Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00046: Ordered trees —to graph⟶ Graphs
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00046: Ordered trees —to graph⟶ Graphs
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2Cc0020;cc-rep-3
[1,0]=>[.,.]=>[[]]=>([(0,1)],2)
[1,0,1,0]=>[.,[.,.]]=>[[[]]]=>([(0,2),(1,2)],3)
[1,1,0,0]=>[[.,.],.]=>[[],[]]=>([(0,2),(1,2)],3)
[1,0,1,0,1,0]=>[.,[.,[.,.]]]=>[[[[]]]]=>([(0,3),(1,2),(2,3)],4)
[1,0,1,1,0,0]=>[.,[[.,.],.]]=>[[[],[]]]=>([(0,3),(1,3),(2,3)],4)
[1,1,0,0,1,0]=>[[.,.],[.,.]]=>[[],[[]]]=>([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0]=>[[.,[.,.]],.]=>[[[]],[]]=>([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,0]=>[[[.,.],.],.]=>[[],[],[]]=>([(0,3),(1,3),(2,3)],4)
[1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,.]]]]=>[[[[[]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],.]]]=>[[[[],[]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,.]]]=>[[[],[[]]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],.]]=>[[[[]],[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],.]]=>[[[],[],[]]]=>([(0,4),(1,4),(2,4),(3,4)],5)
[1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,.]]]=>[[],[[[]]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],.]]=>[[],[[],[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,.]]=>[[[]],[[]]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],.]=>[[[[]]],[]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],.]=>[[[],[]],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,.]]=>[[],[],[[]]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],.]=>[[],[[]],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],.]=>[[[]],[],[]]=>([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],.]=>[[],[],[],[]]=>([(0,4),(1,4),(2,4),(3,4)],5)
[1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,.]]]]]=>[[[[[[]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],.]]]]=>[[[[[],[]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,.]]]]=>[[[[],[[]]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],.]]]=>[[[[[]],[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>[[[[],[],[]]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[.,.]]]]=>[[[],[[[]]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],.]]]=>[[[],[[],[]]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[.,.]]]=>[[[[]],[[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>[[[[[]]],[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],.]]=>[[[[],[]],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[.,.]]]=>[[[],[],[[]]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>[[[],[[]],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],.]]=>[[[[]],[],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],.]]=>[[[],[],[],[]]]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,.]]]]=>[[],[[[[]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],.]]]=>[[],[[[],[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,.]]]=>[[],[[],[[]]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>[[],[[[]],[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],.]]=>[[],[[],[],[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[.,.]]]=>[[[]],[[[]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>[[[]],[[],[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,.]]=>[[[[]]],[[]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],.]=>[[[[[]]]],[]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],.]=>[[[[],[]]],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[.,.]]=>[[[],[]],[[]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],.]=>[[[],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],.]=>[[[[]],[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],.]=>[[[],[],[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[.,[.,.]]]=>[[],[],[[[]]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],.]]=>[[],[],[[],[]]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,.]],[.,.]]=>[[],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],.]=>[[],[[[]]],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],.]=>[[],[[],[]],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],.],[.,.]]=>[[[]],[],[[]]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],.]=>[[[]],[[]],[]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],.]=>[[[[]]],[],[]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],.]=>[[[],[]],[],[]]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],.],[.,.]]=>[[],[],[],[[]]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],.]=>[[],[],[[]],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],.]=>[[],[[]],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],.]=>[[[]],[],[],[]]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],.]=>[[],[],[],[],[]]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[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)
[1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[[[[[[],[]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[[[[],[[]]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[[[[[]],[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>[[[[[],[],[]]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[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)
[1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[[[],[[],[]]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[[[[[]],[[]]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[[[[[[]]],[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>[[[[[],[]],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[[[],[],[[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>[[[[],[[]],[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>[[[[[]],[],[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>[[[[],[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[[],[[[[]]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[[],[[[],[]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[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)
[1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>[[[],[[[]],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>[[[],[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[[[[]],[[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>[[[[]],[[],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[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)
[1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[[[[[[]]]],[]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>[[[[[],[]]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>[[[[],[]],[[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>[[[[],[[]]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>[[[[[]],[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>[[[[],[],[]],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[[],[],[[[]]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>[[[],[],[[],[]]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>[[[],[[]],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>[[[],[[[]]],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>[[[[]],[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>[[[[]],[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>[[[[[]]],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>[[[[],[]],[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],.],[.,.]]]=>[[[],[],[],[[]]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>[[[],[],[[]],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>[[[],[[]],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>[[[[]],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>[[[],[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[],[[[[[]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[],[[[[],[]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[],[[[],[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>[[],[[[[]],[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>[[],[[[],[],[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[],[[],[[[]]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>[[],[[],[[],[]]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>[[],[[[]],[[]]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>[[],[[[[]]],[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>[[],[[[],[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],.],[.,.]]]=>[[],[[],[],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>[[],[[],[[]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>[[],[[[]],[],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>[[],[[],[],[],[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[]],[[[[]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>[[[]],[[[],[]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>[[[]],[[],[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>[[[]],[[[]],[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>[[[]],[[],[],[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[[]]],[[[]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>[[[[]]],[[],[]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[[[[[]]]],[[]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[[[[[[]]]]],[]]=>([(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]=>[[.,[.,[.,[[.,.],.]]]],.]=>[[[[[],[]]]],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[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)
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>[[[[],[[]]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>[[[[[]],[]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],.]=>[[[[],[],[]]],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>[[[],[]],[[[]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>[[[],[]],[[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>[[[],[[]]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>[[[],[[[]]]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],.]=>[[[],[[],[]]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>[[[[]],[]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>[[[[]],[[]]],[]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>[[[[[]]],[]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],.]=>[[[[],[]],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,.]]=>[[[],[],[]],[[]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],.]=>[[[],[],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],.]=>[[[],[[]],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],.]],.]=>[[[[]],[],[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],.]=>[[[],[],[],[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[],[],[[[[]]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>[[],[],[[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[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)
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>[[],[],[[[]],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>[[],[],[[],[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[],[[]],[[[]]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>[[],[[]],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[],[[[]]],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>[[],[[[[]]]],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],.]=>[[],[[[],[]]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[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)
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],.]=>[[],[[],[[]]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],.]=>[[],[[[]],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],.]],.]=>[[],[[],[],[]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[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)
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>[[[]],[],[[],[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>[[[]],[[[]]],[]]=>([(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]=>[[[.,[.,.]],[[.,.],.]],.]=>[[[]],[[],[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[[[]]],[],[[]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>[[[[]]],[[]],[]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>[[[[[]]]],[],[]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],.]=>[[[[],[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,.]]=>[[[],[]],[],[[]]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],.]=>[[[],[]],[[]],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],.]=>[[[],[[]]],[],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],.],.]=>[[[[]],[]],[],[]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],.]=>[[[],[],[]],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,.]]]=>[[],[],[],[[[]]]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>[[],[],[],[[],[]]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[.,.]]=>[[],[],[[]],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],.]=>[[],[],[[[]]],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],.]=>[[],[],[[],[]],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[.,.]]=>[[],[[]],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],.]=>[[],[[]],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],.]=>[[],[[[]]],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],.]],.],.]=>[[],[[],[]],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,.]]=>[[[]],[],[],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],.]=>[[[]],[],[[]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],.]=>[[[]],[[]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],.],.]=>[[[[]]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],.]=>[[[],[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,.]]=>[[],[],[],[],[[]]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],.]=>[[],[],[],[[]],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],.]=>[[],[],[[]],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]=>[[],[[]],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],.]=>[[[]],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],.]=>[[],[],[],[],[],[]]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[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)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[[],[]]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[],[[]]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[[[]],[]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[[],[],[]]]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[[[],[[[]]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[[[[],[[],[]]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[[]],[[]]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[[[[]]],[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[[[[[],[]],[]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[],[],[[]]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[[[[],[[]],[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[[[]],[],[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[[[[],[],[],[]]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[[],[[[[]]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[[[],[[[],[]]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[[[],[[],[[]]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[[[],[[[]],[]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[[[],[[],[],[]]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[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)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[[[[]],[[],[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[[[[]]],[[]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[[[[[]]]],[]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[[[[[[],[]]],[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[[[[[],[]],[[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[[[[],[[]]],[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[[[[[]],[]],[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[[[[],[],[]],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[[[],[],[[[]]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[[[],[],[[],[]]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[],[[]],[[]]]]]=>([(0,7),(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]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[[[],[[[]]],[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[[[],[[],[]],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[[[[]],[],[[]]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[[[[]],[[]],[]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[[[[[]]],[],[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[[[[[],[]],[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[[[],[],[],[[]]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[[[],[],[[]],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[[],[[]],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[[[[]],[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[[[[],[],[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[],[[[[[]]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[],[[[[],[]]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