Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-2Cc0010;cc-rep-3
[1,0]=>[1,0]=>[.,.]=>[.,.]
[1,0,1,0]=>[1,0,1,0]=>[[.,.],.]=>[.,[.,.]]
[1,1,0,0]=>[1,1,0,0]=>[.,[.,.]]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[[.,.],.],.]=>[[.,.],[.,.]]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[.,[.,.]],.]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[.,.],[.,.]]=>[.,[.,[.,.]]]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[.,[[.,.],.]]=>[[[.,.],.],.]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[.,[.,[.,.]]]=>[[.,[.,.]],.]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.]=>[[[.,.],.],[.,.]]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],.]=>[[.,[.,.]],[.,.]]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],.]=>[[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],.]=>[.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],.]=>[.,[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,.]]=>[.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]]=>[.,[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]]=>[[[[.,.],.],.],.]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]]=>[.,[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]]=>[[.,[[.,.],.]],.]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],.]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],.]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],.]=>[[.,[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],.]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],.]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],.]=>[[.,[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],.]],.]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],.]],.]=>[.,[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],.]=>[.,[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],.]=>[.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[.,.]]]],.]=>[.,[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,.]]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[.,.]]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,.]]=>[.,[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]]=>[.,[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]]=>[[[[[.,.],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],.],.]]=>[[[[.,[.,.]],.],.],.]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>[.,[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>[[[[.,.],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,.]]]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>[[.,[[[.,.],.],.]],.]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]]=>[.,[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],.]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],.]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],.]=>[[[.,[[.,.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],.]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],.]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],.]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],.]=>[[.,[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],.]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],.]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],.]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],.]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],.]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],.]=>[[[.,[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],.]=>[[.,[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],.]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],.]=>[[.,[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],.]=>[[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],.]=>[.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],.]=>[.,[[[[.,[.,.]],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],.]=>[[.,.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],.]=>[.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],.]=>[.,[[[.,[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],.]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],.]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],.]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],.]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],.]=>[.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],.]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,.]]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,.]]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,.]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,.]]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>[[[[[[.,.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>[[[[.,.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>[[[.,.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[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]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[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]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[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]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[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]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[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]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[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]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[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]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[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]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[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]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[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]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[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]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[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]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[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]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]=>[.,[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[.,[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[.,[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[.,[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[.,[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]=>[.,[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[.,[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[.,[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.]=>[.,[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]=>[[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]=>[[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]=>[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]=>[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[[.,[[[[.,[[[.,.],.],.]],.],.],.]],.]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]=>[[.,[[.,[[[[.,[.,.]],.],.],.]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]]=>[[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]=>[[.,[[.,[.,[[[[.,.],.],.],.]]],.]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],[.,.]]]]=>[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]=>[[.,[[.,[[[[.,.],.],.],.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]=>[[[[[[.,.],.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]=>[[[[[.,.],.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]=>[[[[.,.],.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]=>[[.,[[.,[.,.]],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[[.,[.,[[[[[.,[.,.]],.],.],.],.]]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]=>[[.,[.,[[.,[[[[.,.],.],.],.]],.]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]=>[[.,[[.,.],[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]=>[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[[.,[.,[[.,.],[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[[.,[.,[.,[[[[.,[.,.]],.],.],.]]]],.]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]=>[[.,[.,[.,[[.,[[[.,.],.],.]],.]]]],.]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]]=>[[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]=>[[.,[.,[.,[[[[.,.],.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[[.,[.,[.,[[.,.],[[[.,.],.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]=>[[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]=>[[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]=>[[[[[[.,[[[.,.],.],.]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[[[[.,[[[.,.],.],[.,.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[[[.,[[[[.,.],.],.],[.,.]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[[[[.,[.,[[[.,.],.],.]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[[[.,[.,[[[[.,.],.],.],.]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]]=>[[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]]=>[[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]]=>[[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]]=>[[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[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]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[[[[[.,.],.],.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[[[[.,.],.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],.],.],.],[[.,.],[.,.]]]
[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]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]=>[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[[[[.,.],.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[[[[[.,.],.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[[[.,.],.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[[[[.,.],.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[[[.,.],.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]=>[[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]=>[[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]=>[[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]=>[[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]=>[[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[[[[[.,[[.,.],.]],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[[[[[.,[.,.]],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]=>[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[.,[[.,[[[[[.,.],.],.],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]=>[[[.,[.,.]],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]=>[.,[[.,[.,[.,.]]],[[[[.,.],.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[[[[[.,.],[[[.,.],.],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[[[[[[.,.],.],[[.,.],.]],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[[[.,[[[[.,.],.],.],.]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[[[[[.,[.,.]],[[.,.],.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>[.,[[[.,[[.,[[.,.],.]],.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]=>[.,[[[.,[[.,.],.]],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>[.,[[[.,[[.,.],.]],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>[.,[[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>[.,[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[.,[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>[.,[[[.,[[.,[[.,.],.]],.]],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>[.,[[[.,[[.,.],.]],[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>[.,[[[.,[[.,[[.,.],.]],.]],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[.,[[[.,[[.,.],.]],.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>[.,[[[.,[[.,.],.]],.],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[.,[[[.,[[.,.],.]],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[.,[[[.,.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[.,[[[.,.],.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[.,[[[.,.],.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>[.,[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>[.,[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>[.,[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[.,[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>[.,[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]=>[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]=>[[[[[.,.],[.,.]],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]=>[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]]=>[.,[[[.,.],.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]=>[.,[[.,.],[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,.],[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]=>[[[[.,.],.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[.,[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[[[[.,[[.,[[.,.],.]],.]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]=>[[[[.,[.,.]],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[[.,.],.],.]]=>[[[.,[[.,.],.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[[[[[.,[[.,.],.]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]=>[[.,.],[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]=>[[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[[.,[[.,.],.]],[[[.,[[.,[[.,[.,.]],.]],.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]=>[.,[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]=>[[.,.],[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[.,[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]=>[.,[.,[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
right rotate
Description
Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
searching the database
Sorry, this map was not found in the database.