1,1,1,1,1]
[[[[[],[],[]],[]],[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[5,1,1,1]
[[[[[],[[]]],[]],[]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[4,1,1,1,1]
[[[[[[]],[]],[]],[]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,1,1,1]
[[[[[[[]]]],[]],[]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[3,1,1,1,1,1]
[[[[[],[[],[]]]],[]]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[4,1,1,1,1]
[[[[[],[[[]]]]],[]]]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[3,1,1,1,1,1]
[[[[[[]],[],[]]],[]]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[4,1,1,1,1]
[[[[[[]],[[]]]],[]]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[3,1,1,1,1,1]
[[[[[[],[]],[]]],[]]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[4,1,1,1,1]
[[[[[[[]]],[]]],[]]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[3,1,1,1,1,1]
[[[[[[],[[]]]]],[]]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[3,1,1,1,1,1]
[[[[[[[]],[]]]],[]]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[3,1,1,1,1,1]
[[[[[[[],[]]]]],[]]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,1,1,1,1]
[[[[[[[[]]]]]],[]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[[[[],[],[],[],[],[]]]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[6,1,1]
[[[[],[],[],[],[[]]]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[5,1,1,1]
[[[[],[],[[[]]],[]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[4,1,1,1,1]
[[[[],[],[[],[],[]]]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[5,1,1,1]
[[[[],[],[[],[[]]]]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[4,1,1,1,1]
[[[[],[],[[[[]]]]]]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[3,1,1,1,1,1]
[[[[],[[]],[],[],[]]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[5,1,1,1]
[[[[],[[],[]],[],[]]]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[5,1,1,1]
[[[[],[[],[],[]],[]]]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[5,1,1,1]
[[[[],[[[]],[]],[]]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[4,1,1,1,1]
[[[[],[[[],[]]],[]]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[4,1,1,1,1]
[[[[],[[[[]]]],[]]]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[4,3,5,6,7,1,2,8]=>[3,1,1,1,1,1]
[[[[],[[],[[]],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[4,1,1,1,1]
[[[[],[[[]],[],[]]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[4,1,1,1,1]
[[[[],[[[]],[[]]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[3,1,1,1,1,1]
[[[[],[[[[]]],[]]]]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[3,1,1,1,1,1]
[[[[],[[[[]],[]]]]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[3,1,1,1,1,1]
[[[[],[[[[],[]]]]]]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[3,1,1,1,1,1]
[[[[],[[[[[]]]]]]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[2,1,1,1,1,1,1]
[[[[[]],[],[],[],[]]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[5,1,1,1]
[[[[[]],[],[[],[]]]]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[4,1,1,1,1]
[[[[[]],[],[[[]]]]]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[3,1,1,1,1,1]
[[[[[]],[[],[]],[]]]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[4,1,1,1,1]
[[[[[]],[[[]]],[]]]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[3,1,1,1,1,1]
[[[[[]],[[],[[]]]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[3,1,1,1,1,1]
[[[[[]],[[[[]]]]]]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[2,1,1,1,1,1,1]
[[[[[[]]],[],[],[]]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[4,1,1,1,1]
[[[[[[]]],[],[[]]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[3,1,1,1,1,1]
[[[[[[]]],[[]],[]]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[3,1,1,1,1,1]
[[[[[],[]],[[],[]]]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[4,1,1,1,1]
[[[[[[]]],[[[]]]]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[2,1,1,1,1,1,1]
[[[[[],[],[]],[],[]]]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[5,1,1,1]
[[[[[[[]]]],[],[]]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[3,1,1,1,1,1]
[[[[[],[[]]],[[]]]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[3,1,1,1,1,1]
[[[[[[],[]]],[[]]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[3,1,1,1,1,1]
[[[[[[[]]]],[[]]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[2,1,1,1,1,1,1]
[[[[[],[],[],[]],[]]]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[7,5,4,3,1,2,6,8]=>[5,1,1,1]
[[[[[[]],[[]]],[]]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[3,1,1,1,1,1]
[[[[[[],[]],[]],[]]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[4,1,1,1,1]
[[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[3,1,1,1,1,1]
[[[[[[],[],[]]],[]]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[4,1,1,1,1]
[[[[[[],[[]]]],[]]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[3,1,1,1,1,1]
[[[[[[[]],[]]],[]]]]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[3,1,1,1,1,1]
[[[[[[[],[]]]],[]]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[3,1,1,1,1,1]
[[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[[[[[],[],[],[],[]]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[5,1,1,1]
[[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[4,1,1,1,1]
[[[[[],[[]],[],[]]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[4,1,1,1,1]
[[[[[],[[[]]],[]]]]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[4,3,5,6,1,2,7,8]=>[3,1,1,1,1,1]