[[[],[[]]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[],[[[[]],[]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[[],[[[],[],[]]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[[],[[],[[[]]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[[],[[],[]]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[[[]],[[]]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[[],[[[[]]],[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[[[],[[[],[]],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[[],[[],[],[[]]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[],[[],[[]],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[[[]],[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[[],[[],[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[]],[[[[]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[]],[[[],[]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[]],[[],[[]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[[]],[[[]],[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[[[]],[[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[[]]],[[[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[[[]]],[[],[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[[[[]]]],[[]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[[[[[]]]]],[]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[[[[[],[]]]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[[[[],[]]],[[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[[[[],[[]]]],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[[[[[]],[]]],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[[[[],[],[]]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[],[]],[[[]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[[[],[]],[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[[],[[]]],[[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[[[[],[[[]]]],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[[[[],[[],[]]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[[[]],[]],[[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[[[[[]],[[]]],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[[[[[[]]],[]],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[[[[[],[]],[]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[[[[],[],[]],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[[[[],[],[[]]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[[[[],[[]],[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[[[[[]],[],[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[[[[],[],[],[]],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[[],[],[[[[]]]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[[],[],[[[],[]]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[[],[],[[],[[]]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[[[],[],[[[]],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[[[],[],[[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[[[],[[]],[[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[[[],[[]],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[[[],[[[]]],[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[[[],[[[[]]]],[]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[[[],[[[],[]]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[[[],[[],[]],[[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[[[],[[],[[]]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[[[],[[[]],[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[[[],[[],[],[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[]],[],[[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[[[[]],[],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[[[]],[[]],[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[[[[]],[[[]]],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[[[[]],[[],[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[[[[]]],[],[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[[[[]]],[[]],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[[[[[]]]],[],[]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[[[[[],[]]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[[[[],[]],[],[[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[[[[],[]],[[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[[[],[[]]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[[[[]],[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[[[[],[],[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[[],[],[],[[[]]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[[[],[],[],[[],[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[[[],[],[[]],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[[],[],[[[]]],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[[[],[],[[],[]],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[[[],[[]],[],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[[],[[]],[[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[[],[[[]]],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[[[],[[],[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[[[[]],[],[],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[[[]],[],[[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[[[]],[[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[[[[]]],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[[[[],[]],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[[[],[],[],[],[[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[[[],[],[],[[]],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[[[],[],[[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[[[],[[]],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[[[[]],[],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[[[],[],[],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[[[[[[]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[],[[[[[],[]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[],[[[[],[[]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[],[[[[[]],[]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[],[[[[],[],[]]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[],[[[],[[[]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[],[[[],[[],[]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[],[[[[]],[[]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[],[[[[[]]],[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[],[[[[],[]],[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[],[[[],[],[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[],[[[],[[]],[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[],[[[[]],[],[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[[],[[[],[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[],[[],[[[[]]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[],[[],[[[],[]]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[],[[],[[],[[]]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[],[[],[[[]],[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[],[[],[[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[],[[[]],[[[]]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[],[[[]],[[],[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[],[[[[]]],[[]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[],[[[[[]]]],[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[],[[[[],[]]],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[],[[[],[]],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[],[[[],[[]]],[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[],[[[[]],[]],[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[[],[[[],[],[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[],[[],[],[[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[],[[],[],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[],[[],[[]],[[]]]]=>([(0,7),(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]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[],[[],[[[]]],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[[],[[],[[],[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[],[[[]],[],[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[],[[[]],[[]],[]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[],[[[[]]],[],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[[],[[[],[]],[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[],[[],[],[],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[[],[[],[],[[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[[],[[],[[]],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[[],[[[]],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[[],[[],[],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[]],[[[[[]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[]],[[[[],[]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[]],[[[],[[]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[]],[[[[]],[]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[]],[[[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[]],[[],[[[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[]],[[],[[],[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[]],[[[]],[[]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[]],[[[[]]],[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[]],[[[],[]],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[]],[[],[],[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[]],[[],[[]],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[]],[[[]],[],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[]],[[],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]]],[[[[]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]]],[[[],[]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]]],[[],[[]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]]],[[[]],[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[[]]],[[],[],[]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[[]]]],[[[]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[[[]]]],[[],[]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[[[]]]]],[[]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[[[[[[]]]]]],[]]=>([(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]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[[[[[],[]]]]],[]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[[[],[]]]],[[]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[[[[],[[]]]]],[]]=>([(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]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[[[[[]],[]]]],[]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[[[[],[],[]]]],[]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]]],[[[]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[[],[]]],[[],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[[],[[]]]],[[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[[[],[[[]]]]],[]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[[[],[[],[]]]],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[[[]],[]]],[[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[[[[]],[[]]]],[]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[[[[[]]],[]]],[]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[[[[],[]],[]]],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[[],[],[]]],[[]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[[[],[],[[]]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[[[],[[]],[]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[[[[]],[],[]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[[[[],[],[],[]]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[]],[[[[]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[]],[[[],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[]],[[],[[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[]],[[[]],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[]],[[],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]]],[[[]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]]],[[],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[[],[[[]]]],[[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[[],[[[[]]]]],[]]=>([(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]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[[],[[[],[]]]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[[],[[],[]]],[[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[[],[[],[[]]]],[]]=>([(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]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[[],[[[]],[]]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[[[],[[],[],[]]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[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)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[]],[[],[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[]]],[[]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[[[]],[[[]]]],[]]=>([(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]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[[[]],[[],[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[[[]]],[]],[[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[[[[]]],[[]]],[]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[[[[[]]]],[]],[]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[[[[],[]]],[]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[]],[[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[[[],[]],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[[[],[[]]],[]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[[[[]],[]],[]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[[[[],[],[]],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[],[]],[[[]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[],[]],[[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[[],[],[[]]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[[],[],[[[]]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[[[],[],[[],[]]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[[],[[]],[]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[[],[[]],[[]]],[]]=>([(0,7),(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]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[[],[[[]]],[]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[[[],[[],[]],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[],[]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[[[]],[],[[]]],[]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[[[]],[[]],[]],[]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[[[[]]],[],[]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[[[[],[]],[],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[[[],[],[],[]],[[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[[[],[],[],[[]]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[[[],[],[[]],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[[[],[[]],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[[[[]],[],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[[[],[],[],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[[[[[]]]]]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[],[],[[[[],[]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[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)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[],[],[[[[]],[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[],[],[[[],[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[],[],[[],[[[]]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[],[],[[],[[],[]]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[],[],[[[]],[[]]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[],[],[[[[]]],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[[],[],[[[],[]],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[],[],[[],[],[[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[[],[],[[],[[]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[[],[],[[[]],[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[],[],[[],[],[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[],[[]],[[[[]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[],[[]],[[[],[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[],[[]],[[],[[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[],[[]],[[[]],[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[],[[]],[[],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[],[[[]]],[[[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[],[[[]]],[[],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[],[[[[]]]],[[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[],[[[[[]]]]],[]]=>([(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]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[],[[[[],[]]]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[],[[[],[]]],[[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[],[[[],[[]]]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[],[[[[]],[]]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[[],[[[],[],[]]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[],[[],[]],[[[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[],[[],[]],[[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