Identifier
Mp00050:
Ordered trees
—to binary tree: right brother = right child⟶
Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0005;cc-rep-2
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[[[[]],[],[[]]]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[[[[]],[[]],[]]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[[[[]],[[],[]]]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[[[[]],[[[]]]]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[]],[],[]]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[]]],[],[]]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[]],[[]]]]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[[[[[]]],[[]]]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[],[]],[]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[[]]],[]]]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[[[[[]],[]],[]]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[[[[],[]]],[]]]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[[[[[]]]],[]]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[],[],[]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[[]]]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[[[],[[]],[]]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[[[[],[[],[]]]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[[[],[[[]]]]]]=>[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[[[[]],[],[]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[[]]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[[[[],[]],[]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[[[[[]]],[]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[[[[],[],[]]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[[[[],[[]]]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[[]],[]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[[[[[],[]]]]]]=>[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[[[[[]]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[],[[]],[],[]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[],[],[],[[]],[[]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[],[],[[],[]],[]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[],[],[],[[[]]],[]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[],[],[],[[],[],[]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[],[],[],[[],[[]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[],[],[[[]],[]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[],[],[],[[[],[]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[],[],[],[[[[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[[]],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[],[],[[]],[],[[]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[],[[]],[[]],[]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[],[],[[]],[[],[]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[],[],[[]],[[[]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[]],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[],[],[[[]]],[],[]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[],[],[[],[]],[[]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[],[[[]]],[[]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[],[[],[],[]],[]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[],[],[[],[[]]],[]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[],[],[[[]],[]],[]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[],[],[[[],[]]],[]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[],[],[[[[]]]],[]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[],[],[[],[],[],[]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[],[],[[],[],[[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[],[[],[[]],[]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[],[],[[],[[],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[],[],[[],[[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[[]],[],[]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[],[],[[[]],[[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[],[[[],[]],[]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[],[],[[[[]]],[]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[],[],[[[],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[],[],[[[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[],[[[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[],[],[[[[[]]]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[[]],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[],[[]],[],[],[[]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[]],[],[[]],[]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[],[[]],[],[[],[]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[],[[]],[],[[[]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[[]],[[]],[],[]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[],[[]],[[]],[[]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[]],[[],[]],[]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[],[[]],[[[]]],[]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[],[[]],[[],[],[]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[],[[]],[[],[[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[]],[]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[],[[]],[[[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[],[[]],[[[[]]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[[],[]],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[],[[[]]],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[],[[],[]],[],[[]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[]]],[],[[]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[],[]],[[]],[]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[],[[[]]],[[]],[]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[],[[],[]],[[],[]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[],[[],[]],[[[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[[[]]],[[],[]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[],[[[]]],[[[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[[],[],[]],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[],[[],[[]]],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[],[[[]],[]],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[],[[[],[]]],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[],[[[[]]]],[],[]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[],[[],[],[]],[[]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[],[[]]],[[]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[[]],[]],[[]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[],[]]],[[]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[[]]]],[[]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[],[]],[]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[],[[],[],[[]]],[]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[],[[],[[]],[]],[]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[],[[],[[],[]]],[]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[],[[],[[[]]]],[]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[],[[[]],[],[]],[]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[],[[[]],[[]]],[]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[],[[[],[]],[]],[]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[],[[[[]]],[]],[]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[],[[[],[],[]]],[]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[],[[[],[[]]]],[]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[],[[[[]],[]]],[]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[],[[[[],[]]]],[]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[],[[[[[]]]]],[]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[],[[],[],[],[],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[[]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[[]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[],[[],[],[[],[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[],[[],[],[[[]]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[[],[[]],[],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[],[[],[[]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[],[]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[],[[],[[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[],[[],[[],[],[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[],[[],[[],[[]]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]],[]]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[[[]]]]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[]],[],[],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[]],[],[[]]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
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[[],[[[[]]],[],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[],[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]],[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[[],[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[[[]]]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[],[],[],[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[],[],[[]]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[],[[]],[]]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[[[]]]]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[[]],[],[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[],[[[[]],[[]]]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[[],[]],[]]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[[[]]],[]]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[],[[[[],[],[]]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[[],[[]]]]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[[[]],[]]]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[],[[[[[],[]]]]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[[[[]]]]]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[]],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[[]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[],[],[[]],[]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[]],[],[],[[],[]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[],[],[[[]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[]],[],[[]],[],[]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[]],[],[[]],[[]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[]],[],[[],[]],[]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[]],[],[[[]]],[]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[]],[],[[],[],[]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[]],[],[[],[[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[]],[],[[[]],[]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[]],[],[[[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[]]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[]],[[]],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[]],[[]],[],[[]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[]],[[]],[[]],[]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[]],[[]],[[],[]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[]],[[[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[]],[[],[]],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[]],[[[]]],[],[]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[]],[[],[]],[[]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[]],[[[]]],[[]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[]],[[],[],[]],[]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[]],[[],[[]]],[]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[]],[[[]],[]],[]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]]]],[]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[]],[[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[]],[[],[],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[]],[[],[[]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[]],[[],[[],[]]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[],[[[]]]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[]],[[[]],[],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[]],[[[]],[[]]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[]],[[[],[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[]],[[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[]],[[[],[],[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[]],[[[],[[]]]