Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-2Cc0021;cc-rep-3
[1,0]=>[1,0]=>[.,.]=>[[],[]]
[1,0,1,0]=>[1,0,1,0]=>[[.,.],.]=>[[[],[]],[]]
[1,1,0,0]=>[1,1,0,0]=>[.,[.,.]]=>[[],[[],[]]]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[[.,.],.],.]=>[[[[],[]],[]],[]]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[.,[.,.]],.]=>[[[],[[],[]]],[]]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[.,.],[.,.]]=>[[[],[]],[[],[]]]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[.,[[.,.],.]]=>[[],[[[],[]],[]]]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[.,[.,[.,.]]]=>[[],[[],[[],[]]]]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]=>[[[[[],[]],[]],[]],[]]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]=>[[[[],[[],[]]],[]],[]]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]=>[[[[],[]],[[],[]]],[]]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]=>[[[],[[[],[]],[]]],[]]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]=>[[[],[[],[[],[]]]],[]]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]=>[[[[],[]],[]],[[],[]]]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]=>[[[],[[],[]]],[[],[]]]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]=>[[[],[]],[[[],[]],[]]]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]=>[[],[[[[],[]],[]],[]]]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]=>[[],[[[],[[],[]]],[]]]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]=>[[[],[]],[[],[[],[]]]]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]=>[[],[[[],[]],[[],[]]]]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]=>[[],[[],[[[],[]],[]]]]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]=>[[],[[],[[],[[],[]]]]]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]=>[[[[[[],[]],[]],[]],[]],[]]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]=>[[[[[],[[],[]]],[]],[]],[]]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]=>[[[[[],[]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]=>[[[[],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]=>[[[[],[[],[[],[]]]],[]],[]]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]=>[[[[[],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]=>[[[[],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]=>[[[[],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]=>[[[],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]=>[[[],[[[],[[],[]]],[]]],[]]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]=>[[[[],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]=>[[[],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]=>[[[],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]=>[[[],[[],[[],[[],[]]]]],[]]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]=>[[[[[],[]],[]],[]],[[],[]]]
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[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]=>[[[[],[]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]=>[[[],[[[],[]],[]]],[[],[]]]
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[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]=>[[[[],[]],[]],[[[],[]],[]]]
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[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]=>[[[],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]=>[[],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]=>[[],[[[[],[[],[]]],[]],[]]]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>[[[],[]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>[[],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]=>[[],[[[],[[[],[]],[]]],[]]]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>[[],[[[],[[],[[],[]]]],[]]]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]=>[[[[],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]=>[[[],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]=>[[[],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]=>[[],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]=>[[],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]=>[[[],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]=>[[],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>[[],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]=>[[],[[],[[[],[[],[]]],[]]]]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]=>[[[],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]=>[[],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]=>[[],[[],[[[],[]],[[],[]]]]]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]=>[[],[[],[[],[[[],[]],[]]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]=>[[],[[],[[],[[],[[],[]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]=>[[[[[[[],[]],[]],[]],[]],[]],[]]
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[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]=>[[[[[[],[]],[[],[]]],[]],[]],[]]
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[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]=>[[[],[[[[],[]],[]],[[],[]]]],[]]
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[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[[],[[[],[]],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[],[[],[[[[],[]],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[],[[],[[[],[[],[]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[[],[]],[[],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[[],[[[],[]],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[],[[],[[[],[]],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[],[[],[[],[[[],[]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[[],[[],[[],[[],[[],[]]]]]],[[],[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[],[]],[]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[[],[[],[]]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[[],[]],[[],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[[],[[[],[]],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[],[[],[[],[]]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[[],[]],[]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[[],[[],[]]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[[],[]],[[[],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[[[[],[]],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[],[[[],[[],[]]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[[],[]],[[],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[[],[]],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[],[[],[[[],[]],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[],[[],[[],[[],[]]]]],[[[],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[],[]],[]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[[],[[],[]]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[[],[]],[[],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[[[],[]],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[],[[],[[],[]]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[],[]],[]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[],[[],[]]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[[[],[]],[[[[[[],[]],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[[],[[[[[[[],[]],[]],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[[[[],[[],[]]],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[[[],[]],[[[[[],[[],[]]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[[],[[[[[[],[]],[[],[]]],[]],[]],[]]]
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[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[[],[[],[[],[]]]],[]],[]],[]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[[],[]],[]],[[[[],[[],[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[],[[],[]]],[[[[],[[],[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[[[],[]],[[[[[],[]],[[],[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[[],[[[[[[],[]],[]],[[],[]]],[]],[]]]
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[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[[],[[[[[],[]],[[[],[]],[]]],[]],[]]]
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[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[[],[[[],[[],[]]],[]]],[]],[]]]
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[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[[[[],[]],[]],[[],[[],[]]]],[]]]
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[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[[],[]],[[[],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[[],[[[[],[]],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[[],[[[[],[]],[]],[[],[]]]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[[],[[[],[[[],[[],[]]],[[],[]]]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[[],[]],[[[],[[],[[[],[]],[]]]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[[],[[[[],[]],[[],[[[],[]],[]]]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[[],[[[],[]],[[[],[]],[]]]],[]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[[],[[],[[[[],[]],[]],[]]]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[[],[[],[[[],[[],[]]],[]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[[],[]],[[[],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[[],[[[[],[]],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[[],[[[],[]],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[[],[[],[[[],[]],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[],[[[],[[],[[],[[[],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[[],[[],[[],[[],[[],[]]]]]],[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[],[]],[]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[[],[[],[]]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[[],[]],[[],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[[],[[[],[]],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[],[[],[[],[]]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