[],[[],[[]]],[[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[],[[],[[[]]]],[]]=>([(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]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[[],[[],[[],[]]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[],[[[]],[]],[[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[],[[[]],[[]]],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[],[[[[]]],[]],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[[],[[[],[]],[]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[[],[[],[],[]],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[[],[[],[],[[]]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[[],[[],[[]],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[[],[[[]],[],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[[],[[],[],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[]],[],[[[[]]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[]],[],[[[],[]]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[]],[],[[],[[]]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[]],[],[[[]],[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[]],[],[[],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[]],[[]],[[[]]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[]],[[]],[[],[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[]],[[[]]],[[]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[]],[[[[]]]],[]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[]],[[[],[]]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[]],[[],[]],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[]],[[],[[]]],[]]=>([(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]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[]],[[[]],[]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[]],[[],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[]]],[],[[[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[]]],[],[[],[]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[[]]],[[]],[[]]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[[]]],[[[]]],[]]=>([(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]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[[]]],[[],[]],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[[[]]]],[],[[]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[[[]]]],[[]],[]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[[[[]]]]],[],[]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[[[],[]]]],[],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[[],[]]],[],[[]]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[[],[]]],[[]],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[[],[[]]]],[],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[[[]],[]]],[],[]]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[[],[],[]]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[],[]],[],[[[]]]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[],[]],[],[[],[]]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[],[]],[[]],[[]]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[],[]],[[[]]],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[],[]],[[],[]],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[],[[]]],[],[[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[],[[]]],[[]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[],[[[]]]],[],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[],[[],[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[[]],[]],[],[[]]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[[]],[]],[[]],[]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[[]],[[]]],[],[]]=>([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[[[]]],[]],[],[]]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[[],[]],[]],[],[]]=>([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[],[],[]],[],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[],[],[]],[[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[],[],[[]]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[],[[]],[]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[[]],[],[]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[[[],[],[],[]],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[[[[]]]]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[],[],[],[[[],[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[],[],[],[[],[[]]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[[],[],[],[[[]],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[],[],[],[[],[],[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[],[],[[]],[[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[[],[],[[]],[[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[],[],[[[]]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[],[],[[[[]]]],[]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[[],[],[[[],[]]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[[],[],[[],[]],[[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[[],[],[[],[[]]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[[],[],[[[]],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[[],[],[[],[],[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[],[[]],[],[[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[[],[[]],[],[[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[],[[]],[[]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[],[[]],[[[]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[[],[[]],[[],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[],[[[]]],[],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[],[[[]]],[[]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[],[[[[]]]],[],[]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[[],[[[],[]]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[[],[[],[]],[],[[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[[],[[],[]],[[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[[],[[],[[]]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[[],[[[]],[]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[[],[[],[],[]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[]],[],[],[[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[]],[],[],[[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[]],[],[[]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[]],[],[[[]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[]],[],[[],[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[]],[[]],[],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[]],[[]],[[]],[]]=>([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[]],[[[]]],[],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[]],[[],[]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[]]],[],[],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[]]],[],[[]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[]]],[[]],[],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[[]]]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[],[]]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[],[]],[],[],[[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[],[]],[],[[]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[],[]],[[]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[],[[]]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[]],[]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[[[],[],[]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[[[]]]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[],[],[],[],[[],[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[],[],[],[[]],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[[],[],[],[[[]]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[[],[],[],[[],[]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[],[],[[]],[],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[[],[],[[]],[[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[[],[],[[[]]],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[[],[],[[],[]],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[],[[]],[],[],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[[],[[]],[],[[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[[],[[]],[[]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[[],[[[]]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[[],[[],[]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[]],[],[],[],[[]]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[]],[],[],[[]],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[]],[],[[]],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[]],[[]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[]]],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[[[],[]],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[[]]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[[],[],[],[],[[]],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[[],[],[],[[]],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[[],[],[[]],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[[],[[]],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[[[]],[],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[]]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[[],[]]]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[],[[]]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[[[]],[]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[[],[],[]]]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[],[[[]]]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[],[[],[]]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[[]],[[]]]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[[[[]]],[]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[[[[[[],[]],[]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[],[],[[]]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[[],[[]],[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[[[]],[],[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[[],[],[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[],[[[[]]]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[[[[],[[[],[]]]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[[[[],[[],[[]]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[[[[],[[[]],[]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[],[[],[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[[[[[]],[[[]]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[[[[[]],[[],[]]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[[[[[[]]],[[]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[[[[[]]]],[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[[[[[[],[]]],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[[],[]],[[]]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[[[[[],[[]]],[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[[[[[[]],[]],[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[[[],[],[]],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[[[[],[],[[[]]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[[[[],[],[[],[]]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[[[[],[[]],[[]]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[[],[[[]]],[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[[[[],[[],[]],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[[[[[]],[],[[]]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[[[[[]],[[]],[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[[[[[[]]],[],[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[[[[[],[]],[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[[[[],[],[],[[]]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[[[[],[],[[]],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[[[[],[[]],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[[[[[]],[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[[],[],[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[],[[[[[]]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[[[],[[[[],[]]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[[[],[[[],[[]]]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[[[],[[[[]],[]]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[[[],[[[],[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[[[],[[],[[[]]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[],[[],[[],[]]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[[[],[[[]],[[]]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[[[],[[[[]]],[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[[[[],[[[],[]],[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[[[],[[],[],[[]]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[[[],[[],[[]],[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[[[],[[[]],[],[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[[[],[[],[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[]],[[[[]]]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[[[[]],[[[],[]]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[[[[]],[[],[[]]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[[[[]],[[[]],[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[[[[]],[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[[[[[]]],[[[]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[[[[[]]],[[],[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[[[[[[]]]],[[]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[[[[[[]]]]],[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[[[[[[],[]]]],[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[[[[[],[]]],[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[[[[[],[[]]]],[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[[[[[[]],[]]],[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[[[[[],[],[]]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[[[[],[]],[[[]]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[[[[],[]],[[],[]]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[[[[],[[]]],[[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[[[[],[[[]]]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[[[],[[],[]]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[[[[[]],[]],[[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[[[[[]],[[]]],[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[[[[[[]]],[]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[[[[[],[]],[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[[[[],[],[]],[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[[[[],[],[[]]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[[[[],[[]],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[[[[[]],[],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[[[],[],[],[]],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[[[],[],[[[[]]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[[[],[],[[[],[]]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[[[],[],[[],[[]]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[[[],[],[[[]],[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[[[],[],[[],[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[[[],[[]],[[[]]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[[[],[[]],[[],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[[[[],[[[]]],[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[[[],[[[[]]]],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[[[],[[[],[]]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[[[[],[[],[]],[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[[[],[[],[[]]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[[[],[[[]],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[[[],[[],[],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[[[[]],[],[[[]]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[[[[]],[],[[],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[[[[]],[[]],[[]]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[[[[]],[[[]]],[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[[[[]],[[],[]],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[[[[[]]],[],[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[[[[[]]],[[]],[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[[[[[[]]]],[],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[[[[[],[]]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[[[[],[]],[],[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[[[[],[]],[[]],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[[[[],[[]]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[[[[[]],[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[[[[],[],[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[[[],[],[],[[[]]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[[[],[],[],[[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[[[],[],[[]],[[]]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[[[],[],[[[]]],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[[[],[],[[],[]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[[[],[[]],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[[[],[[]],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[[[],[[[]]],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[[[],[[],[]],