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[]],[[[[]],[]]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[]],[[[[],[]]]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[[[[[]]]]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[]],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[]]],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[[]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[]]],[],[],[[]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[],[]],[],[[]],[]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[]]],[],[[]],[]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[]],[],[[],[]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[[[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[]]],[],[[],[]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[]]],[],[[[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[],[]],[[]],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[]]],[[]],[],[]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[],[]],[]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[],[]],[[[]]],[]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]]],[[],[]],[]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]]],[[[]]],[]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[]],[[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[],[]],[[],[[]]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[]],[[[[]]]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[]]],[[],[],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[]]],[[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[]]],[[[],[]]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[]]],[[[[]]]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[]],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[[]]],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[]],[]],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[]]],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[],[[]]],[],[[]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[]],[]],[],[[]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[]]],[],[[]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[],[],[]],[[]],[]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[]]],[[]],[]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[]],[]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[[]]]],[[]],[]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[],[]],[[],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[],[],[]],[[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[]],[]],[[],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[[]]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[]]],[[],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[],[]]],[[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[[]]]],[[],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[[]]]],[[[]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[],[]],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[[]]],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[],[[]],[]],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[],[[],[]]],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[],[[[]]]],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]],[],[]],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[]],[[]]],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[]],[]],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[]]],[]],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[[]]]],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]],[]]],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[],[]]]],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[[]]]]],[],[]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[],[],[]],[[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[],[],[[]]],[[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[[]],[]],[[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[[],[]]],[[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[[[]]]],[[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[]],[],[]],[[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]],[[]]],[[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[]],[[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[],[],[]]],[[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[],[[]]]],[[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[[]],[]]],[[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[[],[]]]],[[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[[[]]]]],[[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[[]]],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[],[[]],[]],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[],[],[[],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[],[],[[[]]]],[]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[[]],[],[]],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[],[[]],[[]]],[]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[],[]],[]],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[],[[],[],[]]],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[],[[],[[]]]],[]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[[]],[]]],[]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[],[[[],[]]]],[]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[],[[[[]]]]],[]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[]],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[]],[],[[]]],[]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[]],[]],[]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]]]],[]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[],[]],[],[]],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[]]],[],[]],[]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[],[]],[[]]],[]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[[]]],[[]]],[]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[],[],[]],[]],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[[]]],[]],[]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[[]],[]],[]],[]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[],[]]],[]],[]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[[]]]],[]],[]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[],[]]],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[[]]]],[]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[],[[]],[]]],[]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]]],[]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[[[]]]]],[]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[[]],[],[]]],[]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[]],[[]]]],[]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[[]]],[]]],[]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[[],[],[]]]],[]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[[],[[]]]]],[]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[[]],[]]]],[]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[[],[]]]]],[]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[[[[]]]]]],[]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[],[],[[]],[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[],[],[[],[]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[],[],[[[]]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[],[[]],[],[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[],[[]],[[]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[],[[],[]],[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[],[[[]]],[]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[],[],[]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[],[[],[[]]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]],[]]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[],[[[[]]]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[]],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[]],[],[[]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[]],[[]],[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[]],[[],[]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[]],[[[]]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[]],[],[]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[[]]],[],[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[],[],[]],[]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[[]]],[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[[]],[]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[[],[]]],[]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[[[]]]],[]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[[]]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[[]],[]]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[[[]]]]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[[[]],[],[]]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[[]],[[]]]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[[[[]]],[]]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[[],[],[]]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[[[],[[]]]]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[[[[]],[]]]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[[[],[]]]]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[[[[[]]]]]]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[]],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[[]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[[]],[],[[]],[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[[],[]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[]],[],[[[]]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[]],[[]],[],[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[]],[[]],[[]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[]],[[],[]],[]]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[]],[[[]]],[]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[[]],[[],[],[]]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]],[[],[[]]]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[]],[[[]],[]]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[]],[[[],[]]]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[]],[[[[]]]]]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[],[]],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[]]],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[],[]],[],[[]]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[[]]],[],[[]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[[],[]],[[]],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[[]]],[[]],[]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[[],[]],[[],[]]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[],[]],[[[]]]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[[]]],[[],[]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[[]]],[[[]]]]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[],[],[]],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[[]]],[],[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[[]],[]],[],[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[[],[]]],[],[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[[[]]]],[],[]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[],[],[]],[[]]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[],[[]]],[[]]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[[]],[]],[[]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[[[],[]]],[[]]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[[[]]]],[[]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[],[],[],[]],[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[[]]],[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[],[[]],[]],[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[],[[],[]]],[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[[[]]]],[]]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[[]],[],[]],[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[[]],[[]]],[]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[[],[]],[]],[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[[]]],[]],[]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[[],[],[]]],[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[[],[[]]]],[]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[[]],[]]],[]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[[[],[]]]],[]