[[],[]],[]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[[],[[],[]]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[[],[]],[[[],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[[[[],[]],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[],[[[],[[],[]]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[[],[]],[[],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[[],[]],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[],[[],[[[],[]],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[],[[],[[],[[],[]]]]],[[],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[],[]],[]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[[],[[],[]]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[[],[]],[[],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[[[],[]],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[],[[],[[],[]]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[],[]],[]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[],[[],[]]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[],[]],[[[[[],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[[],[]],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[[[],[[],[]]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[[],[]],[[[[],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[[],[[[[[],[]],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[[],[[[],[]],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[],[[[[],[[],[[],[]]]],[]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[[],[]],[]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[],[[],[]]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[[],[]],[[[[],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[[],[[[[[],[]],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[],[[[[],[[],[]]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[[],[]],[[[],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[[],[[[[],[]],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[[],[[[[],[]],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[[],[[[],[[],[]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[[],[]],[[[],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[[],[[[[],[]],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[[],[[[],[]],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[],[[[],[[],[[[],[]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[[],[[],[[],[[],[]]]]],[[],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[],[]],[]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[[],[[],[]]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[[],[]],[[],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[[[],[]],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[],[[],[[],[]]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[],[]],[]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[],[[],[]]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[],[]],[[[[],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[[],[]],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[[],[[[[],[[],[]]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[[],[]],[[[],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[[],[[[[],[]],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[[],[[[],[]],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[[],[[],[[],[]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[],[]],[]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[],[[],[]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[],[]],[[[],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[],[[[[],[]],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[[],[[],[]]],[[[[],[]],[]],[]]]]
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[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[],[[[],[]],[[[[[],[]],[]],[]],[]]]]
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[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[[],[[[],[[],[]]],[]]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[[[[[],[]],[[],[[],[]]]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[[[],[[[],[]],[[],[]]]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[[],[[],[[[],[]],[]]]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[],[[],[[],[[],[]]]]],[[],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[[[[[[],[]],[]],[]],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[[[[],[[],[]]],[]],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[[[[[],[]],[[],[]]],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[[[],[[[],[]],[]]],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[[],[[],[[],[]]]],[[[],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[[[],[]],[]],[[[[],[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[[[],[[],[]]],[[[[],[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[[[[],[]],[[[[[],[]],[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[[],[[[[[[],[]],[]],[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[[],[[[[[],[[],[]]],[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[[[[],[]],[[[[],[[],[]]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[[],[[[[[],[]],[[],[]]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[[],[[[[],[[[],[]],[]]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[],[[[[],[[],[[],[]]]],[]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[[[[[],[]],[]],[[[],[[],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[[[],[[],[]]],[[[],[[],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[[[[],[]],[[[[],[]],[[],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[[],[[[[[],[]],[]],[[],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[[],[[[[],[[],[]]],[[],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[[[[],[]],[[[],[[[],[]],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[[],[[[[],[]],[[[],[]],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[[],[[[],[[[[],[]],[]],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[],[[[],[[[],[[],[]]],[]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[[[[],[]],[[[],[[],[[],[]]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[[],[[[[],[]],[[],[[],[]]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[[],[[[],[[[],[]],[[],[]]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[],[[[],[[],[[[],[]],[]]]],[]]],[]],[]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[[],[[[],[[],[[],[[],[]]]]],[]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[[[[[[],[]],[]],[]],[[],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[[],[[],[]]],[]],[[],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[[[[[],[]],[[],[]]],[[],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[[],[[[],[]],[]]],[[],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[[],[[],[[],[]]]],[[],[[],[]]]],[]],[]]
[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]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[[[[[],[]],[]],[[[],[]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[[[],[[],[]]],[[[],[]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[[[],[]],[[[[],[]],[]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[[],[[[[[],[]],[]],[]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[[],[[[[],[[],[]]],[]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[[[[],[]],[[[],[[],[]]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[[],[[[[],[]],[[],[]]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[[],[[[],[[[],[]],[]]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[],[[[],[[],[[],[]]]],[[],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[[[[[],[]],[]],[[],[[[],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[[[],[[],[]]],[[],[[[],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[[[],[]],[[[],[]],[[[],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[[],[[[[],[]],[]],[[[],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[[],[[[],[[],[]]],[[[],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[[[],[]],[[],[[[[],[]],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[[],[[[],[]],[[[[],[]],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[[],[[],[[[[[],[]],[]],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[],[[],[[[[],[[],[]]],[]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[[[],[]],[[],[[[],[[],[]]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[[],[[[],[]],[[[],[[],[]]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[[],[[],[[[[],[]],[[],[]]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[],[[],[[[],[[[],[]],[]]],[]]]],[]],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[[],[[],[[[],[[],[[],[]]]],[]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[[[],[]],[]],[[],[[],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[[[],[[],[]]],[[],[[],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[[[[],[]],[[[],[]],[[],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[[],[[[[],[]],[]],[[],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[[],[[[],[[],[]]],[[],[[],[]]]]],[]],[]]