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[[[[]],[],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[[[[]],[],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[[[[]],[[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[[[[[]]],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[[[[],[]],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[[[[],[],[],[],[[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[[[],[],[],[[]],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[[[],[],[[]],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[[[],[[]],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[[[[]],[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[[],[],[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[[[[[[]]]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[],[[[[[],[]]]]]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[],[[[[],[[]]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[],[[[[[]],[]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[[],[[[[],[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[[],[[[],[[[]]]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[],[[[],[[],[]]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[[],[[[[]],[[]]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[],[[[[[]]],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[[],[[[[],[]],[]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[[],[[[],[],[[]]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[[],[[[],[[]],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[[],[[[[]],[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[[],[[[],[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[],[[],[[[[]]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[],[[],[[[],[]]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[],[[],[[],[[]]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[],[[],[[[]],[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[],[[],[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[],[[[]],[[[]]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[],[[[]],[[],[]]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[[],[[[[]]],[[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[[],[[[[[]]]],[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[[],[[[[],[]]],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[],[[[],[]],[[]]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[],[[[],[[]]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[],[[[[]],[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[],[[[],[],[]],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[[],[[],[],[[[]]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[[],[[],[],[[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[],[[]],[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[],[[],[[[]]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[],[[],[[],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[],[[[]],[],[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[],[[[]],[[]],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[],[[[[]]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[],[[[],[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[[],[[],[],[],[[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[],[[],[],[[]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[],[[],[[]],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[],[[[]],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[],[[],[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[]],[[[[[]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[[]],[[[[],[]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[]],[[[],[[]]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[[]],[[[[]],[]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[[]],[[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[]],[[],[[[]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[[]],[[],[[],[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[]],[[[]],[[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[[]],[[[[]]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[[[]],[[[],[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[[]],[[],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[[]],[[],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[[]],[[[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[[]],[[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[[[[]]],[[[[]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[[[[[]]],[[[],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[[[[[]]],[[],[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[[[[]]],[[[]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[[[[]]],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[[[[[[]]]],[[[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[[[[[]]]],[[],[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[[[[[]]]]],[[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[[[[[[]]]]]],[]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[[[[[[],[]]]]],[]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[[[[[],[]]]],[[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[[[[[[],[[]]]]],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[[[[[[[]],[]]]],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[[[[[[],[],[]]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[[[[[],[]]],[[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[[[[],[]]],[[],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[[[[],[[]]]],[[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[[[[[],[[[]]]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[[[[[],[[],[]]]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[[[[[]],[]]],[[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[[[[[[]],[[]]]],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[[[[[[[]]],[]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[[[[[[],[]],[]]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[[[[],[],[]]],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[[[[[],[],[[]]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[[[[[],[[]],[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[[[[[[]],[],[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[[[[[],[],[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[[[],[]],[[[[]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[[[],[]],[[[],[]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[[[],[]],[[],[[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[[],[]],[[[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[[[],[]],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[[[],[[]]],[[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[[[],[[]]],[[],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[[[],[[[]]]],[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[[[[],[[[[]]]]],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[[[[],[[[],[]]]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[[[],[[],[]]],[[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[[[[],[[],[[]]]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[[[[],[[[]],[]]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[[[[],[[],[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[[[[]],[]],[[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[[[[]],[]],[[],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[[[[]],[[]]],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[[[[[]],[[[]]]],[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[[[[[]],[[],[]]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[[[[[]]],[]],[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[[[[[[]]],[[]]],[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[[[[[[[]]]],[]],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[[[[[[],[]]],[]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[[[[],[]],[]],[[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[[[[[],[]],[[]]],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[[[[[],[[]]],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[[[[[]],[]],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[[[[[],[],[]],[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[[[[],[],[]],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[[[],[],[]],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[[[],[],[[]]],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[[[[],[],[[[]]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[[[[],[],[[],[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[[[],[[]],[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[[[[],[[]],[[]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[[[[],[[[]]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[[[[],[[],[]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[[[[]],[],[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[[[[[]],[],[[]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[[[[[]],[[]],[]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[[[[[[]]],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[[[[[],[]],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[[[],[],[],[]],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[[[[],[],[],[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[[[[],[],[[]],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[[[[],[[]],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[[[[[]],[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[[[[],[],[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[],[],[[[[[]]]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[[],[],[[[[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[[],[],[[[],[[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[[],[],[[[[]],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[[],[],[[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[[],[],[[],[[[]]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[[],[],[[],[[],[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[[],[],[[[]],[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[[],[],[[[[]]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[[],[],[[[],[]],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[[],[],[[],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[[],[],[[],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[[],[],[[[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[[],[],[[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[[],[[]],[[[[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[[],[[]],[[[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]],[[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[[],[[]],[[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[[[],[[]],[[],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[[[],[[[]]],[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[[],[[[]]],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[[],[[[[]]]],[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[[],[[[[[]]]]],[]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[[[],[[[[],[]]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[[],[[[],[]]],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[[[],[[[],[[]]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[[[],[[[[]],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[[[],[[[],[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[[],[[],[]],[[[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[[],[[],[]],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[],[[],[[]]],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[[],[[],[[[]]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[[[],[[],[[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[],[[[]],[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[[[],[[[]],[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[[[],[[[[]]],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[[[],[[[],[]],[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[[],[[],[],[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[[[],[[],[],[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[[[],[[],[[]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[[[],[[[]],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[[[],[[],[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[[[[]],[],[[[[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[[[[]],[],[[[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[[[[]],[],[[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[[]],[],[[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[[]],[],[[],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[]],[[]],[[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[[]],[[]],[[],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[[[]],[[[]]],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[[[[]],[[[[]]]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[[[[]],[[[],[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[[[]],[[],[]],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[[[[]],[[],[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[[[]],[[[]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[[[[]],[[],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[[[[]]],[],[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[[[[]]],[],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[[[[]]],[[]],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[[[[[]]],[[[]]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[[[[[]]],[[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[[[[[]]]],[],[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[[[[[[]]]],[[]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[[[[[[[]]]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[[[[[[],[]]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[[[[],[]]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[[[[[],[]]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[[[[[],[[]]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[[[[[[]],[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[[[[[],[],[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[[[],[]],[],[[[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[[[],[]],[],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[[[[],[]],[[]],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[[[[],[]],[[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[[[[],[]],[[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[[],[[]]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[[[[],[[]]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[[[[],[[[]]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[[[[],[[],[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[[[[]],[]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[[[[]],[]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[[[[[]],[[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[[[[[[]]],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[[[[],[]],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[[[],[],[]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[[[[],[],[]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[[[[],[],[[]]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[[[],[[]],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[[[[]],[],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[[[],[],[],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[[[],[],[],[[[[]]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[[[],[],[],[[[],[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[[[],[],[],[[],[[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[[],[],[],[[[]],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[[],[],[],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[[],[],[[]],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[[],[],[[]],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[[],[],[[[]]],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[[[],[],[[[[]]]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[[[],[],[[[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[[],[],[[],[]],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[[[],[],[[],[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[[[],[],[[[]],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[[[],[],[[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[[],[[]],[],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[[],[[]],[],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[],[[]],[[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[[[],[[]],[[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[[[],[[]],[[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[[],[[[]]],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[[[],[[[]]],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[[],[[[[]]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[[],[[[],[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[[],[[],[]],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[[[],[[],[]],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[[],