[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[4,1,1,1,1]
[[[[[],[[],[[]]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[3,1,1,1,1,1]
[[[[[],[[[[]]]]]]]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[2,1,1,1,1,1,1]
[[[[[[]],[],[],[]]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,1,1,1,1]
[[[[[[]],[[],[]]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[3,1,1,1,1,1]
[[[[[[]],[[[]]]]]]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[2,1,1,1,1,1,1]
[[[[[[],[],[]],[]]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[4,1,1,1,1]
[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[3,1,1,1,1,1]
[[[[[[[],[]]],[]]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[3,1,1,1,1,1]
[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[2,1,1,1,1,1,1]
[[[[[[],[],[],[]]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[4,1,1,1,1]
[[[[[[],[[]],[]]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[3,1,1,1,1,1]
[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[],[[[]]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[]],[],[]]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[],[]],[]]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[],[],[]]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,1,1,1,1,1]
[[[[[[[],[[]]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[[],[]]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
[[[[[[],[]],[]],[]],[]],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,1,1,1]
[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,1,1,1,1]
[[[[[[[[[]]]]]]]],[]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[],[[[[[[[[]]]]]]]]]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[[]]]]]]]]],[]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[],[[[[[[[],[]]]]]]]]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[[],[[[[[[[[[]]]]]]]]]]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[[]]]]]]]]]],[]]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1]
[[],[[[[[[[[[[]]]]]]]]]]]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,1,1,1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9]
[[],[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[8,1]
[[],[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[8,1]
[[],[],[],[],[[],[],[],[]]]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[8,1]
[[],[],[],[[],[],[],[],[]]]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[8,1]
[[],[],[[],[],[],[],[],[]]]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[8,1]
[[],[[],[],[],[],[],[],[]]]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[8,1]
[[[],[],[],[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[8,1]
[[],[],[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10]
[[],[],[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[9,1]
[[],[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,1,1]
[[],[],[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[9,1]
[[],[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>[7,1,1]
[[],[],[],[],[],[[],[],[],[]]]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[9,1]
[[],[],[],[],[[],[],[],[],[]]]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[9,1]
[[[[]],[],[],[],[],[],[]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[7,1,1]
[[[],[],[],[],[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,1]
[[[]],[],[],[],[],[],[],[]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,1]
[[[],[]],[],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[8,1]
[[[],[],[],[]],[],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[8,1]
[[[],[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[8,1]
[[[],[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1]
[[[]],[],[],[],[],[],[],[],[]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,1]
[[[[]]],[],[],[],[],[],[]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,1,1]
[[[],[]],[],[],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1]
[[[],[],[],[]],[],[],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[9,1]
[[[],[],[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[9,1]
[[[],[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[7,1,1]
[[[],[],[],[],[],[],[[]]]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[7,1,1]
[[[],[],[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1]
[[[[],[],[],[],[],[],[]]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[7,1,1]
[[[[],[],[],[],[],[]]],[]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[7,1,1]
[[[[],[],[],[],[],[]],[]]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[7,1,1]
[[[[],[],[],[],[]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[7,1,1]
[[[],[],[],[],[],[],[],[],[],[]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[10,1]
[[[],[[[[[[[]]]]]]]]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[]]]]]]],[]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[[[],[[[[[[[[]]]]]]]]]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[2,1,1,1,1,1,1,1,1]
[[[]],[[[[[[]]]]]],[]]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[3,1,1,1,1,1,1]
[[[[],[[[[[[]]]]]]]]]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[]]]]]],[]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,1,1,1,1,1,1,1]
[[],[[[[[[]]]]]],[[]]]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[[[[[[[[[[]]]]]]]],[]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1]
