Identifier
Mp00048:
Ordered trees
—left-right symmetry⟶
Ordered trees
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0010;cc-rep-2Cc0005;cc-rep-3
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[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
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[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
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[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
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[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
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[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
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[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
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[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
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[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
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[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
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[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
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[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
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[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to binary tree: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
searching the database
Sorry, this map was not found in the database.