[[],[[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[[],[[[]],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[[],[[],[],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[[[]],[],[],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[[[]],[],[],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[[[]],[],[[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[[[[]],[],[[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[[[[]],[],[[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[[[]],[[]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[[]],[[]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[[[]],[[[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[[[]],[[],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[[[[]]],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[[[[[]]],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[[[[]]],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[[[[[]]]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[[[[],[]]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[[[],[]],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[[[[],[]],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[[[],[]],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[[[],[[]]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[[[[]],[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[[[],[],[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[[],[],[],[],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[[],[],[],[],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[[[],[],[],[[]],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[[[],[],[],[[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[[[],[],[],[[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[[[],[],[[]],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[[[],[],[[]],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[[],[],[[[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[[],[],[[],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[[],[[]],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[[[],[[]],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[[],[[]],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[[],[[[]]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[[],[[],[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[[[]],[],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[[[]],[],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[[[]],[],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[[[]],[[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[[[[]]],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[[[],[]],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[[[],[],[],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[[[],[],[],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[[],[],[],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[[[],[],[[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[[],[[]],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[[[]],[],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[[[[[[[]]]]]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[],[[[[[[],[]]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[[[[[],[[]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[],[[[[[[]],[]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[],[[[[[],[],[]]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[[[[],[[[]]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[[[[],[[],[]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[],[[[[[]],[[]]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[],[[[[[[]]],[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[],[[[[[],[]],[]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[[[[],[],[[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[],[[[[],[[]],[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[],[[[[[]],[],[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[],[[[[],[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[[[],[[[[]]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[[[],[[[],[]]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[[[],[[],[[]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[],[[[],[[[]],[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[],[[[],[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[],[[[[]],[[[]]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[],[[[[]],[[],[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[],[[[[[]]],[[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[],[[[[[[]]]],[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[],[[[[[],[]]],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[],[[[[],[]],[[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[],[[[[],[[]]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[],[[[[[]],[]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[],[[[[],[],[]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[[[],[],[[[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[],[[[],[],[[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[],[[[],[[]],[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[],[[[],[[[]]],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[],[[[],[[],[]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[],[[[[]],[],[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[],[[[[]],[[]],[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[],[[[[[]]],[],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[],[[[[],[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[],[[[],[],[],[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[],[[[],[],[[]],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[],[[[],[[]],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[],[[[[]],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[],[[[],[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[],[[[[[]]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[],[[[[],[]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[],[[[],[[]]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[],[[],[[[[]],[]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[],[[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[],[[],[[[]]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[],[[],[[],[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[],[[],[[[]],[[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[],[[],[[[[]]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[],[[],[[[],[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[],[[],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[],[[],[[],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[],[[],[[[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[],[[],[[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[],[[[]],[[[[]]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[],[[[]],[[[],[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[],[[[]],[[],[[]]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[],[[[]],[[[]],[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[[]],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[],[[[[]]],[[[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[[[]]],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[[[[]]]],[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[[[[[]]]]],[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[],[[[[[],[]]]],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[],[[[[],[]]],[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[[[],[[]]]],[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[[[[]],[]]],[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[[[],[],[]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[],[[[],[]],[[[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[[],[]],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[[],[[]]],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[[],[[[]]]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[[],[[],[]]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[[[]],[]],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[],[[[[]],[[]]],[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[],[[[[[]]],[]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[],[[[[],[]],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[[],[],[]],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[[],[],[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[],[[[],[[]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[],[[[[]],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[],[[[],[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[],[],[[[[]]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[],[],[[[],[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[],[],[[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[],[[],[],[[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[],[[],[],[[],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[],[[],[[]],[[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[],[[],[[]],[[],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[],[[],[[[]]],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[],[[],[[[[]]]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[],[[],[[[],[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[],[[],[[],[]],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[],[[],[[],[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[],[[],[[[]],[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[],[[],[[],[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[],[[[]],[],[[[]]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[],[[[]],[],[[],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[],[[[]],[[]],[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[],[[[]],[[[]]],[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[],[[[]],[[],[]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[],[[[[]]],[],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[],[[[[]]],[[]],[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[],[[[[[]]]],[],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[],[[[[],[]]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[],[]],[],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[],[[[],[]],[[]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[],[[[],[[]]],[],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[[]],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[],[[[],[],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[],[],[],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[],[[],[],[],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[],[[],[],[[]],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[],[],[[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[],[[],[],[[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[],[[],[[]],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[],[[],[[]],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[],[[[]]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[],[[],[[],[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[]],[],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[],[[[]],[],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[]],[[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[]]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[],[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[],[[],[],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[],[[],[],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[],[[],[],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[],[[],[[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[]],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[],[[],[],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[[[[[[]]]]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[[[[[],[]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[[[[],[[]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[[[[[]],[]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[]],[[[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[[[],[[[]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[]],[[[],[[],[]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[[[[]],[[]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[[[[[]]],[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[]],[[[[],[]],[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[]],[[[],[],[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[]],[[[],[[]],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[]],[[[[]],[],[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[]],[[[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[],[[[[]]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[],[[[],[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[],[[],[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[],[[[]],[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[]],[[],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[[]],[[[]]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[[]],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[[[]]],[[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[[[[]]]],[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[]],[[[[],[]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[[],[]],[[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[[],[[]]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[[[]],[]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[]],[[[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[],[],[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[]],[[],[],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[],[[]],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[],[[[]]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[]],[[],[[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[]],[],[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[]],[[]],[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[[]]],[],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[]],[[],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[]],[[],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[]],[[],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[]],[[],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[]]],[[[[[]]]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[]]],[[[[],[]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[]]],[[[],[[]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[[]]],[[[[]],[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[[]]],[[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[]]],[[],[[[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[[]]],[[],[[],[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[[]]],[[[]],[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[[]]],[[[[]]],[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[[]]],[[[],[]],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[[]]],[[],[],[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[[]]],[[],[[]],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[[]]],[[[]],[],[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[[]]],[[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[[]]]],[[[[]]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[[[]]]],[[[],[]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[[[]]]],[[],[[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[[[]]]],[[[]],[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[[[]]]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[[[[]]]]],[[[]]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[[[[]]]]],[[],[]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[[[[[]]]]]],[[]]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[[[[[[]]]]]]],[]]=>([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[[[[[[],[]]]]]],[]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[[[[],[]]]]],[[]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[[[[[],[[]]]]]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[[[[[[]],[]]]]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[[[[[],[],[]]]]],[]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[[[],[]]]],[[[]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[[[],[]]]],[[],[]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[[[],[[]]]]],[[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[[[[],[[[]]]]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[[[[],[[],[]]]]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[[[[]],[]]]],[[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[[[[[[]],[[]]]]],[]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[[[[[[]]],[]]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[[[[[[],[]],[]]]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[[[],[],[]]]],[[]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[[[[],[],[[]]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[[[[],[[]],[]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[[[[[[]],[],[]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[[[[],[],[],[]]