[[],[[[],[],[],[],[],[]]]]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[7,1,1]
[[[[[[[[[[[]]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1]
[[],[],[[[[[[[]]]]]]]]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[3,1,1,1,1,1,1]
[[[]],[],[],[],[],[],[[]]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,1,1]
[[[],[],[],[],[],[],[],[[]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[8,1,1]
[[[],[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[7,1,1]
[[[],[],[],[],[],[[]],[]]]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[7,1,1]
[[[]],[],[],[],[],[[],[]]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[7,1,1]
[[[]],[],[],[],[],[[]],[]]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,1,1]
[[[]],[],[],[],[],[],[],[[]]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[8,1,1]
[[[]],[],[],[],[],[],[],[],[],[]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,1]
[[[]],[[[[[[[]]]]]]]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,1,1,1,1,1,1,1]
[[[[]]],[[[[[[]]]]]]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[]]]]],[[[[]]]]]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[]]]]]]],[[]]]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[]],[[[[[[[[]]]]]]]]]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,1,1,1,1,1,1,1,1]
[[[],[]],[[[[[[]]]]]]]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[3,1,1,1,1,1,1]
[[[[[[[],[]]]]]],[[]]]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[4,5,2,1,3,6,7,8,9]=>[3,1,1,1,1,1,1]
[[[[[[[[[],[]]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[],[],[]]]]]]]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[[[[[[[[[[],[]]]]]]]]]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[],[[]]]]]]]]]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[10,1]
[[[],[[]],[],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[7,1,1]
[[[[],[]],[],[],[],[],[]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,1,2,4]=>[7,1,1]
[[[[]],[],[],[],[],[],[],[]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[8,1,1]
[[[[[[[[[]]]]],[]]]]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[]]]],[]]]]]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[]]],[]]]]]]]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[[]],[]]]]]]]]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[[[[[[]]]]]]],[],[]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[[[[[[[[[[]]]]]]],[]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]]]]]],[]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]]]]],[]]]]]]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]]]],[]]]]]]]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]]],[]]]]]]]]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[[[[[[[]],[]]]]]]]]]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[[[[],[]]],[],[],[],[],[]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[7,1,1]
[[[],[[[[[[]]]]]]],[]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[3,1,1,1,1,1,1]
[[[[[[[],[[[]]]]]]]]]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[3,4,5,1,2,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[[[],[[[[[[]]]]]],[]]]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[3,1,1,1,1,1,1]
[[],[[[[[[[]]]]]]],[]]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[[],[],[],[[]],[],[],[],[]]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,1]
[[],[],[],[],[],[[]],[],[],[]]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,1]
[[[],[],[],[]],[],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[8,9,7,6,4,3,2,1,5]=>[7,1,1]
[[],[],[[]],[],[],[],[],[]]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,1]
[[[[[[[[],[]]]]]],[]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[[[[[[[[[[[]]]]]]]]],[]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[[[[[[[[[],[]]]]]]],[]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[[[[[[[]]]]]],[],[],[]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,1,1,1,1,1]
[[[[[[]]]]],[],[],[],[]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,1,1,1,1]
[[[[[]]]],[],[],[],[],[]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,1,1,1]
[[[[[[[[[]]]]]]]],[],[]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[[[[[[[[]]]]]],[]],[]]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[[[[[[[[]]]]]]],[],[],[]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]
[[[[[[[]]]]]],[],[],[],[]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,1,1,1,1,1]
[[[[[[]]]]],[],[],[],[],[]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,1,1,1,1]
[[[[[]]]],[],[],[],[],[],[]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,1,1,1]
[[[[]]],[],[],[],[],[],[],[]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,1,1]
[[],[[[[[[[[]]]]]]]],[]]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[[],[],[],[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[11,9,10,8,7,6,5,4,3,2,1]=>[10,1]
[[[],[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[7,1,1]
[[[[],[],[],[],[],[],[]],[]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[8,1,1]
Map
Zeilberger's Strahler bijection
Description
Zeilberger's Strahler bijection between ordered and binary trees.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
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