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[[[[]]]]],[]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[[]]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[[]],[]]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[[[]]]]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[],[[]],[],[]]]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[],[[]],[[]]]]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[],[]],[]]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[[[]]],[]]]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[[],[],[]]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[],[[],[[]]]]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[[[]],[]]]]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[[[],[]]]]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[],[[[[]]]]]]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[[]],[],[],[]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[]],[],[[]]]]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[[]],[[]],[]]]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[[]],[[],[]]]]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[]],[[[]]]]]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[[],[]],[],[]]]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[[]]],[],[]]]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[[],[]],[[]]]]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[[[]]],[[]]]]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[[],[],[]],[]]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[[],[[]]],[]]]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[[]],[]],[]]]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[[],[]]],[]]]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[[[[]]]],[]]]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[[],[],[],[]]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[[],[],[[]]]]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[],[[]],[]]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[],[[],[]]]]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[[[]]]]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[[[]],[],[]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[[]],[[]]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[[],[]],[]]]]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[[[[]]],[]]]]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[[],[],[]]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[[],[[]]]]]]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[[]],[]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[[],[]]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[[[[[]]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[[]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[],[],[],[],[],[[]],[]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[],[],[],[],[],[[],[]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[],[],[],[],[],[[[]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[],[],[[]],[],[]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[],[],[],[],[[]],[[]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[],[],[],[[],[]],[]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[],[],[],[],[[[]]],[]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[],[],[],[],[[],[],[]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[],[],[],[],[[],[[]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[],[],[],[[[]],[]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[],[],[],[],[[[],[]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[],[],[],[],[[[[]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[],[],[],[[]],[],[[]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[],[],[[]],[[]],[]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[],[],[],[[]],[[],[]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[],[],[],[[]],[[[]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[],[[],[]],[],[]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[],[],[],[[[]]],[],[]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[],[],[],[[],[]],[[]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[],[],[[[]]],[[]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[],[],[[],[],[]],[]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[],[],[],[[],[[]]],[]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[],[],[],[[[]],[]],[]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[],[],[],[[[],[]]],[]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[],[],[],[[[[]]]],[]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[],[],[],[[],[],[],[]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[],[],[],[[],[],[[]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[],[],[[],[[]],[]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[],[],[],[[],[[],[]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[],[],[],[[],[[[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[],[[[]],[],[]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[],[],[],[[[]],[[]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[],[],[[[],[]],[]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[],[],[],[[[[]]],[]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[],[],[],[[[],[],[]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[],[],[],[[[],[[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[],[],[[[[]],[]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[],[],[],[[[[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[],[],[],[[[[[]]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[],[],[[]],[],[],[[]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[],[[]],[],[[]],[]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[],[],[[]],[],[[],[]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[],[],[[]],[],[[[]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[]],[[]],[],[]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[],[],[[]],[[]],[[]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[],[[]],[[],[]],[]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[],[],[[]],[[[]]],[]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[],[],[[]],[[],[],[]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[],[],[[]],[[],[[]]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[],[[]],[[[]],[]]]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[],[],[[]],[[[],[]]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[],[],[[]],[[[[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[],[],[[],[]],[],[[]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[],[[[]]],[],[[]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[],[[],[]],[[]],[]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[],[],[[[]]],[[]],[]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[],[],[[],[]],[[],[]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[],[],[[],[]],[[[]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[]]],[[],[]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[],[],[[[]]],[[[]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[]],[],[]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[],[],[[],[[]]],[],[]]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[],[],[[[]],[]],[],[]]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[],[],[[[],[]]],[],[]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[],[],[[[[]]]],[],[]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[],[],[[],[],[]],[[]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[],[[],[[]]],[[]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[],[[[]],[]],[[]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[],[[[],[]]],[[]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[],[[[[]]]],[[]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[],[[],[],[],[]],[]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[],[],[[],[],[[]]],[]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[],[],[[],[[]],[]],[]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[],[],[[],[[],[]]],[]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
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[[],[[]],[[],[[],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
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[[[]],[],[],[[[]],[]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[]],[],[],[[[],[]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[],[[[[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[]],[],[[]],[],[],[]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[]],[],[[]],[],[[]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[]],[],[[]],[[]],[]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[]],[],[[]],[[],[]]]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[],[[]],[[[]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[]],[],[[],[]],[],[]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[]],[],[[[]]],[],[]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[]],[],[[],[]],[[]]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[]],[],[[[]]],[[]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[]],[],[[],[],[]],[]]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[]],[],[[],[[]]],[]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[]],[],[[[]],[]],[]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[]],[],[[[],[]]],[]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[]],[],[[[[]]]],[]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[]],[],[[],[],[],[]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[]],[],[[],[],[[]]]]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[]],[],[[],[[]],[]]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[]],[],[[],[[],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[],[[],[[[]]]]]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[]],[],[[[]],[],[]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[]],[],[[[]],[[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[]],[],[[[],[]],[]]]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[]],[],[[[[]]],[]]]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[]],[],[[[],[],[]]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[]],[],[[[],[[]]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[]],[],[[[[]],[]]]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[]],[],[[[[],[]]]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[[[]]]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[]],[[]],[],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[]],[[]],[],[],[[]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[]],[[]],[],[[]],[]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[]],[[]],[],[[],[]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[]],[],[[[]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[]],[[]],[[]],[],[]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[]],[[]],[[]],[[]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[]],[[]],[[],[]],[]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[]],[[]],[[[]]],[]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[]],[[]],[[],[],[]]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[]],[[]],[[],[[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[]],[[]],[[[]],[]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[]],[[]],[[[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[[]],[[[[]]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[]],[[],[]],[],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[]],[[[]]],[],[],[]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[]],[[],[]],[],[[]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[]],[[[]]],[],[[]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[]],[[],[]],[[]],[]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[]],[[[]]],[[]],[]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[]],[[],[]],[[],[]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[],[]],[[[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[]],[[[]]],[[],[]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[]]],[[[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[]],[[],[],[]],[],[]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[]],[[],[[]]],[],[]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[]],[[[]],