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[[],[]]],[[[[]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[[],[]]],[[[],[]]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[[],[]]],[[],[[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[[],[]]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[[],[[]]]],[[[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[[],[[]]]],[[],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[[],[[[]]]]],[[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[[[[],[[[[]]]]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[[[[],[[[],[]]]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[[],[[],[]]]],[[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[[[[],[[],[[]]]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[[[[],[[[]],[]]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[[[[],[[],[],[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[[[]],[]]],[[[]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[[[]],[]]],[[],[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[[[]],[[]]]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[[[[[]],[[[]]]]],[]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[[[[[]],[[],[]]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[[[[]]],[]]],[[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[[[[[[]]],[[]]]],[]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[[[[[[]]]],[]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[[[[[],[]]],[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[[[],[]],[]]],[[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[[[[[],[]],[[]]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[[[[[],[[]]],[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[[[[[]],[]],[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[[[[],[],[]],[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[[],[],[]]],[[[]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[[],[],[]]],[[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[[],[],[[]]]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[[[],[],[[[]]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[[[[],[],[[],[]]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[[],[[]],[]]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[[[[],[[]],[[]]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[[[],[[[]]],[]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[[[[],[[],[]],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[[[]],[],[]]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[[[[[]],[],[[]]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[[[[]],[[]],[]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[[[[[]]],[],[]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[[[[],[]],[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[[],[],[],[]]],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[[[[],[],[],[[]]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[[[[],[],[[]],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[[[[],[[]],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[[[[[]],[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[[[],[],[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[[[[[]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[[[[],[]]]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[[[],[[]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[[[[]],[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[]],[[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[],[[[]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[],[[],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[[]],[[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[[[]]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[[],[]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[]],[[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]]],[[[[]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]]],[[[],[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]]],[[],[[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[[]]]],[[[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[[]]]],[[],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[[[]]]]],[[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[[[],[[[[[]]]]]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[[],[[[[],[]]]]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[[],[]]]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[[[],[[[],[[]]]]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[[[],[[[[]],[]]]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[[[],[[[],[],[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[],[]]],[[[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[],[]]],[[],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[],[[]]]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[[[],[[],[[[]]]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[[[],[[],[[],[]]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[[]],[]]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[[[],[[[]],[[]]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[[[],[[[[]]],[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[[[],[[[],[]],[]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[],[],[]]],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[[[],[[],[],[[]]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[[[],[[],[[]],[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[[],[[[]],[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[[],[[],[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[[]],[]],[[[[]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[[]],[]],[[[],[]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[[]],[]],[[],[[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[[]],[]],[[[]],[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[[]],[]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[[]],[[]]],[[[]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[[]],[[]]],[[],[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[[]],[[[]]]],[[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[[[]],[[[[]]]]],[]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[[[]],[[[],[]]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[[]],[[],[]]],[[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[[[[]],[[],[[]]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[[[]],[[[]],[]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[[[]],[[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[[[]]],[]],[[[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[[[]]],[]],[[],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[[[]]],[[]]],[[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[[[[]]],[[[]]]],[]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[[[]]],[[],[]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[[[[]]]],[]],[[]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[[[[[]]]],[[]]],[]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[[[[[[]]]]],[]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[[[[[[],[]]]],[]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[[[],[]]],[]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[[[],[]]],[[]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[[[[],[[]]]],[]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[[[[[]],[]]],[]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[[[[],[],[]]],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[[],[]],[]],[[[]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[[],[]],[]],[[],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[[],[]],[[]]],[[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[[[],[]],[[[]]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[[[[],[]],[[],[]]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[[],[[]]],[]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[[[],[[]]],[[]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[[[[],[[[]]]],[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[[[],[[],[]]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[[[]],[]],[]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[[[]],[]],[[]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[[[]],[[]]],[]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[[[[[]]],[]],[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[[[],[]],[]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[[],[],[]],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[[[],[],[]],[[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[[],[],[[]]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[[[],[[]],[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[[[]],[],[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[[[],[],[],[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[],[]],[[[[]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[],[]],[[[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[],[]],[[],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[],[]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[],[[]]],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[],[[]]],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[],[[[]]]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[[[],[],[[[[]]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[[[],[],[[[],[]]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[],[[],[]]],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[[[],[],[[],[[]]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[[[],[],[[[]],[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[[],[],[[],[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[]],[]],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[]],[]],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[]],[[]]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[]],[[[]]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[[[],[[]],[[],[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]]],[]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[[],[[[]]],[[]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[[],[[[[]]]],[]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[[],[[[],[]]],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[],[]],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[],[]],[[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[[],[[],[[]]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[[],[[[]],[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[[],[[],[],[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[[]],[],[]],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[[]],[],[]],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[[]],[],[[]]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[[[]],[],[[[]]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[[[]],[],[[],[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[]],[[]],[]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[[]],[[]],[[]]],[]]=>([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[[[]],[[[]]],[]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[[[]],[[],[]],[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[[[]]],[],[]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[[[[]]],[],[[]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[[[]]],[[]],[]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[[[[[]]]],[],[]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[[[],[]]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[[],[]],[],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[[],[]],[],[[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[[[],[]],[[]],[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[[[],[[]]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[[[]],[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[[[],[],[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[],[],[]],[[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[],[],[]],[[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[],[],[[]]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[],[],[[[]]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[[],[],[],[[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[],[[]],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[[],[],[[]],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[[[],[],[[[]]],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[[],[],[[],[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[]],[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[[],[[]],[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[[],[[]],[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[[],[[[]]],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[[],[[],[]],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[[]],[],[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[[[]],[],[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[[[]],[],[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[[[]],[[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[[[]]],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[[[[],[]],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[],[],[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[[[],[],[],[],[[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[[],[],[],[[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[[],[],[[]],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[[],[[]],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[[[]],[],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[[],[],[],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[[[[[[]]]]]]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[],[],[[[[[],[]]]]]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[],[],[[[[],[[]]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[],[],[[[[[]],[]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[],[],[[[[],[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[[],[[[]]]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[],[],[[[],[[],[]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[],[],[[[[]],[[]]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[],[],[[[[[]]],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[],[],[[[[],[]],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[],[],[[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[],[],[[[],[[]],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[],[],[[[[]],[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[],[],[[[],[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[],[],[[],[[[[]]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[],[],[[],[[[],[]]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[],[],[[],[[],[[]]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[],[],[[],[[[]],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[],[],[[],[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[],[],[[[]],[[[]]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[],[],[[[]],[[],[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[],[],[[[[]]],[[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[],[],[[[[[]]]],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[],[],[[[[],[]]],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[],[],[[[],[]],[[]]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[],[],[[[],[[]]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[],[],[[[[]],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[],[],[[[],[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[],[],[[],[],[[[]]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[],[],[[],[],[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[],[],[[],[[]],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[],[],[[],[[[]]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[],[],[[],[[],[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[],[],[[[]],[],[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[],[],[[[]],[[]],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[],[],[[[[]]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[],[],[[[],[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[],[],[[],[],[],[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[],[],[[],[],[[]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[],[],[[],[[]],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[],[],[[[]],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[],[],[[],[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[],[[]],[[[[[]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[],[[]],[[[[],[]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[[],[[]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[],[[]],[[[[]],[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[],[[]],[[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[],[[]],[[],[[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[],[[]],[[],[[],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[],[[]],[[[]],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[],[[]],[[[[]]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[],