[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]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[[[[],[]],[[],[[[],[]],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[[[],[[[],[]],[[[],[]],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[[],[[],[[[[],[]],[]],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[],[[],[[[],[[],[]]],[[],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[[[[],[]],[[],[[],[[[],[]],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[[[],[[[],[]],[[],[[[],[]],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[[],[[],[[[],[]],[[[],[]],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[[],[[],[[],[[[[],[]],[]],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[[[],[[],[[],[[[],[[],[]]],[]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[[[[],[]],[[],[[],[[],[[],[]]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[[[],[[[],[]],[[],[[],[[],[]]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[[],[[],[[[],[]],[[],[[],[]]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[[[],[[],[[],[[[],[]],[[],[]]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[[[],[[],[[],[[],[[[],[]],[]]]]]],[]],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[[],[[],[[],[[],[[],[[],[]]]]]]],[]],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[[],[]],[]],[]],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[[[[[],[[],[]]],[]],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[[],[]],[[],[]]],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[[],[[[],[]],[]]],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[[[],[[],[[],[]]]],[]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[[],[]],[]],[[],[]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[[],[[],[]]],[[],[]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[[[[[],[]],[[[],[]],[]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[[],[[[[],[]],[]],[]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[[],[[[],[[],[]]],[]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[[],[]],[[],[[],[]]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[[],[[[],[]],[[],[]]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[[[],[[],[[[],[]],[]]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[[],[[],[[],[[],[]]]]],[]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[[],[]],[]],[]],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[[[[],[[],[]]],[]],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[[],[]],[[],[]]],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[[],[[[],[]],[]]],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[[],[[],[[],[]]]],[[],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[[],[]],[]],[[[],[]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[[[],[[],[]]],[[[],[]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[[[],[]],[[[[],[]],[]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[[],[[[[[],[]],[]],[]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[[],[[[[],[[],[]]],[]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[[[],[]],[[[],[[],[]]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[[],[[[[],[]],[[],[]]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[[],[[[],[[[],[]],[]]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[],[[[],[[],[[],[]]]],[]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[[[],[]],[]],[[],[[],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[[],[[],[]]],[[],[[],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[[],[]],[[[],[]],[[],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[[],[[[[],[]],[]],[[],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[[],[[[],[[],[]]],[[],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[[[],[]],[[],[[[],[]],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[[],[[[],[]],[[[],[]],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[[],[[],[[[[],[]],[]],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[],[[],[[[],[[],[]]],[]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[[[],[]],[[],[[],[[],[]]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[[],[[[],[]],[[],[[],[]]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[[[],[[],[[[],[]],[[],[]]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[],[[],[[],[[[],[]],[]]]]],[[],[]]],[]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[[],[[],[[],[[],[[],[]]]]]],[[],[]]],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[[],[]],[]],[]],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[[],[[],[]]],[]],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[[],[]],[[],[]]],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[[],[[[],[]],[]]],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[[],[[],[[],[]]]],[]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[[[[[],[]],[]],[[],[]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[[],[[],[]]],[[],[]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[[],[]],[[[],[]],[]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[[],[[[[],[]],[]],[]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[[],[[[],[[],[]]],[]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[[[],[]],[[],[[],[]]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[[],[[[],[]],[[],[]]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[[],[[],[[[],[]],[]]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[],[[],[[],[[],[]]]]],[[[],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[[[],[]],[]],[]],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[[[],[[],[]]],[]],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[[[[],[]],[[],[]]],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[[],[[[],[]],[]]],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[],[[],[[],[]]]],[[[[],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[[[[],[]],[]],[[[[[],[]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[[],[[],[]]],[[[[[],[]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[[[],[]],[[[[[[],[]],[]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[[],[[[[[[[],[]],[]],[]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[[],[[[[[[],[[],[]]],[]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[[[],[]],[[[[[],[[],[]]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[[],[[[[[[],[]],[[],[]]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[[[],[[[[[],[[[],[]],[]]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[],[[[[[],[[],[[],[]]]],[]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[[[[],[]],[]],[[[[],[[],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[[],[[],[]]],[[[[],[[],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[[[],[]],[[[[[],[]],[[],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[[],[[[[[[],[]],[]],[[],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[[],[[[[[],[[],[]]],[[],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[[[],[]],[[[[],[[[],[]],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[[],[[[[[],[]],[[[],[]],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[[],[[[[],[[[[],[]],[]],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[],[[[[],[[[],[[],[]]],[]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[[[],[]],[[[[],[[],[[],[]]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[[],[[[[[],[]],[[],[[],[]]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[[],[[[[],[[[],[]],[[],[]]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[],[[[[],[[],[[[],[]],[]]]],[]],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[[],[[[[],[[],[[],[[],[]]]]],[]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[[[],[]],[]],[]],[[[],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[[],[[],[]]],[]],[[[],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[[[[],[]],[[],[]]],[[[],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[[],[[[],[]],[]]],[[[],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[[],[[],[[],[]]]],[[[],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[[[[],[]],[]],[[[[],[]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[[],[[],[]]],[[[[],[]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[[[],[]],[[[[[],[]],[]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[[],[[[[[[],[]],[]],[]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[[],[[[[[],[[],[]]],[]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[[],[]],[[[[],[[],[]]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[[],[[[[[],[]],[[],[]]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[[],[[[[],[[[],[]],[]]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[],[[[[],[[],[[],[]]]],[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[[[],[]],[]],[[[],[[[],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[[],[[],[]]],[[[],[[[],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[[[],[]],[[[[],[]],[[[],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[[],[[[[[],[]],[]],[[[],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[[],[[[[],[[],[]]],[[[],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[[[],[]],[[[],[[[[],[]],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[[],[[[[],[]],[[[[],[]],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[[],[[[],[[[[[],[]],[]],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[],[[[],[[[[],[[],[]]],[]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[[[],[]],[[[],[[[],[[],[]]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[[],[[[[],[]],[[[],[[],[]]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[[],[[[],[[[[],[]],[[],[]]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[[],[[[],[[[],[[],[[],[]]]],[]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[[[[],[]],[]],[[[],[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[[],[[],[]]],[[[],[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[[[],[]],[[[[],[]],[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[[[],[[[[[],[]],[]],[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[[],[[[[],[[],[]]],[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[[[],[]],[[[],[[[],[]],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[[],[[[[],[]],[[[],[]],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[],[[[],[[[[],[]],[]],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[[[],[]],[[[],[[],[[[],[]],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[[],[[[[],[]],[[],[[[],[]],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[[],[[[],[[],[[[[],[]],[]],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[[],[[[],[[],[