Identifier
Mp00048:
Ordered trees
—left-right symmetry⟶
Ordered trees
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0010;cc-rep-2Cc0005;cc-rep-3
[[]]=>[[]]=>[.,.]=>[1,0]
[[],[]]=>[[],[]]=>[[.,.],.]=>[1,1,0,0]
[[[]]]=>[[[]]]=>[.,[.,.]]=>[1,0,1,0]
[[],[],[]]=>[[],[],[]]=>[[[.,.],.],.]=>[1,1,1,0,0,0]
[[],[[]]]=>[[[]],[]]=>[[.,[.,.]],.]=>[1,1,0,1,0,0]
[[[]],[]]=>[[],[[]]]=>[[.,.],[.,.]]=>[1,1,0,0,1,0]
[[[],[]]]=>[[[],[]]]=>[.,[[.,.],.]]=>[1,0,1,1,0,0]
[[[[]]]]=>[[[[]]]]=>[.,[.,[.,.]]]=>[1,0,1,0,1,0]
[[],[],[],[]]=>[[],[],[],[]]=>[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]
[[],[],[[]]]=>[[[]],[],[]]=>[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]
[[],[[]],[]]=>[[],[[]],[]]=>[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]
[[],[[],[]]]=>[[[],[]],[]]=>[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]
[[],[[[]]]]=>[[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]
[[[]],[],[]]=>[[],[],[[]]]=>[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]
[[[]],[[]]]=>[[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]
[[[],[]],[]]=>[[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]
[[[[]]],[]]=>[[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]
[[[],[],[]]]=>[[[],[],[]]]=>[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]
[[[],[[]]]]=>[[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0]
[[[[]],[]]]=>[[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0]
[[[[],[]]]]=>[[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0]
[[[[[]]]]]=>[[[[[]]]]]=>[.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]
[[],[],[],[],[]]=>[[],[],[],[],[]]=>[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]]]=>[[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]
[[],[],[[]],[]]=>[[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]
[[],[],[[],[]]]=>[[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]
[[],[],[[[]]]]=>[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]
[[],[[]],[],[]]=>[[],[],[[]],[]]=>[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]
[[],[[]],[[]]]=>[[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]
[[],[[],[]],[]]=>[[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]
[[],[[[]]],[]]=>[[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]
[[],[[],[],[]]]=>[[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]
[[],[[],[[]]]]=>[[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]
[[],[[[]],[]]]=>[[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]
[[],[[[],[]]]]=>[[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]
[[],[[[[]]]]]=>[[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[]]=>[[],[],[],[[]]]=>[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]
[[[]],[],[[]]]=>[[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]
[[[]],[[]],[]]=>[[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]
[[[]],[[],[]]]=>[[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]
[[[]],[[[]]]]=>[[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[]]=>[[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]
[[[[]]],[],[]]=>[[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]
[[[],[]],[[]]]=>[[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]
[[[[]]],[[]]]=>[[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[]]=>[[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[]]=>[[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[]]=>[[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[]]=>[[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[]]=>[[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]]]=>[[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]]]=>[[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]]]=>[[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]]]=>[[[[],[]],[]]]=>[.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]]]=>[[[[[]]],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]]]=>[[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]]]=>[[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]]]=>[[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]]]=>[[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]]]=>[[[[],[],[]]]]=>[.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]]]=>[[[[[]],[]]]]=>[.,[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]]]=>[[[[],[[]]]]]=>[.,[.,[[.,.],[.,.]]]]=>[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]
[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]]]=>[[[],[]],[],[],[]]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]]]=>[[[[]]],[],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]]]=>[[[],[[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]]]=>[[[[],[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]]]=>[[[[[]]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]]]=>[[[],[]],[[]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]]]=>[[[[]]],[[]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]]]=>[[[],[[]],[]],[]]=>[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]]]=>[[[[],[]],[]],[]]=>[[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]]]=>[[[[[],[]]]],[]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]]]=>[[[[[[]]]]],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]]]=>[[[],[]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]]]=>[[[[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[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]
[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[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]
[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[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]
[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[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]
[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[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]
[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[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]
[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[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]
[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[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]
[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[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]
[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[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]
[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[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]
[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[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]
[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[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]
[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[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]
[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[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]
[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[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]
[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[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]
[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[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]
[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[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]
[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[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]
[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to 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.