Identifier
-
Mp00026:
Dyck paths
—to ordered tree⟶
Ordered trees
St000974: Ordered trees ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0021;cc-rep
[1,0]=>[[]]=>1
[1,0,1,0]=>[[],[]]=>0
[1,1,0,0]=>[[[]]]=>2
[1,0,1,0,1,0]=>[[],[],[]]=>0
[1,0,1,1,0,0]=>[[],[[]]]=>0
[1,1,0,0,1,0]=>[[[]],[]]=>0
[1,1,0,1,0,0]=>[[[],[]]]=>1
[1,1,1,0,0,0]=>[[[[]]]]=>3
[1,0,1,0,1,0,1,0]=>[[],[],[],[]]=>0
[1,0,1,0,1,1,0,0]=>[[],[],[[]]]=>0
[1,0,1,1,0,0,1,0]=>[[],[[]],[]]=>0
[1,0,1,1,0,1,0,0]=>[[],[[],[]]]=>0
[1,0,1,1,1,0,0,0]=>[[],[[[]]]]=>0
[1,1,0,0,1,0,1,0]=>[[[]],[],[]]=>0
[1,1,0,0,1,1,0,0]=>[[[]],[[]]]=>0
[1,1,0,1,0,0,1,0]=>[[[],[]],[]]=>0
[1,1,0,1,0,1,0,0]=>[[[],[],[]]]=>1
[1,1,0,1,1,0,0,0]=>[[[],[[]]]]=>1
[1,1,1,0,0,0,1,0]=>[[[[]]],[]]=>0
[1,1,1,0,0,1,0,0]=>[[[[]],[]]]=>1
[1,1,1,0,1,0,0,0]=>[[[[],[]]]]=>2
[1,1,1,1,0,0,0,0]=>[[[[[]]]]]=>4
[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]=>0
[1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[[]]]=>0
[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]=>0
[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]=>0
[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]=>0
[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]=>0
[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]=>0
[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]=>0
[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]=>0
[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]=>0
[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]=>0
[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]=>0
[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]=>0
[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]=>0
[1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[],[]]=>0
[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]=>0
[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]=>0
[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]=>0
[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]=>0
[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]=>0
[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]=>0
[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]=>0
[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]=>1
[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]=>1
[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]=>0
[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]=>1
[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]=>1
[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]=>1
[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]=>0
[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]=>0
[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]=>0
[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]=>1
[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]=>1
[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]=>0
[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]=>1
[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]=>2
[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]=>2
[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]=>0
[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]=>1
[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]=>2
[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]=>3
[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[[]]]=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[[],[]]]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[[[]]]]=>0
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]]]=>0
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[[],[],[]]]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[[],[[]]]]=>0
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]=>0
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[[[]],[]]]=>0
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[[[],[]]]]=>0
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[[[[]]]]]=>0
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[],[[]]]=>0
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[],[]]]=>0
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[[]]]]=>0
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[],[]],[[]]]=>0
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[]]]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[[]]]]=>0
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]=>0
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[]]]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[],[[],[]]]]=>0
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[],[[[]]]]]=>0
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>0
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[[]]],[[]]]=>0
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[],[]]]=>0
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]]]]=>0
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]=>0
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]],[]]]=>0
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[[],[],[]]]]=>0
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[[],[[]]]]]=>0
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[[[]]],[]]]=>0
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[[[]],[]]]]=>0
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[[[],[]]]]]=>0
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[[[[]]]]]]=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[]]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[[]]]=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[],[[]],[]]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[],[[],[]]]=>0
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[],[[[]]]]=>0
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[],[]]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]]]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[],[]],[]]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[],[],[]]]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[],[[]]]]=>0
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[]]],[]]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]]]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[[],[]]]]=>0
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]]]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[]],[],[],[]]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[]],[],[[]]]=>0
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[]]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[]]]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[[]]]]=>0
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[]],[],[]]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[]],[[]]]=>0
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[]]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[]]]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[[]]]]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[[]]],[]]=>0
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[]]]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[[],[]]]]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[[[]]]]]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]]],[],[]]=>0
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]]],[[]]]=>0
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[]],[]]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[],[]]]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]]]]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[]]=>0
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]],[]]]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[[],[],[]]]]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[],[[]]]]]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[[[]]]],[]]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[]]],[]]]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[[[]],[]]]]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[[[],[]]]]]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[[[[]]]]]]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]]],[],[],[]]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]]],[],[[]]]=>0
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[]]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]]],[[],[]]]=>0
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[]]]]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[]],[],[]]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]]]=>0
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[]],[]]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[]]]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[]]]]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]]],[]]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[]]]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[],[]]]]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[[]]]]]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[],[]]],[],[]]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[],[]],[]],[]]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]],[],[]]]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]]]]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[]]],[]]=>0
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[]],[]]]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[]]]]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[]]]]]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[[]]]],[]]=>0
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[[],[[]]],[]]]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[]]]]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[[],[]]]]]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[[],[[[]]]]]]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[],[]]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[]]]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[]]],[]],[]]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]]],[],[]]]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[]]]]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[]]],[]]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]]]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[],[]]]]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]]]]]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[],[]]]],[]]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]]],[]]]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[]],[]]]]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[]]]]]=>3