[]],[],[]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[]],[[[],[]]],[],[]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[]],[[[[]]]],[],[]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[]],[[],[],[]],[[]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[]],[[],[[]]],[[]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[]],[[[]],[]],[[]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[]],[[[],[]]],[[]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[]],[[[[]]]],[[]]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[]],[[],[],[],[]],[]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[[]]],[]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[],[[]],[]],[]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[],[[],[]]],[]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[],[[[]]]],[]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[]],[],[]],[]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[]],[[]]],[]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[],[]],[]],[]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[[]]],[]],[]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[],[],[]]],[]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[],[[]]]],[]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[[[]],[]]],[]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[[[],[]]]],[]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[[[[]]]]],[]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[],[],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[[],[],[],[[]]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[]],[[],[],[[]],[]]]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[]],[[],[],[[],[]]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[[[]]]]]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[]],[[],[[]],[],[]]]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[]],[[],[[]],[[]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[]],[[],[[],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[]],[[],[[[]]],[]]]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[]],[[],[[],[],[]]]]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[]],[[],[[],[[]]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[]],[[],[[[]],[]]]]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[]],[[],[[[],[]]]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[[],[[[[]]]]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[]],[[[]],[],[],[]]]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[]],[[[]],[],[[]]]]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[]],[[[]],[[]],[]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[]],[[[]],[[],[]]]]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[[[]]]]]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[]],[[[],[]],[],[]]]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[]],[[[[]]],[],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[]],[[[],[]],[[]]]]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[]],[[[[]]],[[]]]]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[]],[[[],[],[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[]],[[[],[[]]],[]]]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[]],[[[[]],[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[]],[[[[],[]]],[]]]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[]],[[[[[]]]],[]]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[]],[[[],[],[],[]]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[]],[[[],[],[[]]]]]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[]],[[[],[[]],[]]]]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[]],[[[],[[],[]]]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[[],[[[]]]]]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[]],[[[[]],[],[]]]]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[]],[[[[]],[[]]]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[]],[[[[],[]],[]]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[]],[[[[[]]],[]]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[]],[[[[],[],[]]]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[]],[[[[],[[]]]]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[]],[[[[[]],[]]]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[]],[[[[[],[]]]]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[[[[[[]]]]]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[]]],[],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[],[[]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[]]],[],[],[],[[]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[],[]],[],[],[[]],[]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[]]],[],[],[[]],[]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[]],[],[],[[],[]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[],[[[]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[]]],[],[],[[],[]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[]]],[],[],[[[]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[],[]],[],[[]],[],[]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[]]],[],[[]],[],[]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[],[]],[],[[]],[[]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[]]],[],[[]],[[]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[],[]],[],[[],[]],[]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[],[]],[],[[[]]],[]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[]]],[],[[],[]],[]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]]],[],[[[]]],[]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[]],[],[[],[],[]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[],[]],[],[[],[[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[],[]],[],[[[]],[]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[],[[[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[],[]],[],[[[[]]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[]]],[],[[],[],[]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[],[[],[[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[]]],[],[[[]],[]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[]]],[],[[[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[]]],[],[[[[]]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[],[]],[[]],[],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[]]],[[]],[],[],[]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[],[]],[[]],[],[[]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[]]],[[]],[],[[]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[],[]],[[]],[[]],[]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[]]],[[]],[[]],[]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[]],[[]],[[],[]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[],[]],[[]],[[[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[]]],[[]],[[],[]]]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[]]],[[]],[[[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[],[]],[[],[]],[],[]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[],[]],[[[]]],[],[]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[]]],[[],[]],[],[]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[]]],[[[]]],[],[]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[],[]],[[],[]],[[]]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[],[]],[[[]]],[[]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[]]],[[],[]],[[]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[]]],[[[]]],[[]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[],[]],[[],[],[]],[]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[],[]],[[],[[]]],[]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[]],[[[]],[]],[]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[],[]],[[[],[]]],[]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[],[]],[[[[]]]],[]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]]],[[],[],[]],[]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[]]],[[],[[]]],[]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]]],[[[]],[]],[]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]]],[[[],[]]],[]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]]],[[[[]]]],[]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[]],[[],[],[],[]]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[],[]],[[],[],[[]]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[]],[[],[[]],[]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[]],[[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[]],[[[],[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[]],[[[[]]],[]]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[]],[[[],[],[]]]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[]],[[[],[[]]]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[]],[[[[]],[]]]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[[],[]]]]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[]],[[[[[]]]]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[]]],[[],[],[],[]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]]],[[],[],[[]]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[[]]],[[],[[]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[[]]],[[],[[],[]]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[]]],[[],[[[]]]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[]]],[[[]],[],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[]]],[[[]],[[]]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[[]]],[[[],[]],[]]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]]],[[[[]]],[]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[[]]],[[[],[],[]]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[],[[]]]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[]]],[[[[]],[]]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[]]],[[[[],[]]]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[]]],[[[[[]]]]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[]],[]],[],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[]]]],[],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[[]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[],[[]]],[],[],[[]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[]],[]],[],[],[[]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[],[]]],[],[],[[]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[[]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[],[],[]],[],[[]],[]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[]]],[],[[]],[]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[]],[]],[],[[]],[]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]],[]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[]]]],[],[[]],[]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[],[],[]],[],[[],[]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[],[],[]],[],[[[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[],[[]]],[],[[],[]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[],[[]]],[],[[[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[]],[]],[],[[],[]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[]],[]],[],[[[]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[]]],[],[[],[]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[],[]]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[[]]]],[],[[],[]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]]]],[],[[[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[],[],[]],[[]],[],[]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[],[[]]],[[]],[],[]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[]],[]],[[]],[],[]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[]]],[[]],[],[]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[]]]],[[]],[],[]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[],[],[]],[[]],[[]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[],[[]]],[[]],[[]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[]],[]],[[]],[[]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[],[]]],[[]],[[]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]]],[[]],[[]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[],[],[]],[[],[]],[]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[],[],[]],[[[]]],[]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[[]]],[[