[[],[[],[]]],[]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[[[],[]],[[[],[[],[[],[[],[]]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[[],[[[[],[]],[[],[[],[[],[]]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[[[],[[[],[[[],[]],[[],[[],[]]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[[],[[[],[[],[[[],[]],[[],[]]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[[[],[[[],[[],[[],[[[],[]],[]]]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[[],[[[],[[],[[],[[],[[],[]]]]]],[]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[[],[]],[]],[]],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[[],[[],[]]],[]],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[[],[]],[[],[]]],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[[],[[[],[]],[]]],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[[],[[],[[],[]]]],[]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[[[],[]],[]],[[],[]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[[],[[],[]]],[[],[]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[[],[]],[[[],[]],[]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[[],[[[[],[]],[]],[]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[],[[[],[[],[]]],[]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[[],[]],[[],[[],[]]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[[],[[[],[]],[[],[]]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[[[],[[],[[[],[]],[]]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[[],[[],[[],[[],[]]]]],[[],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[[[[[],[]],[]],[]],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[[[],[[],[]]],[]],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[[[],[]],[[],[]]],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[[],[[[],[]],[]]],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[],[[],[[],[]]]],[[[],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[[[[],[]],[]],[[[[],[]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[[],[[],[]]],[[[[],[]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[[[],[]],[[[[[],[]],[]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[[[],[[[[[[],[]],[]],[]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[[],[[[[[],[[],[]]],[]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[[[],[]],[[[[],[[],[]]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[[],[[[[[],[]],[[],[]]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[],[[[[],[[[],[]],[]]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[[],[[[[],[[],[[],[]]]],[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[[[],[]],[]],[[[],[[],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[],[[],[]]],[[[],[[],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[[[],[]],[[[[],[]],[[],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[[],[[[[[],[]],[]],[[],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[],[[[[],[[],[]]],[[],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[[[],[]],[[[],[[[],[]],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[[[],[]],[[[],[]],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[[],[[[],[[[[],[]],[]],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[],[[[],[[[],[[],[]]],[]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[[[],[]],[[[],[[],[[],[]]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[[],[[[[],[]],[[],[[],[]]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[[],[[[],[[[],[]],[[],[]]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[],[[[],[[],[[[],[]],[]]]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[[],[[[],[[],[[],[[],[]]]]],[[],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[[[[[],[]],[]],[]],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[[[],[[],[]]],[]],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[[[[],[]],[[],[]]],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[[],[[[],[]],[]]],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[],[[],[[],[]]]],[[],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[[[[],[]],[]],[[[],[]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[[],[]]],[[[],[]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[[[],[]],[[[[],[]],[]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[[],[[[[[],[]],[]],[]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[[],[[[[],[[],[]]],[]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[[[],[]],[[[],[[],[]]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[[[],[[[[],[]],[[],[]]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[],[[[],[[],[[],[]]]],[[[],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[[[],[]],[]],[[],[[[[],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[[],[[],[]]],[[],[[[[],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[[[],[]],[[[],[]],[[[[],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[[],[[[[],[]],[]],[[[[],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[[],[[[],[[],[]]],[[[[],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[[[],[]],[[],[[[[[],[]],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[[],[[[],[]],[[[[[],[]],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[[],[[],[[[[[[],[]],[]],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[[[],[[],[[[[[],[[],[]]],[]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[[[],[]],[[],[[[[],[[],[]]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[[],[[[],[]],[[[[],[[],[]]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[[[],[[],[[[[[],[]],[[],[]]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[[],[[],[[[[],[[[],[]],[]]],[]],[]]]],[]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[[],[[],[[[[],[[],[[],[]]]],[]],[]]]],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[[[],[]],[]],[[],[[[],[[],[]]],[]]]],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[[],[[],[]]],[[],[[[],[[],[]]],[]]]],[]]
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[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[[[],[[[[],[]],[]],[[[],[[],[]]],[]]]],[]]
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[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[],[[[],[[],[]]],[]]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[[[],[]],[[],[[],[]]]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[[],[[[],[]],[[],[]]]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[[],[[[],[]],[]]]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[],[[],[[],[[],[]]]]],[[],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[[[],[]],[]],[]],[[[],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[[],[[],[]]],[]],[[[],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[[[],[]],[[],[]]],[[[],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[[],[]],[]]],[[[],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[[[],[]],[]],[[[[],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[[],[[],[]]],[[[[],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[[[],[]],[[[[[],[]],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[[[[[[],[]],[]],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[],[[[[[],[[],[]]],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[[],[]],[[[[],[[],[]]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[[[[],[]],[[],[]]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[],[[[[],[[[],[]],[]]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[],[[[[],[[],[[],[]]]],[]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[[],[]],[]],[[[],[[],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[[[],[]],[[[[],[]],[[],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[[[[[],[]],[]],[[],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[[[],[[[],[]],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[[],[]],[[[],[]],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[[],[[[[],[]],[]],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[[[],[]],[[[],[[],[[],[]]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[[],[]],[[],[[],[]]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[],[[[],[[[],[]],[[],[]]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[[],[[],[[[],[]],[]]]],[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[],[[[],[[],[[],[[],[]]]]],[]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[[[],[]],[]],[]],[[],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[[],[[],[]]],[]],[[],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[[[[],[]],[[],[]]],[[],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[[],[]],[]]],[[],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[],[[],[[],[]]]],[[],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[[[[],[]],[]],[[[],[]],[[],[]]]],[[],[]]]
[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]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[],[]],[[[[],[]],[]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[[],[]],[]],[]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[],[[[[],[[],[]]],[]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[],[]],[[[],[[],[]]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[[],[]],[[],[]]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[],[[[],[[[],[]],[]]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[],[[[],[[],[[],[]]]],[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[[],[]],[]],[[],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[[],[[],[]]],[[],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[[[],[]],[[[],[]],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[[[[],[]],[]],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[],[[[],[[],[]]],[[[],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[[],[]],[[],[[[[],[]],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[[],[]],[[[[],[]],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[],[[],[[[[[],[]],[]],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[[],[[[[],[[],[]]],[]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[[[],[]],[[],[[[],[[],[]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[[],[]],[[[],[[],[]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[],[[],[[[[],[]],[[],[]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[[],[[[],[[[],[]],[]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[],[[],[[[],[[],[[],[]]]],[]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[[[[],[]],[]],[[],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[[],[[],[]]],[[],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[[[],[]],[[[],[]],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[[[[],[]],[]],[[],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[],[[[],[[],[]]],[[],[[],[]]]]],[[],[]]]