[[]],[[[],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[],[[]],[[],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[],[[]],[[],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[],[[]],[[[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[],[[]],[[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[],[[[]]],[[[[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[],[[[]]],[[[],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[],[[[]]],[[],[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[],[[[]]],[[[]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[],[[[]]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[],[[[[]]]],[[[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[],[[[[]]]],[[],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[],[[[[[]]]]],[[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[],[[[[[[]]]]]],[]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[[],[[[[[],[]]]]],[]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[],[[[[],[]]]],[[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[[],[[[[],[[]]]]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[[],[[[[[]],[]]]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[],[[[[],[],[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[],[[[],[]]],[[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[],[[[],[]]],[[],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[],[[[],[[]]]],[[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[[],[[[],[[[]]]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[[],[[[],[[],[]]]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[],[[[[]],[]]],[[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[[],[[[[]],[[]]]],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[[],[[[[[]]],[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[[],[[[[],[]],[]]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[],[[[],[],[]]],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[[],[[[],[],[[]]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[],[[[],[[]],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[],[[[[]],[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[],[[[],[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[],[[],[]],[[[[]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[],[[],[]],[[[],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[],[[],[]],[[],[[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[],[[],[]],[[[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[],[[],[]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[],[[],[[]]],[[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[],[[],[[]]],[[],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[],[[],[[[]]]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[],[[],[[[[]]]]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[[],[[],[[[],[]]]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[],[[],[[],[]]],[[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[],[[],[[],[[]]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[],[[],[[[]],[]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[],[[],[[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[],[[[]],[]],[[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[],[[[]],[]],[[],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[],[[[]],[[]]],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[],[[[]],[[[]]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[],[[[]],[[],[]]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[],[[[[]]],[]],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[],[[[[]]],[[]]],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[],[[[[[]]]],[]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[],[[[[],[]]],[]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[],[[[],[]],[]],[[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[],[[[],[]],[[]]],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[],[[[],[[]]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[],[[[[]],[]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[],[[[],[],[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[],[[],[],[]],[[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[],[[],[],[]],[[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[],[[],[],[[]]],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[],[[],[],[[[]]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[],[[],[],[[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[],[[],[[]],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[],[[],[[]],[[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[],[[],[[[]]],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[],[[],[[],[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[],[[[]],[],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[],[[[]],[],[[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[],[[[]],[[]],[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[],[[[[]]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[],[[[],[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[],[[],[],[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[],[[],[],[],[[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[],[[],[],[[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[],[[],[[]],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[],[[[]],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[],[[],[],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[[[[[]]]]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[]],[],[[[[],[]]]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[[],[[]]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[]],[],[[[[]],[]]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[]],[],[[],[[[]]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[]],[],[[],[[],[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[]],[],[[[]],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[]],[],[[[[]]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[]],[],[[[],[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[]],[],[[],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[]],[],[[],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[]],[],[[[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[]],[],[[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[]],[[]],[[[[]]]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[]],[[]],[[[],[]]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[]],[[]],[[],[[]]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[]],[[]],[[[]],[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[]],[[]],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[]],[[[]]],[[[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[]],[[[]]],[[],[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[]],[[[[]]]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[]],[[[[[]]]]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[]],[[[[],[]]]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[]],[[[],[]]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[]],[[[],[[]]]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[]],[[[[]],[]]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[]],[[[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[]],[[],[]],[[[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[]],[[],[]],[[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[]],[[],[[]]],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[]],[[],[[[]]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[]],[[],[[],[]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[]],[[[]],[]],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[]],[[[]],[[]]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[]],[[[[]]],[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[]],[[[],[]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[]],[[],[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[]],[[],[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[]],[[],[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[]],[[[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[]],[[],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[]]],[],[[[[]]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[]]],[],[[[],[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[]]],[],[[],[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[]]],[],[[[]],[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[]]],[],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[]]],[[]],[[[]]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[]]],[[]],[[],[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[]]],[[[]]],[[]]]=>([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[[]]],[[[[]]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[]]],[[[],[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[]]],[[],[]],[[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[]]],[[],[[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[[]]],[[[]],[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[]]],[[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[[]]]],[],[[[]]]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[[]]]],[],[[],[]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[[]]]],[[]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[[[]]]],[[[]]],[]]=>([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[[]]]],[[],[]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[[[[]]]]],[],[[]]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[[[[]]]]],[[]],[]]=>([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[[[[[]]]]]],[],[]]=>([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[[[[[],[]]]]],[],[]]=>([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[[],[]]]],[],[[]]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[[],[]]]],[[]],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[[[[],[[]]]]],[],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[[[[[]],[]]]],[],[]]=>([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[[[],[],[]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[]]],[],[[[]]]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[]]],[],[[],[]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[]]],[[]],[[]]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[[[],[]]],[[[]]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[[],[]]],[[],[]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[[],[[]]]],[],[[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[[[],[[]]]],[[]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[[],[[[]]]]],[],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[[],[[],[]]]],[],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[[]],[]]],[],[[]]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[[]],[]]],[[]],[]]=>([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[[]],[[]]]],[],[]]=>([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[[[[]]],[]]],[],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[[],[]],[]]],[],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[[],[],[]]],[],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[[],[],[]]],[[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[[],[],[[]]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[[],[[]],[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[[]],[],[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[[],[],[],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[],[]],[],[[[[]]]]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[],[]],[],[[[],[]]]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[],[]],[],[[],[[]]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[],[]],[],[[[]],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[],[]],[],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[],[]],[[]],[[[]]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[],[]],[[]],[[],[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[],[]],[[[]]],[[]]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[[],[]],[[[[]]]],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[],[]],[[[],[]]],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[],[]],[[],[]],[[]]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[],[]],[[],[[]]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[],[]],[[[]],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[],[]],[[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[],[[]]],[],[[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[],[[]]],[],[[],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[],[[]]],[[]],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[],[[]]],[[[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[],[[]]],[[],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[],[[[]]]],[],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[],[[[]]]],[[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[[],[[[[]]]]],[],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[[],[[[],[]]]],[],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[],[[],[]]],[],[[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[],[[],[]]],[[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[[],[[],[[]]]],[],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[],[[[]],[]]],[],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[],[[],[],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[]],[]],[],[[[]]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[]],[]],[],[[],[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[]],[]],[[]],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[]],[]],[[[]]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[[]],[]],[[],[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[]],[[]]],[],[[]]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[[]],[[]]],[[]],[]]=>([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[[]],[[[]]]],[],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[[]],[[],[]]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[[]]],[]],[],[[]]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[[]]],[]],[[]],[]]=>([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[[]]],[[]]],[],[]]=>([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[[[[]]]],[]],[],[]]=>([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[[],[]]],[]],[],[]]=>([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[]],[]],[],[[]]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[[],[]],[]],[[]],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[[],[]],[[]]],[],[]]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[[],[[]]],[]],[],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[[]],[]],[]],[],[]]=>([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[[],[],[]],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[],[],[]],[],[[[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[],[],[]],[],[[],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[],[],[]],[[]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[],[],[]],[[[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[],[],[]],[[],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[],[],[[]]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[],[],[[]]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[],[],[[[]]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[],[],[[],[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[[],[[]],[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[],[[]],[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[],[[]],[[]]],[],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[],[[[]]],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[],[[],[]],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[[]],[],[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[[]],[],[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[[]],[],[[]]],[],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[[]],[[]],[]],[],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[[]]],[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[[],[]],[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[[],[],[],[]],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[],[],[],[]],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[],[],[],[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[],[],[[]],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[],[[]],[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[[]],[],[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[],[],[],[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[[[[[]]]]]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[],[],[],[[[[],[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[],[],[],[[[],[[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[],[],[],[[[[]],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[],[],[],[[[],[],[]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[],[],[],[[],[[[]]]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[],[],[],[[],[[],[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[],[],[],[[[]],[