Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Mp00011: Binary trees —to graph⟶ Graphs
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0020;cc-rep-2
[1,0]=>[.,.]=>([],1)
[1,0,1,0]=>[.,[.,.]]=>([(0,1)],2)
[1,1,0,0]=>[[.,.],.]=>([(0,1)],2)
[1,0,1,0,1,0]=>[.,[.,[.,.]]]=>([(0,2),(1,2)],3)
[1,0,1,1,0,0]=>[.,[[.,.],.]]=>([(0,2),(1,2)],3)
[1,1,0,0,1,0]=>[[.,.],[.,.]]=>([(0,2),(1,2)],3)
[1,1,0,1,0,0]=>[[.,[.,.]],.]=>([(0,2),(1,2)],3)
[1,1,1,0,0,0]=>[[[.,.],.],.]=>([(0,2),(1,2)],3)
[1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,.]]]]=>([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],.]]]=>([(0,3),(1,2),(2,3)],4)
[1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,.]]]=>([(0,3),(1,3),(2,3)],4)
[1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],.]]=>([(0,3),(1,2),(2,3)],4)
[1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],.]]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,.]]]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],.]]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,.]]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],.]=>([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,.]]=>([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],.]=>([(0,3),(1,3),(2,3)],4)
[1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4)
[1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],.]=>([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,.]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,.]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[.,.]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,.]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],.]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],.],[.,.]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
searching the database
Sorry, this map was not found in the database.