[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]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[[[],[]],[[],[[[],[]],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[[],[]],[[[],[]],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[],[[],[[[[],[]],[]],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[],[[],[[[],[[],[]]],[[],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[[[],[]],[[],[[],[[[],[]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[[],[]],[[],[[[],[]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[],[[],[[[],[]],[[[],[]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[],[[],[[],[[[[],[]],[]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[],[[],[[],[[[],[[],[]]],[]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[],[]],[[],[[],[[],[[],[]]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[[],[]],[[],[[],[[],[]]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[],[[],[[[],[]],[[],[[],[]]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[],[[],[[],[[[],[]],[[],[]]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[],[[],[[],[[],[[[],[]],[]]]]]],[[],[]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[],[[],[[],[[],[[],[[],[]]]]]]],[[],[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[[],[]],[]],[]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[[[[],[[],[]]],[]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[[[[[],[]],[[],[]]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[[],[[[],[]],[]]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[[],[[],[]]]],[]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[[[[[],[]],[]],[[],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[[[],[[],[]]],[[],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[[[],[]],[[[],[]],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[[],[[[[],[]],[]],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[],[[[],[[],[]]],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[[[[],[]],[[],[[],[]]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[[],[[[],[]],[[],[]]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[[],[[[],[]],[]]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[],[[],[[],[[],[]]]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[[[[[],[]],[]],[]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[[[],[[],[]]],[]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[[],[]],[[],[]]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[[],[[[],[]],[]]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[[[[],[]],[]],[[[],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[[],[]],[[[[],[]],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[[[[[],[]],[]],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[],[[[[],[[],[]]],[]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[[],[]],[[[],[[],[]]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[[[],[]],[[],[]]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[],[[[],[[],[[],[]]]],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[[[[],[]],[]],[[],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[[],[]],[[[],[]],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[[[[],[]],[]],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[],[[[],[[],[]]],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[[],[]],[[],[[[],[]],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[],[[],[[[[],[]],[]],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[],[[],[[[],[[],[]]],[]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[[[],[]],[[],[[],[[],[]]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[[],[]],[[],[[],[]]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[],[[],[[[],[]],[[],[]]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[],[[],[[],[[[],[]],[]]]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[],[[],[[],[[],[[],[]]]]]],[[[],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[[],[]],[]],[]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[[],[[],[]]],[]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[[[],[]],[[],[]]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[[],[[[],[]],[]]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[[[],[]],[]],[[],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[[[],[]],[[[],[]],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[[[[],[]],[]],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[],[[[],[[],[]]],[]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[[],[]],[[],[[],[]]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[[],[]],[[],[]]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[],[[],[[[],[]],[]]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[[],[]],[]],[]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[[],[[],[]]],[]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[[[],[]],[[],[]]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[[[],[]],[]]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]]
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[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[],[[],[]]],[[[[[[],[]],[]],[]],[]],[]]]
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[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[[[[],[]],[[],[]]],[]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[[],[[[],[]],[]]],[]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[],[[],[[],[]]]],[]],[[[],[[],[]]],[]]]
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[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[],[[],[]]],[[],[]]],[[[],[[],[]]],[]]]
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[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[[[[],[]],[]],[]]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[],[[[],[[],[]]],[]]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[[[],[]],[[],[[],[]]]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[[],[]],[[],[]]]],[[[],[[],[]]],[]]]
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[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[],[[],[[],[[],[]]]]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[[],[]],[]],[]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[[],[[],[]]],[]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[[],[]],[[],[]]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[[[],[]],[]]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[[],[[],[]]]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[[[],[]],[]],[[[[[],[]],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[],[[],[]]],[[[[[],[]],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[[],[]],[[[[[[],[]],[]],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[[],[[[[[[[],[]],[]],[]],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[],[[[[[[],[[],[]]],[]],[]],[[],[]]],[]]]
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[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[[],[[[[[[],[]],[[],[]]],[]],[[],[]]],[]]]
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[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[[],[]],[[[[[],[]],[[],[]]],[[],[]]],[]]]
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[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[[],[[[[[],[]],[[[],[]],[]]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[[],[[[[],[[[[],[]],[]],[]]],[[],[]]],[]]]
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[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[],[[[[],[]],[[[],[]],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[[],[[[],[[[[],[]],[]],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[[],[[[],[[[],[[],[]]],[[],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[[],[]],[[[],[[],[[[],[]],[[],[]]]]],[]]]
