Identifier
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-2
[.,.]=>[1,0]=>[.,.]
[.,[.,.]]=>[1,0,1,0]=>[[.,.],.]
[[.,.],.]=>[1,1,0,0]=>[.,[.,.]]
[.,[.,[.,.]]]=>[1,0,1,0,1,0]=>[[[.,.],.],.]
[.,[[.,.],.]]=>[1,0,1,1,0,0]=>[[.,.],[.,.]]
[[.,.],[.,.]]=>[1,1,0,0,1,0]=>[[.,[.,.]],.]
[[.,[.,.]],.]=>[1,1,0,1,0,0]=>[.,[[.,.],.]]
[[[.,.],.],.]=>[1,1,1,0,0,0]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]
[.,[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]
[.,[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]
[.,[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]
[.,[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]
[[.,.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]
[[.,.],[[.,.],.]]=>[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]
[[.,[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]
[[[.,.],.],[.,.]]=>[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]
[[.,[.,[.,.]]],.]=>[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]
[[.,[[.,.],.]],.]=>[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]
[[[.,.],[.,.]],.]=>[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]
[[[.,[.,.]],.],.]=>[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]
[[[[.,.],.],.],.]=>[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]
[.,[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]
[.,[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]
[.,[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]
[.,[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]
[.,[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]
[.,[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]
[.,[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]
[.,[[[.,.],.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]
[.,[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]
[.,[[.,[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]
[.,[[[.,.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]
[.,[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]
[.,[[[[.,.],.],.],.]]=>[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]
[[.,.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]
[[.,.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]]
[[.,.],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]
[[.,.],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]
[[.,.],[[[.,.],.],.]]=>[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]
[[.,[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]
[[[.,.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]
[[[.,.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]]
[[.,[.,[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]
[[[.,.],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]
[[[.,[.,.]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]
[[[[.,.],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]
[[.,[.,[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]
[[.,[.,[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]
[[.,[[.,[.,.]],.]],.]=>[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]
[[[.,.],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]
[[[.,.],[[.,.],.]],.]=>[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]
[[[.,[.,.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]
[[[[.,.],.],[.,.]],.]=>[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]
[[[.,[[.,.],.]],.],.]=>[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]
[[[[.,.],[.,.]],.],.]=>[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]
[[[[.,[.,.]],.],.],.]=>[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]
[[[[[.,.],.],.],.],.]=>[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]
[.,[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]
[.,[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],.]
[.,[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]
[.,[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]
[.,[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]
[.,[.,[[[.,[.,.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]
[.,[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]
[.,[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]
[.,[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]
[.,[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]
[.,[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],.]
[.,[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]
[.,[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]
[.,[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]
[.,[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]
[.,[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]
[.,[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]
[.,[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]
[.,[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]
[.,[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]
[.,[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]
[.,[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]
[.,[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]
[.,[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]
[.,[[[[[.,.],.],.],.],.]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.]
[[.,.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],.]
[[.,.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]
[[.,.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]
[[.,.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],.]
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]
[[[.,.],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]
[[[.,.],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]
[[[.,.],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]
[[[.,.],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],.]
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]
[[[.,.],[.,.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],.]
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]
[[[[.,.],.],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]
[[[[.,.],.],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]
[[[.,.],[[.,.],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]
[[[[.,.],.],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],.]
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],.]
[[[[.,.],[.,.]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],.]
[[[[[.,.],.],.],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]]
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]
[[[.,.],[.,[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]
[[[.,.],[[.,.],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]
[[[.,.],[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]
[[[.,.],[[[.,.],.],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,.]]]]
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]
[[[[.,.],.],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]
[[[[.,.],.],[[.,.],.]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]
[[[[.,.],[.,.]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]
[[[[[.,.],.],.],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]
[[[.,[[[.,.],.],.]],.],.]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]]
[[[[.,.],[.,[.,.]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]
[[[[.,.],[[.,.],.]],.],.]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]
[[[[[.,.],.],[.,.]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]
[[[[.,[[.,.],.]],.],.],.]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]
[[[[[.,.],[.,.]],.],.],.]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]
[[[[[.,[.,.]],.],.],.],.]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]
[[[[[[.,.],.],.],.],.],.]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],.]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],.]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],.]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],.]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],.]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],.]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],.]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],.]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],.]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],.]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],.]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
searching the database
Sorry, this map was not found in the database.