Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0005;cc-rep-2
[1,0]=>[.,.]=>[1,0]
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[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[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]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[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]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[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]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[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]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[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]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[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]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ 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.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ 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.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
searching the database
Sorry, this map was not found in the database.