],[]],[]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[],[[]]],[[[]]],[]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[]],[[],[]],[]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[]],[[[]]],[]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[],[]]],[[],[]],[]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]]],[[[]]],[]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[[]]]],[[],[]],[]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[[]]]],[[[]]],[]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[]],[[],[],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[],[],[]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[],[]],[[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[],[]],[[[],[]]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[],[]],[[[[]]]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[]],[]],[[],[],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[]],[]],[[[]],[]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[]],[]],[[[],[]]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[]],[]],[[[[]]]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[]]],[[],[],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[],[]]],[[],[[]]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[]]],[[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[],[]]],[[[],[]]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[],[]]],[[[[]]]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[]]]],[[],[],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[[]]]],[[],[[]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[[]]]],[[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[[[]]]],[[[],[]]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[[[]]]],[[[[]]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[],[]],[],[],[]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[],[[]],[]],[],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[[],[]]],[],[],[]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[[[]]]],[],[],[]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[]],[],[]],[],[],[]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[]],[[]]],[],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[]]],[]],[],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[],[[]]]],[],[],[]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]],[]]],[],[],[]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[[]]]]],[],[],[]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[[]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[],[],[[]]],[],[[]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[],[[]],[]],[],[[]]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[],[[],[]]],[],[[]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[],[[[]]]],[],[[]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[]],[],[]],[],[[]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[]],[[]]],[],[[]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]],[]],[],[[]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]],[]],[],[[]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[],[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[],[[]]]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]],[]]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[[[],[]]]],[],[[]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[[]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[],[],[],[]],[[]],[]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[],[[]]],[[]],[]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[]],[]],[[]],[]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[],[]]],[[]],[]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[]]]],[[]],[]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[],[]],[[]],[]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[]],[[]]],[[]],[]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]],[]],[[]],[]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[[]]],[]],[[]],[]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[],[]]],[[]],[]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[[]]]],[[]],[]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[[]],[]]],[[]],[]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]],[]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[[[]]]]],[[]],[]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[],[],[],[]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[],[],[],[]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[],[[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[],[[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[[]],[]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]],[]],[[[]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[],[]]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[],[[],[]]],[[[]]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[[]]]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[[]]]],[[[]]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[]],[],[]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[],[]],[[[]]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[]],[[]]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[]],[[]]],[[[]]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[]],[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[],[]],[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[[]]],[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[[[]]],[]],[[[]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[],[]]],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[],[],[]]],[[[]]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]]],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[],[[]]]],[[[]]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[[]],[]]],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]]],[[[]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[[[],[]]]],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[[],[]]]],[[[]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[[[[]]]]],[[],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[[[[]]]]],[[[]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[],[],[],[],[]],[],[]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[],[[]]],[],[]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[],[],[[]],[]],[],[]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[],[],[[],[]]],[],[]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[],[],[[[]]]],[],[]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[],[[]],[],[]],[],[]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[[]],[[]]],[],[]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[],[[],[]],[]],[],[]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[[[]]],[]],[],[]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[[],[],[]]],[],[]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[[],[[]]]],[],[]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[],[[[]],[]]],[],[]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[[[],[]]]],[],[]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[],[[[[]]]]],[],[]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]],[],[],[]],[],[]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[]],[],[[]]],[],[]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]],[[]],[]],[],[]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]],[[],[]]],[],[]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]],[[[]]]],[],[]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[]],[],[]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[]]],[],[]],[],[]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[[],[]],[[]]],[],[]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[]]],[],[]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[],[]],[]],[],[]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[],[[]]],[]],[],[]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[]],[]],[]],[],[]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[[[],[]]],[]],[],[]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[[[[]]]],[]],[],[]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[],[],[],[]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]],[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[],[[],[]]]],[],[]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[],[[[]]]]],[],[]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[]],[],[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]]]],[],[]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[[],[]],[]]],[],[]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]]],[]]],[],[]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[[[],[],[]]]],[],[]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[],[[]]]]],[],[]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[[[]],[]]]],[],[]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[[[],[]]]]],[],[]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[[[[]]]]]],[],[]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[],[],[],[],[]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[],[],[],[[]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[],[[]],[]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[],[[],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[],[[[]]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[[]],[],[]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[[]],[[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[]],[]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[[],[],[]]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[],[[],[[]]]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[[[]],[]]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[[[],[]]]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[[[[]]]]],[[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[]],[],[],[]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]],[],[[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[]],[[]],[]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[]],[[],[]]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[]],[[[]]]],[[]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[],[]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[],[]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[],[]],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[[]]],[[]]],[[]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[],[]],[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[],[[]]],[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[[]],[]],[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[[[],[]]],[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[[[]]]],[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[],[],[],[]]],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[],[],[[]]]],[[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[[]],[]]],[[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[],[[],[]]]],[[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[],[[[]]]]],[[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[[]],[],[]]],[[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]],[[]]]],[[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[[],[]],[]]],[[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[[[]]],[]]],[[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[[[],[],[]]]],[[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[[],[[]]]]],[[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[[[]],[]]]],[[]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[[[],[]]]]],[[]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[[[[[]]]]]],[[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[],[],[],[],[],[]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[],[[]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[],[],[[]],[]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[],[],[],[[],[]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[],[],[],[[[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[],[]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[],[],[[]],[[]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[],[[],[]],[]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[],[],[[[]]],[]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[],[],