[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]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[[],[[[[],[]],[[],[[[],[]],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[[],[[[],[[[],[]],[[[],[]],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[[],[[[],[[],[[[[],[]],[]],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[[],[[[],[[],[[[],[[],[]]],[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[[],[]],[[[],[[],[[],[[[],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[[],[[[[],[]],[[],[[],[[[],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[[],[[[],[[[],[]],[[],[[[],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[[],[[[],[[],[[[],[]],[[[],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[[],[[[],[[],[[],[[[[],[]],[]],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[[],[[[],[[],[[],[[[],[[],[]]],[]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[],[]],[[[],[[],[[],[[],[[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[],[[[[],[]],[[],[[],[[],[[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[[],[[[],[[[],[]],[[],[[],[[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[[],[[[],[[],[[[],[]],[[],[[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[[],[[[],[[],[[],[[[],[]],[[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[],[[[],[[],[[],[[],[[[],[]],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[],[[[],[[],[[],[[],[[],[[],[]]]]]]],[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[[],[]],[]],[]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[[[],[[],[]]],[]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[[[[],[]],[[],[]]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[[],[]],[]]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[[],[[],[[],[]]]],[]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[[[[],[]],[]],[[],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[[],[]],[]],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[],[[[],[[],[]]],[]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[[],[]],[[],[[],[]]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[[],[[[],[]],[[],[]]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[],[[],[[],[[],[]]]]],[]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[[[[],[]],[]],[]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[[],[]],[]]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[],[]],[]],[[[],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[[],[]],[[[[],[]],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[[],[]],[]],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[],[[[[],[[],[]]],[]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[],[]],[[[],[[],[]]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[[],[]],[[],[]]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[],[[[],[[[],[]],[]]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[],[[[],[[],[[],[]]]],[]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[[[],[]],[]],[[],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[[],[]],[[[],[]],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[[[[],[]],[]],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[],[[],[[[[],[]],[]],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[[],[[[],[[],[]]],[]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[],[]],[[],[[],[[],[]]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[[],[]],[[],[[],[]]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[],[[],[[[],[]],[[],[]]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[],[[],[]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[],[[],[[],[[],[[],[]]]]]],[[],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[[],[]],[]],[]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[[],[[],[]]],[]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[[[],[]],[[],[]]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[[],[[[],[]],[]]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[[],[[],[]]]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[[],[]],[]],[[],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[[],[]]],[[],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[[],[]],[[[],[]],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[[[[],[]],[]],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[],[[[],[[],[]]],[]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[[],[]],[[],[[],[]]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[[],[]],[[],[]]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[],[[],[[[],[]],[]]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[],[[],[[],[[],[]]]]],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[[],[]],[]],[]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[[],[[],[]]],[]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[[],[]],[[],[]]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[[[],[]],[]]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[],[[],[[],[]]]],[[[[],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[[[],[]],[]],[[[[[],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[],[[],[]]],[[[[[],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[],[]],[[[[[[],[]],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[[],[[[[[[[],[]],[]],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[],[[[[[[],[[],[]]],[]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[],[]],[[[[[],[[],[]]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[],[[[[[[],[]],[[],[]]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[],[[[[[],[[[],[]],[]]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[],[[[[[],[[],[[],[]]]],[]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[[[],[]],[]],[[[[],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[[],[]]],[[[[],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[],[]],[[[[[],[]],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[[],[[[[[[],[]],[]],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[],[[[[[],[[],[]]],[[],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[],[]],[[[[],[[[],[]],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[],[[[[[],[]],[[[],[]],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[],[[[[],[[[[],[]],[]],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[],[[[[],[[[],[[],[]]],[]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[],[]],[[[[],[[],[[],[]]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[],[[[[[],[]],[[],[[],[]]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[],[[[[],[[[],[]],[[],[]]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[],[[[[],[[],[[[],[]],[]]]],[]],[[],[]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[],[[[[],[[],[[],[[],[]]]]],[]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[[],[]],[]],[]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[[],[]]],[]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[[],[]],[[],[]]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[[[],[]],[]]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[],[[],[[],[]]]],[[[],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[[[],[]],[]],[[[[],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[],[]],[[[[[],[]],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[[],[[[[[[],[]],[]],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[],[[[[[],[[],[]]],[]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[],[]],[[[[],[[],[]]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[],[[[[[],[]],[[],[]]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[[],[[[[],[[[],[]],[]]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[],[[[[],[[],[[],[]]]],[[],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[[[],[]],[]],[[[],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[],[[],[]]],[[[],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[],[]],[[[[],[]],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[],[[[[[],[]],[]],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[],[[[[],[[],[]]],[[[],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[],[]],[[[],[[[[],[]],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[],[[[[],[]],[[[[],[]],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[],[[[],[[[[[],[]],[]],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[],[[[],[[[[],[[],[]]],[]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[],[]],[[[],[[[],[[],[]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[],[[[[],[]],[[[],[[],[]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[],[[[],[[[[],[]],[[],[]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[],[[[],[[[],[[[],[]],[]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[],[[[],[[[],[[],[[],[]]]],[]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[[],[]],[]],[[[],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[],[[],[]]],[[[],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[],[]],[[[[],[]],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[],[[[[[],[]],[]],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[],[[[[],[[],[]]],[[],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[],[]],[[[],[[[],[]],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[],[[[[],[]],[[[],[]],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[],[[[],[[[[],[]],[]],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[],[[[],[[[],[[],[]]],[[],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[],[]],[[[],[[],[[[],[]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[],[[[[],[]],[[],[[[],[]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[],[[[],[[[],[]],[[[],[]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[],[[[],[[],[[[[],[]],[]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[],[[[],[[],[[[],[[],[]]],[]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[],[]],[[[],[[],[[],[[],[]]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[],[[[[],[]],[[],[[],[[],[]]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[],[[[],[[[],[]],[[],[[],[]]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[],[[[],[[],[[[],[]],[[],[]]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[],[[[],[[],[[],[[[],[]],[]]]]],[[],[]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[],[[[],[[],[[],[[],[[],[]]]]]],[[],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[[],[]],[]],[]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[[[],[[],[]]],[]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[[[],[]],[[],[]]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[[],[[[],[]],[]]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[[],[[],[]]]],[]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[[[[],[]],[]],[[],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[[],[]],[[[],[]],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[[[[],[]],[]],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[],[[[],[[],[]]],[]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[[],[]