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[],[],[],[[[[]]],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[],[],[],[[[],[]],[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[],[],[],[[],[],[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[],[],[],[[],[[]],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[],[],[],[[[]],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[],[],[],[[],[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[],[],[[]],[[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[],[],[[]],[[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[],[],[[]],[[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[[],[],[[]],[[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[],[],[[]],[[],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[],[],[[[]]],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[],[],[[[]]],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[],[],[[[[]]]],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[],[],[[[[[]]]]],[]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[],[],[[[[],[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[],[],[[[],[]]],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[],[],[[[],[[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[],[],[[[[]],[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[],[],[[[],[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[],[],[[],[]],[[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[],[],[[],[]],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[],[],[[],[[]]],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[],[],[[],[[[]]]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[],[],[[],[[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[],[],[[[]],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[],[],[[[]],[[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[],[],[[[[]]],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[],[],[[[],[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[],[],[[],[],[]],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[],[],[[],[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[],[],[[],[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[],[],[[[]],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[],[],[[],[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[],[[]],[],[[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[],[[]],[],[[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[],[[]],[],[[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[],[[]],[],[[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[],[[]],[],[[],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[],[[]],[[]],[[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[],[[]],[[]],[[],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[],[[]],[[[]]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[],[[]],[[[[]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[],[[]],[[[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[],[[]],[[],[]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[],[[]],[[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[],[[]],[[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[],[[]],[[],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[],[[[]]],[],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[],[[[]]],[],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[],[[[]]],[[]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[],[[[]]],[[[]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[],[[[]]],[[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[],[[[[]]]],[],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[],[[[[]]]],[[]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[],[[[[[]]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[],[[[[],[]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[],[[[],[]]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[],[[[],[]]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[],[[[],[[]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[],[[[[]],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[],[[[],[],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[],[[],[]],[],[[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[],[[],[]],[],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[],[[],[]],[[]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[],[[],[]],[[[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[],[[],[]],[[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[[],[[],[[]]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[],[[],[[]]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[],[[],[[[]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[],[[],[[],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[],[[[]],[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[],[[[]],[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[],[[[]],[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[],[[[[]]],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[],[[[],[]],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[[],[[],[],[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[],[[],[],[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[],[[],[],[[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[],[[],[[]],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[],[[[]],[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[],[[],[],[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[]],[],[],[[[[]]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[]],[],[],[[[],[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[]],[],[],[[],[[]]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[]],[],[],[[[]],[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[]],[],[],[[],[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[]],[],[[]],[[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[]],[],[[]],[[],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[]],[],[[[]]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[]],[],[[[[]]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[]],[],[[[],[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[]],[],[[],[]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[]],[],[[],[[]]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[]],[],[[[]],[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[]],[],[[],[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[]],[[]],[],[[[]]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[]],[[]],[],[[],[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]],[[]]]=>([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[]],[[]],[[[]]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[]],[[]],[[],[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[]],[[[]]],[],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[]],[[[]]],[[]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[]],[[[[]]]],[],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[]],[[[],[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[]],[[],[]],[],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[]],[[],[]],[[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[]],[[],[[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[]],[[[]],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[]],[[],[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[]]],[],[],[[[]]]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[]]],[],[],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[]]],[],[[]],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[]]],[],[[[]]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[]]],[],[[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[]]],[[]],[],[[]]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[]]],[[]],[[]],[]]=>([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[]]],[[[]]],[],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[]]],[[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[]]]],[],[],[[]]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[[]]]],[],[[]],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[]]]],[[]],[],[]]=>([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[[[]]]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[]]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[[[[],[]]],[],[],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[[],[]]],[],[[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[],[]]],[[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[],[[]]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[]],[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[],[],[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[],[]],[],[],[[[]]]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[],[]],[],[],[[],[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[],[]],[],[[]],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[],[]],[],[[[]]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[],[]],[],[[],[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[],[]],[[]],[],[[]]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[],[]],[[]],[[]],[]]=>([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[],[]],[[[]]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[],[]],[[],[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[],[[]]],[],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[],[[]]],[],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[],[[]]],[[]],[],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[],[[[]]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[],[[],[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[[]],[]],[],[],[[]]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[]],[]],[],[[]],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[]],[]],[[]],[],[]]=>([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[]],[[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[]]],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[],[]],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[],[],[]],[],[],[[]]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[],[],[]],[],[[]],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[],[],[]],[[]],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[],[],[[]]],[],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[],[[]],[]],[],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[]],[],[]],[],[],[]]=>([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[],[],[],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[],[[[[]]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[],[],[],[],[[[],[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[],[],[],[],[[],[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[],[],[],[],[[[]],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[],[],[],[],[[],[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[],[],[],[[]],[[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[],[],[],[[]],[[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[],[],[],[[[]]],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[],[],[],[[[[]]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[],[],[],[[[],[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[],[],[],[[],[]],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[],[],[],[[],[[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[],[],[],[[[]],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[],[],[],[[],[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[],[],[[]],[],[[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[],[],[[]],[],[[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[],[],[[]],[[]],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[],[],[[]],[[[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[],[],[[]],[[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[],[],[[[]]],[],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[],[],[[[]]],[[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[],[],[[[[]]]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[],[],[[[],[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[],[],[[],[]],[],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[],[],[[],[]],[[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[],[],[[],[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[],[],[[[]],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[],[],[[],[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[],[[]],[],[],[[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[],[[]],[],[],[[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[],[[]],[],[[]],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[],[[]],[],[[[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[],[[]],[],[[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[],[[]],[[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[],[[]],[[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[],[[]],[[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[],[[]],[[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[],[[[]]],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[],[[[]]],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[],[[[]]],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[],[[[[]]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[],[[[],[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[],[[],[]],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[],[[],[]],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[],[[],[]],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[],[[],[[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[],[[[]],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[],[[],[],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[]],[],[],[],[[[]]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[]],[],[],[],[[],[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[]],[],[],[[]],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[]],[],[],[[[]]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[]],[],[],[[],[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[]],[],[[]],[],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[]],[],[[]],[[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[]],[],[[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[]],[],[[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[]],[[]],[],[],[[]]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[]],[[]],[],[[]],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[]],[[]],[[]],[],[]]=>([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[]],[[[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[]],[[],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[[[]]],[],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[]]],[],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[]]],[],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[]]],[[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[]]]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[],[]]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[],[]],[],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[],[]],[],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[],[]],[],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[],[]],[[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[],[[]]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[]],[]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[],[],[]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[],[[[]]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[[],[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[],[],[],[],[[]],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[],[],[],[],[[[]]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[],[],[],[],[[],[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[],[],[],[[]],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[],[],[],[[]],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[],[],[],[[[]]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[],[],[],[[],[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[],[],[[]],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[],[],[[]],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[],[],[[]],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[],[],[[[]]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[],[[]],[],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[],[[]],[],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[],[[]],[],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[]],[],[],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[]],[],[],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[]],[],[],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[[]]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[[]],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[[]],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
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 ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
searching the database
Sorry, this map was not found in the database.