[[],[],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[],[],[[],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[],[[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[],[],[[[],[]]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[],[],[[[[]]]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[[]],[],[],[]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[],[[]],[],[[]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[]],[]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[],[[]],[[],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[],[[]],[[[]]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[[],[]],[],[]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[],[[[]]],[],[]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[],[[],[]],[[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[],[]],[]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[],[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[],[[[],[]]],[]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[],[[[[]]]],[]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[],[[],[],[],[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[],[[],[],[[]]]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[[]],[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[],[[],[[],[]]]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[],[[],[[[]]]]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[[[]],[],[]]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[],[[[]],[[]]]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[],[]],[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[],[[[[]]],[]]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[],[[[],[],[]]]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[],[[[],[[]]]]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[[[]],[]]]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[],[[[[],[]]]]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[],[[[[[]]]]]],[]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[]],[],[],[],[]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[]],[],[],[[]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[],[[]],[]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[],[[],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[]]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[]],[],[]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[]],[[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[],[]],[]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[[]]],[]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[],[],[]]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[],[[]]]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[[[]],[]]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[[[],[]]]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[[[]]]]],[]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[],[]],[],[],[]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[]]],[],[],[]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[[]]],[],[[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[[],[]],[[]],[]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[[]]],[[]],[]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[],[]]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[],[]],[[[]]]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[[]]],[[],[]]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[[[]]],[[[]]]],[]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[[],[],[]],[],[]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[],[[]]],[],[]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[]],[]],[],[]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[[[],[]]],[],[]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[[[[]]]],[],[]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[[],[],[]],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[],[[]]],[[]]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[[]],[]],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[[[],[]]],[[]]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[[[[]]]],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[[],[],[],[]],[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[],[[]]],[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]],[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[],[[],[]]],[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[],[[[]]]],[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[[]],[],[]],[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[]]],[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[[],[]],[]],[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]]],[]],[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[[],[],[]]],[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[[[],[[]]]],[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[[[[]],[]]],[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[[[[],[]]]],[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[[[[[]]]]],[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[[],[],[],[],[]]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[],[[]]]],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[],[],[[]],[]]],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[],[],[[],[]]]],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[],[[[]]]]],[]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[],[[]],[],[]]],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[],[[]],[[]]]],[]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[],[[],[]],[]]],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[],[[[]]],[]]],[]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[],[],[]]]],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[[],[[]]]]],[]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[],[[[]],[]]]],[]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[],[[[],[]]]]],[]]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[],[[[[]]]]]],[]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[]],[],[],[]]],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[[[]],[],[[]]]],[]]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[[[]],[[]],[]]],[]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[[],[]]]],[]]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[[[]]]]],[]]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[[[[],[]],[],[]]],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]]],[],[]]],[]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[[[[],[]],[[]]]],[]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[[[[]]],[[]]]],[]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[[[],[],[]],[]]],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[[]]],[]]],[]]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[[[[]],[]],[]]],[]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[[[],[]]],[]]],[]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[[[[[]]]],[]]],[]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[[[],[],[],[]]]],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[[],[],[[]]]]],[]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[[[],[[]],[]]]],[]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[[[],[[],[]]]]],[]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[[],[[[]]]]]],[]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[[[[]],[],[]]]],[]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[[[[[]],[[]]]]],[]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[[[[[],[]],[]]]],[]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[[[[]]],[]]]],[]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[[[[],[],[]]]]],[]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[[[[],[[]]]]]],[]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[[[[[]],[]]]]],[]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[[[[[],[]]]]]],[]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[[[[[[]]]]]]],[]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[],[],[],[],[],[],[]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[[]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[],[],[],[[]],[]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[],[],[],[[],[]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[],[],[],[[[]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[],[],[[]],[],[]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[],[],[[]],[[]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[],[],[[],[]],[]]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[],[],[[[]]],[]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[],[[],[],[]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[],[],[[],[[]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[],[],[[[]],[]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[],[],[[[],[]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[],[],[[[[]]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[],[[]],[],[],[]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[],[[]],[],[[]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[],[[]],[[]],[]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[],[[]],[[],[]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[],[[]],[[[]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[],[[],[]],[],[]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[],[[[]]],[],[]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[],[[],[]],[[]]]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[],[[[]]],[[]]]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[],[[],[],[]],[]]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[],[[],[[]]],[]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[],[[[]],[]],[]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[],[[[],[]]],[]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[],[[[[]]]],[]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[],[],[]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[[],[],[[]]]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[],[[]],[]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[],[[],[]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[],[[[]]]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[[]],[],[]]]]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[[]],[[]]]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[],[]],[]]]]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[[[]]],[]]]]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[[],[],[]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[[],[[]]]]]]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[[[[]],[]]]]]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[[[[],[]]]]]]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[[[[[]]]]]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[],[[]],[],[],[],[]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[],[[]],[],[],[[]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[]],[],[[]],[]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[]],[],[[],[]]]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[]],[],[[[]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[]],[[]],[],[]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[]],[[]],[[]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[]],[[],[]],[]]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[]],[[[]]],[]]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[],[],[]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[]],[[],[[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[]],[[[]],[]]]]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[]],[[[],[]]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[]],[[[[]]]]]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[]],[],[],[]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[],[[[]]],[],[],[]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[[],[]],[],[[]]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[],[[[]]],[],[[]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[[],[]],[[]],[]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]]],[[]],[]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[]],[[],[]]]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[],[[],[]],[[[]]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