],[[],[[],[]]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[[],[]],[[],[]]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[],[[],[[[],[]],[]]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[],[[],[[],[[],[]]]]],[[],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[[],[]],[]],[]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[[],[]],[[],[]]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[[],[]],[]],[[[[],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[],[]],[[[[[],[]],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[],[[[[[[],[]],[]],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[],[[[[[],[[],[]]],[]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[],[]],[[[[],[[],[]]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[],[[[[[],[]],[[],[]]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[],[[[[],[[[],[]],[]]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[],[[[[],[[],[[],[]]]],[]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[[],[]],[]],[[[],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[],[]],[[[[],[]],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[],[[[[[],[]],[]],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[],[[[[],[[],[]]],[[],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[],[[[[],[]],[[[],[]],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[],[[[],[[[[],[]],[]],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[],[[[],[[[],[[],[]]],[]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[],[]],[[[],[[],[[],[]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[],[[[[],[]],[[],[[],[]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[],[[[],[[[],[]],[[],[]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[],[[[],[[],[[[],[]],[]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[],[[[],[[],[[],[[],[]]]]],[[[],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[[],[]],[]],[]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[[],[[],[]]],[]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[[],[]],[[],[]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[[[],[]],[]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[[],[]],[]],[[[],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[],[]],[[[[],[]],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[],[[[[[],[]],[]],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[],[[[[],[[],[]]],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[[],[[[[],[]],[[],[]]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[],[[[],[[[],[]],[]]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[],[[[],[[],[[],[]]]],[[[[],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[[],[]],[]],[[],[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[],[[],[]]],[[],[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[],[]],[[[],[]],[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[],[[[[],[]],[]],[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[],[[[],[[],[]]],[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[[],[]],[[],[[[[[[],[]],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[],[[[],[]],[[[[[[],[]],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[],[[],[[[[[[[],[]],[]],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[],[[],[[[[[[],[[],[]]],[]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[[],[]],[[],[[[[[],[[],[]]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[],[[[],[]],[[[[[],[[],[]]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[],[[],[[[[[[],[]],[[],[]]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[],[[],[[[[[],[[[],[]],[]]],[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[],[[],[[[[[],[[],[[],[]]]],[]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[[],[]],[]],[[],[[[[],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[[],[]]],[[],[[[[],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[]],[[[],[]],[[[[],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[],[[[[],[]],[]],[[[[],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[],[[[],[[],[]]],[[[[],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[],[]],[[],[[[[[],[]],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[],[[[],[]],[[[[[],[]],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[],[[],[[[[[[],[]],[]],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[],[[],[[[[[],[[],[]]],[[],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[[],[]],[[],[[[[],[[[],[]],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[],[[[],[]],[[[[],[[[],[]],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[],[[],[[[[[],[]],[[[],[]],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[],[[],[[[[],[[[[],[]],[]],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[],[[],[[[[],[[[],[[],[]]],[]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[[],[]],[[],[[[[],[[],[[],[]]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[],[[[],[]],[[[[],[[],[[],[]]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[],[[],[[[[[],[]],[[],[[],[]]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[],[[],[[[[],[[[],[]],[[],[]]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[],[[],[[[[],[[],[[[],[]],[]]]],[]],[]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[],[[],[[[[],[[],[[],[[],[]]]]],[]],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[[],[]],[]],[]],[[],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[[],[[],[]]],[]],[[],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[[],[]],[[],[]]],[[],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[[[],[]],[]]],[[],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[],[[],[[],[]]]],[[],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[[],[]],[]],[[[],[]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[],[[],[]]],[[[],[]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[],[]],[[[[],[]],[]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[],[[[[[],[]],[]],[]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[],[[[[],[[],[]]],[]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[],[]],[[[],[[],[]]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[],[[[[],[]],[[],[]]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[],[[[],[[[],[]],[]]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[],[[[],[[],[[],[]]]],[[[],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[[[],[]],[]],[[],[[[[],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[],[[],[]]],[[],[[[[],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[],[]],[[[],[]],[[[[],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[],[[[[],[]],[]],[[[[],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[],[[[],[[],[]]],[[[[],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[[],[]],[[],[[[[[],[]],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[],[[[],[]],[[[[[],[]],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[],[[],[[[[[[],[]],[]],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[],[[],[[[[[],[[],[]]],[]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[[],[]],[[],[[[[],[[],[]]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[],[[[],[]],[[[[],[[],[]]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[],[[],[[[[[],[]],[[],[]]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[],[[],[[[[],[[[],[]],[]]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[],[[],[[[[],[[],[[],[]]]],[[],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[[],[]],[]],[[],[[[],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[],[[],[]]],[[],[[[],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[],[[[[],[]],[]],[[[],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[],[[[],[[],[]]],[[[],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[[],[]],[[],[[[[],[]],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[],[[[],[]],[[[[],[]],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[],[[],[[[[[],[]],[]],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[],[[],[[[[],[[],[]]],[[[],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[[],[]],[[],[[[],[[[[],[]],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[],[[[],[]],[[[],[[[[],[]],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[],[[],[[[[],[]],[[[[],[]],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[],[[],[[[],[[[[[],[]],[]],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[],[[],[[[],[[[[],[[],[]]],[]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[[],[]],[[],[[[],[[[],[[],[]]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[],[[[],[]],[[[],[[[],[[],[]]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[],[[],[[[[],[]],[[[],[[],[]]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[],[[],[[[],[[[[],[]],[[],[]]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[],[[],[[[],[[[],[[[],[]],[]]],[]]],[]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[],[[],[[[],[[[],[[],[[],[]]]],[]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[[],[]],[]],[[],[[[],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[],[[],[]]],[[],[[[],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[],[]],[[[],[]],[[[],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[],[[[[],[]],[]],[[[],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[],[[[],[[],[]]],[[[],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[[],[]],[[],[[[[],[]],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[],[[[],[]],[[[[],[]],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[],[[],[[[[[],[]],[]],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[],[[],[[[[],[[],[]]],[[],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[[],[]],[[],[[[],[[[],[]],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[],[[[],[]],[[[],[[[],[]],