[],[[[]]],[[],[]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[[[]]],[[[]]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[[],[],[]],[],[]]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[[]]],[],[]]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[],[[[]],[]],[],[]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[[],[]]],[],[]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[],[[[[]]]],[],[]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[[],[],[]],[[]]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[],[[],[[]]],[[]]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]],[]],[[]]]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[[],[]]],[[]]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[],[[[[]]]],[[]]]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[[],[],[],[]],[]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[],[[]]],[]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[[]],[]],[]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[],[[],[[],[]]],[]]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[],[[],[[[]]]],[]]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[[[]],[],[]],[]]]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[[]],[[]]],[]]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[],[]],[]],[]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[],[[[[]]],[]],[]]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[[[],[],[]]],[]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[],[[[],[[]]]],[]]]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[[[]],[]]],[]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[[[],[]]]],[]]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[],[[[[[]]]]],[]]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[[],[],[],[],[]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[],[[]]]]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[],[[]],[]]]]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[],[[],[]]]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[],[[[]]]]]]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[],[[],[[]],[],[]]]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[[]],[[]]]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[],[[],[]],[]]]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[],[[],[[[]]],[]]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[],[[],[],[]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[[],[[],[[]]]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[[],[[[]],[]]]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[],[[],[[[],[]]]]]]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[],[[],[[[[]]]]]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[],[[[]],[],[],[]]]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[[]]]]]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[[[]],[[]],[]]]]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[[],[]]]]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[[[]],[[[]]]]]]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[[[],[]],[],[]]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[],[[[[]]],[],[]]]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[[[],[]],[[]]]]]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[],[[[[]]],[[]]]]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[[[],[],[]],[]]]]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[],[[[],[[]]],[]]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[[[]],[]],[]]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[[[[],[]]],[]]]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[],[[[[[]]]],[]]]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[[[],[],[],[]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[[[],[],[[]]]]]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[],[[[],[[]],[]]]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[],[[[],[[],[]]]]]]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[],[[[],[[[]]]]]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[],[[[[]],[],[]]]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[[[[]],[[]]]]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[[],[]],[]]]]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[],[[[[[]]],[]]]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[[[],[],[]]]]]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[[[[],[[]]]]]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[],[[[[[]],[]]]]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[[[[],[]]]]]]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[],[[[[[[]]]]]]]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[]],[],[],[],[],[]]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[[]]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[]],[],[],[[]],[]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[],[[],[]]]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[[[]],[],[],[[[]]]]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[]],[],[[]],[],[]]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[]],[],[[]],[[]]]]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[]],[],[[],[]],[]]]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[]],[],[[[]]],[]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[[[]],[],[[],[],[]]]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[]],[],[[],[[]]]]]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[]],[],[[[]],[]]]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[]],[],[[[],[]]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[]],[],[[[[]]]]]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[]],[[]],[],[],[]]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[]],[[]],[],[[]]]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[]],[[]],[[]],[]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[[]],[[]],[[],[]]]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[[]],[[]],[[[]]]]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[]],[[],[]],[],[]]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[]],[[[]]],[],[]]]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[]],[[],[]],[[]]]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[]],[[[]]],[[]]]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[[[]],[[],[],[]],[]]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[]],[[],[[]]],[]]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[]],[[[]],[]],[]]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[]],[[[],[]]],[]]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[[[]]]],[]]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[[[]],[[],[],[],[]]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[]],[[],[],[[]]]]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[]],[[],[[]],[]]]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[[],[[],[]]]]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[]],[[],[[[]]]]]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[]],[[[]],[],[]]]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[]],[[[]],[[]]]]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[]],[[[],[]],[]]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[[[[]]],[]]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[]],[[[],[],[]]]]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[]],[[[],[[]]]]]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[]],[[[[]],[]]]]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[]],[[[[],[]]]]]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[]],[[[[[]]]]]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[]],[],[],[],[]]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[]]],[],[],[],[]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[[[],[]],[],[],[[]]]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[[[[]]],[],[],[[]]]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[[[],[]],[],[[]],[]]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[[[[]]],[],[[]],[]]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[[[],[]],[],[[],[]]]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[],[]],[],[[[]]]]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[[]]],[],[[],[]]]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[[[[]]],[],[[[]]]]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[[[],[]],[[]],[],[]]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[[]]],[[]],[],[]]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[]],[[]],[[]]]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[[]]],[[]],[[]]]]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[],[]],[[],[]],[]]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[[[]]],[]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[[[[]]],[[],[]],[]]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[[[[]]],[[[]]],[]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[[[],[]],[[],[],[]]]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[],[]],[[],[[]]]]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[],[]],[[[]],[]]]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[],[]],[[[],[]]]]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[],[]],[[[[]]]]]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[]]],[[],[],[]]]]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[[[[]]],[[],[[]]]]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[[]]],[[[]],[]]]]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[[[[]]],[[[],[]]]]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[[[[]]],[[[[]]]]]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[[[],[],[]],[],[],[]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[],[[]]],[],[],[]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[[]],[]],[],[],[]]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[[[[],[]]],[],[],[]]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[[[[[]]]],[],[],[]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[[[],[],[]],[],[[]]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[],[[]]],[],[[]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[[[[]],[]],[],[[]]]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[[[],[]]],[],[[]]]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[[[[[]]]],[],[[]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[[[],[],[]],[[]],[]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[],[[]]],[[]],[]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[[[[]],[]],[[]],[]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[[[[],[]]],[[]],[]]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[[[[[]]]],[[]],[]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[[],[],[]],[[],[]]]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[],[],[]],[[[]]]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[],[[]]],[[],[]]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[],[[]]],[[[]]]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[[]],[]],[[],[]]]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[[[]],[]],[[[]]]]]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[[[[],[]]],[[],[]]]]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[[[],[]]],[[[]]]]]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[[[[[]]]],[[],[]]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[[[[]]]],[[[]]]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[[[],[],[],[]],[],[]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[],[[]]],[],[]]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[]],[],[]]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[],[[],[]]],[],[]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[],[[[]]]],[],[]]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[[]],[],[]],[],[]]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[[[[]],[[]]],[],[]]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[[[[],[]],[]],[],[]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[[[[[]]],[]],[],[]]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[[[[],[],[]]],[],[]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[[[[],[[]]]],[],[]]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[[[[[]],[]]],[],[]]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[[[[[],[]]]],[],[]]]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[[[[[[]]]]],[],[]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[[[],[],[],[]],[[]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[],[],[[]]],[[]]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[[]],[]],[[]]]]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[[[],[[],[]]],[[]]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[],[[[]]]],[[]]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[[]],[],[]],[[]]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[[[[]],[[]]],[[]]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[[[],[]],[]],[[]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[[[[[]]],[]],[[]]]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[[[],[],[]]],[[]]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[[[[],[[]]]],[[]]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[[[]],[]]],[[]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[[[[[],[]]]],[[]]]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[[[[[[]]]]],[[]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[],[],[],[],[]],[]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[],[[]]],[]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[],[],[[]],[]],[]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[],[],[[],[]]],[]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[],[[[]]]],[]]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]],[],[]],[]]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[],[[]],[[]]],[]]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[],[[],[]],[]],[]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[],[[[]]],[]],[]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[],[[],[],[]]],[]]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[[],[[]]]],[]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[],[[[]],[]]],[]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[],[[[],[]]]],[]]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[],[[[[]]]]],[]]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[[[[]],[],[],[]],[]]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[[[[]],[],[[]]],[]]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[[[[]],[[]],[]],[]]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[[],[]]],[]]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[[[[]],[[[]]]],[]]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[[[[],[]],[],[]],[]]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[[[[[]]],[],[]],[]]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[[[[],[]],[[]]],[]]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[[[[[]]],[[]]],[]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[[[[],[],[]],[]],[]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[[[[],[[]]],[]],[]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[[[[[]],[]],[]],[]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[[[[[],[]]],[]],[]]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[[[[[[]]]],[]],[]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[[[[],[],[],[]]],[]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[[[[],[],[[]]]],[]]]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[[[[],[[]],[]]],[]]]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[[[[],[[],[]]]],[]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[[[[],[[[]]]]],[]]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[[[[[]],[],[]]],[]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[[[[[]],[[]]]],[]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[[[[],[]],[]]],[]]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[[[[[[]]],[]]],[]]]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[[[[[],[],[]]]],[]]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[[[[[],[[]]]]],[]]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[[[[[]],[]]]],[]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[[[[[[],[]]]]],[]]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[[[[[[[]]]]]],[]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[[],[],[],[],[],[]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[],[[]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[],[[]],[]]]]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[],[[],[]]]]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[],[[[]]]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[],[],[[]],[],[]]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[],[],[[]],[[]]]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[],[[],[]],[]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[],[[[]]],[]]]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[],[],[]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[],[],[[],[[]]]]]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[],[[[]],[]]]]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[],[[[],[]]]]]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[],[],[[[[]]]]]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[],[[]],[],[],[]]]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[[]]]]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[],[[]],[[]],[]]]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[],[[]],[[],[]]]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[],[[]],[[[]]]]]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[],[[],[]],[],[]]]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[],[[[]]],[],[]]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[],[]],[[]]]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]],[[]]]]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[],[[],[],[]],[]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[[],[[]]],[]]]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[],[[[]],[]],[]]]]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[],[[[],[]]],[]]]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[],[[[[]]]],[]]]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[],[[],[],[],[]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[],[[],[],[[]]]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[],[[],[[]],[]]]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[],[[],[[],[]]]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[],[[],[[[]]]]]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[[]],[],[]]]]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[],[[[]],[[]]]]]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[],[[[],[]],[]]]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[[[[]]],[]]]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[],[[[],[],[]]]]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[[[],[[]]]]]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[],[[[[]],[]]]]]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[],[[[[],[]]]]]]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[],[[[[[]]]]]]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[]],[],[],[],[]]]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[[[[]],[],[],[[]]]]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[[[[]],[],[[]],[]]]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[[[[]],[],[[],[]]]]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[[[[]],[],[[[]]]]]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[[[[]],[[]],[],[]]]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[[]],[[]]]]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[[]],[[],[]],[]]]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[[[[]],[[[]]],[]]]]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[[[]],[[],[],[]]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[[[[]],[[],[[]]]]]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[[]],[[[]],[]]]]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[[[[]],[[[],[]]]]]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[[[[]]]]]]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[[[[],[]],[],[],[]]]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]]],[],[],[]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[[[[],[]],[],[[]]]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[[[[[]]],[],[[]]]]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[[[[],[]],[[]],[]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[[[[[]]],[[]],[]]]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[[[],[]],[[],[]]]]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[[[[],[]],[[[]]]]]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[[[[[]]],[[],[]]]]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[[[[[]]],[[[]]]]]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[[[[],[],[]],[],[]]]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[[]]],[],[]]]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[[[[[]],[]],[],[]]]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[[[[[],[]]],[],[]]]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[[[[[]]]],[],[]]]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[[[[],[],[]],[[]]]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[[[[],[[]]],[[]]]]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[[]],[]],[[]]]]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[[[[[],[]]],[[]]]]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[[[[[[]]]],[[]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[[],[],[],[]],[]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[[[[],[],[[]]],[]]]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[[[[],[[]],[]],[]]]]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[[[[],[[],[]]],[]]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[[[],[[[]]]],[]]]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[[[[]],[],[]],[]]]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[[[[[]],[[]]],[]]]]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[[[[[],[],[]]],[]]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[[[[],[[]]]],[]]]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[[[[[]],[]]],[]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[[[[],[]]]],[]]]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[[[[],[],[],[],[]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[],[],[],[[]]]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[[[[],[],[[]],[]]]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[[[[],[],[[],[]]]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[],[[[]]]]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[[[[],[[]],[[]]]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[],[[],[]],[]]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[[],[[[]]],[]]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[[[],[[],[[]]]]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[],[[[]],[]]]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[[[],[[[],[]]]]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[[[],[[[[]]]]]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[]],[],[],[]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[[[[[]],[],[[]]]]]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[[[[[]],[[]],[]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[[[[[]],[[],[]]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[[[[[]],[[[]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[[[[[],[]],[],[]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[[[[[]]],[],[]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[[[[],[]],[[]]]]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[[[],[],[]],[]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[[[],[[]]],[]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[[[[],[]]],[]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[[[[],[],[[]]]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[[[[],[[]],[]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[[[[]],[],[]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[[[[[[],[]],[]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[[[[],[],[]]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[[[[[],[[]]]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[[[[[],[]]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
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 Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
searching the database
Sorry, this map was not found in the database.