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[],[[],[[[[],[]],[[[],[]],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[],[[],[[[],[[[[],[]],[]],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[],[[],[[[],[[[],[[],[]]],[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[[],[]],[[],[[[],[[],[[[],[]],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[],[[[],[]],[[[],[[],[[[],[]],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[],[[],[[[[],[]],[[],[[[],[]],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[],[[],[[[],[[[],[]],[[[],[]],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[],[[],[[[],[[],[[[[],[]],[]],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[],[[],[[[],[[],[[[],[[],[]]],[]]]],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[],[]],[[],[[[],[[],[[],[[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[],[[[],[]],[[[],[[],[[],[[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[],[[],[[[[],[]],[[],[[],[[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[],[[],[[[],[[[],[]],[[],[[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[],[[],[[[],[[],[[[],[]],[[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[],[[],[[[],[[],[[],[[[],[]],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[],[[],[[[],[[],[[],[[],[[],[]]]]]],[]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[],[]],[]],[]],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[[],[]]],[]],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[[],[]],[[],[]]],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[[],[]],[]]],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[[],[[],[]]]],[]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[],[]],[]],[[],[]]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[[],[]],[]],[]]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[],[[[],[[],[]]],[]]],[[],[[],[[],[]]]]]
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[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[[],[]],[[],[]]]],[[],[[],[[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[],[[],[[[],[]],[]]]],[[],[[],[[],[]]]]]
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[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[],[[],[]]],[]],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[],[]],[[],[]]],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[[[],[]],[]]],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[],[[],[[],[]]]],[[[],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[[],[]],[]],[[[[],[]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[],[[],[]]],[[[[],[]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[],[]],[[[[[],[]],[]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[],[[[[[[],[]],[]],[]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[],[[[[[],[[],[]]],[]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[],[]],[[[[],[[],[]]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[],[[[[[],[]],[[],[]]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[],[[[[],[[[],[]],[]]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[],[[[[],[[],[[],[]]]],[]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[[],[]]],[[[],[[],[]]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[],[]],[[[[],[]],[[],[]]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[],[[[[[],[]],[]],[[],[]]],[[],[[],[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[],[[[[],[[],[]]],[[],[]]],[[],[[],[]]]]]
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[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[],[[[],[[[],[]],[]]],[[],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[],[[[],[[],[[],[]]]],[[],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[],[]],[]],[[],[[[],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[],[[],[]]],[[],[[[],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[],[]],[[[],[]],[[[],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[],[[[[],[]],[]],[[[],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[],[[[],[[],[]]],[[[],[]],[[],[[],[]]]]]]
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[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[],[[[],[]],[[[[],[]],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[],[[],[[[[[],[]],[]],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[],[[],[[[[],[[],[]]],[]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[],[]],[[],[[[],[[],[]]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[],[[[],[]],[[[],[[],[]]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[],[[],[[[[],[]],[[],[]]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[],[[],[[[],[[[],[]],[]]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[],[[],[[[],[[],[[],[]]]],[[],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[],[]],[]],[[],[[],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[],[[],[]]],[[],[[],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[]],[[[],[]],[[],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[],[[[[],[]],[]],[[],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[],[[[],[[],[]]],[[],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[[],[]],[[],[[[],[]],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[],[[[],[]],[[[],[]],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[],[[],[[[[],[]],[]],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[],[[],[[[],[[],[]]],[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[[],[]],[[],[[],[[[[],[]],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[],[[[],[]],[[],[[[[],[]],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[],[[],[[[],[]],[[[[],[]],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[],[[],[[],[[[[[],[]],[]],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[],[[],[[],[[[[],[[],[]]],[]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[],[]],[[],[[],[[[],[[],[]]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[],[[[],[]],[[],[[[],[[],[]]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[],[[],[[[],[]],[[[],[[],[]]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[],[[],[[],[[[[],[]],[[],[]]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[],[[],[[],[[[],[[[],[]],[]]],[[],[]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[],[[],[[],[[[],[[],[[],[]]]],[[],[]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[],[]],[]],[[],[[],[[],[[[],[]],[]]]]]]
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[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[],[[[],[]],[[[],[]],[[],[[[],[]],[]]]]]]
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[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[],[[],[[[],[[],[]]],[[],[[[],[]],[]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[[],[]],[[],[[],[[[],[]],[[[],[]],[]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[],[[[],[]],[[],[[[],[]],[[[],[]],[]]]]]]
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[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[],[[],[[],[[[[],[]],[]],[[[],[]],[]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[],[[],[[],[[[],[[],[]]],[[[],[]],[]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[],[]],[[],[[],[[],[[[[],[]],[]],[]]]]]]
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[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[],[]],[[],[[[],[]],[[],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[],[[[],[]],[[[],[]],[[],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[],[[],[[[[],[]],[]],[[],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[],[[],[[[],[[],[]]],[[],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[],[]],[[],[[],[[[],[]],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[],[[[],[]],[[],[[[],[]],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[],[[],[[[],[]],[[[],[]],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[],[[],[[],[[[[],[]],[]],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[],[[],[[],[[[],[[],[]]],[[],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[],[]],[[],[[],[[],[[[],[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[],[[[],[]],[[],[[],[[[],[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[],[[],[[[],[]],[[],[[[],[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[],[[],[[],[[[],[]],[[[],[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[],[[],[[],[[],[[[[],[]],[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[],[[],[[],[[],[[[],[[],[]]],[[],[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[],[]],[[],[[],[[],[[],[[[],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[],[[[],[]],[[],[[],[[],[[[],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[],[[],[[[],[]],[[],[[],[[[],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[],[[],[[],[[[],[]],[[],[[[],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[],[[],[[],[[],[[[],[]],[[[],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[],[[],[[],[[],[[],[[[[],[]],[]],[]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[],[[],[[],[[],[[],[[[],[[],[]]],[]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[]],[[],[[],[[],[[],[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[],[[[],[]],[[],[[],[[],[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[],[[],[[[],[]],[[],[[],[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[],[[],[[],[[[],[]],[[],[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[],[[],[[],[[],[[[],[]],[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[],[[],[[],[[],[[],[[[],[]],[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[],[[],[[],[[],[[],[[],[[[],[]],[]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[],[[],[[],[[],[[],[[],[[],[[],[]]]]]]]]]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
searching the database
Sorry, this map was not found in the database.