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]]]]]]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[]]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]]],[]]]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]]],[]]]]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[]]]]]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[],[]]]]]]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]]]]]]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[[]]]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[[],[]]]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[[[]]]]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[[]],[[]]]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[]]]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[[],[[]]]]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[[[]],[]]]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[[[],[]]]]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[[[[]]]]]=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[[]],[],[[]]]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[[]],[[],[]]]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[[]],[[[]]]]=>0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[]],[[]]]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[]]]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[[]]]]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[[]],[]]]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[[],[]]]]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[[[]]]]]=>0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[[[]]],[[]]]=>0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[[[]],[],[]]]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[[[]],[[]]]]=>0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[[[],[]],[]]]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[]]]]=>0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[[[],[[]]]]]=>0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[[[[]]],[]]]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[[[]],[]]]]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[[[[],[]]]]]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[[[[[]]]]]]=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[[]]]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[[],[]]]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[[[]]]]=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]],[[]]]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[]],[[],[]],[]]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[]]]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[]],[[],[[]]]]=>0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]=>0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[]],[[[]],[]]]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[],[[]],[[[],[]]]]=>0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[],[[]],[[[[]]]]]=>0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[]],[],[[]]]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[]],[[],[]]]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[]],[[[]]]]=>0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[]],[[]]]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[]]]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[[]]]]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[[]],[]]]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[[],[]]]]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[[[]]]]]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[[]]],[[]]]=>0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[[]],[],[]]]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[[]],[[]]]]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]=>0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[[],[]],[]]]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[]]]]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[]]]]]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]=>0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[[[]]],[]]]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[[[]],[]]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[]]]]]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[[[[]]]]]]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[[]]],[],[[]]]=>0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[[]]],[[],[]]]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[[]]],[[[]]]]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[[]],[]],[[]]]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[]]]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[[]]]]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[[]],[[]],[]]]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[[]],[[],[]]]]=>0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[[]],[[[]]]]]=>0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[]]],[[]]]=>0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[]],[],[]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[]],[[]]]]=>0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[]],[]]]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[]]]]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[[]]]]]=>0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]=>0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[[]]],[]]]=>0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[[]],[]]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]]]]=>0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[[[]]]]]]=>0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[[[]]]],[[]]]=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]=>0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[[[]]],[],[]]]=>0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[[[]]],[[]]]]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]=>0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[[[]],[]],[]]]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[[[]],[],[]]]]=>0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[[[]],[[]]]]]=>0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]=>0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[]],[]]]]=>0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[]]]]]=>0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[[]]]]]]=>0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[[[[]]]],[]]]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[[[[]]],[]]]]=>0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[[[[]],[]]]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[[[[],[]]]]]]=>0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[[[[[]]]]]]]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[]]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[[]]]=>0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[[]],[]]=>0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[[],[]]]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[[[]]]]=>0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[[]],[],[]]=>0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[[]],[[]]]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[[],[]],[]]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[]]]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[[],[[]]]]=>0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[[[]]],[]]=>0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[[[]],[]]]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[[[],[]]]]=>0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[[[]]]]]=>0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[]]=>0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[[]],[],[[]]]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[[]],[]]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[[]],[[],[]]]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[[]],[[[]]]]=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[]],[],[]]=>0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[]],[[]]]=>0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[]],[]]=>0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[]]]=>0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[[]]]]=>0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[[]]],[]]=>0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[[]],[]]]=>0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[[],[]]]]=>0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[[[]]]]]=>0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[[[]]],[],[]]=>0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[[[]]],[[]]]=>0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[[[]],[]],[]]=>0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[[[]],[],[]]]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[[[]],[[]]]]=>0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[[[],[]]],[]]=>0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[[[],[]],[]]]=>0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[]]]]=>0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[[[],[[]]]]]=>0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[[[[]]]],[]]=>0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[[[[]]],[]]]=>0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[[[[]],[]]]]=>0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[[[[],[]]]]]=>0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[[[[[]]]]]]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[]]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[[]]]=>0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[[]],[]]=>0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[[],[]]]=>0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[[[]]]]=>0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[]],[[]],[],[]]=>0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[]],[[]],[[]]]=>0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[]],[[],[]],[]]=>0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[]],[[],[],[]]]=>0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[],[]],[[],[[]]]]=>0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[[]]],[]]=>0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[]],[[[]],[]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[]],[[[],[]]]]=>0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[]],[[[[]]]]]=>0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[]]=>0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[]],[],[[]]]=>0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[]],[[]],[]]=>0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[]],[[],[]]]=>0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[],[]],[[[]]]]=>0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[]],[],[]]=>0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[]],[[]]]=>0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[]]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[]]]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[[]]]]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[[]]],[]]=>0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[[]],[]]]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[[],[]]]]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[[[]]]]]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[]]],[],[]]=>0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[[]]],[[]]]=>0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[[]],[]],[]]=>0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[[]],[],[]]]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[[]],[[]]]]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[[],[]]],[]]=>0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[[],[]],[]]]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[]]]]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[[],[[]]]]]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[[[]]]],[]]=>0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[[[]]],[]]]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[[[]],[]]]]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[[[],[]]]]]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[[[[]]]]]]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[]]=>0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[[]]],[],[[]]]=>0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[[]]],[[]],[]]=>0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[[]]],[[],[]]]=>0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[[]]],[[[]]]]=>0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[[]],[]],[],[]]=>0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[[]],[]],[[]]]=>0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[]],[]]=>0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[]]]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[[]]]]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[[]],[[]]],[]]=>0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[[]],[[]],[]]]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[[]],[[],[]]]]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[[]],[[[]]]]]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[]]],[],[]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[]]],[[]]]=>0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[]],[]],[]]=>0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[]],[],[]]]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[]],[[]]]]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[]]],[]]=>0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[]],[]]]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[]]]]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[[]]]]]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[[]]]],[]]=>0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[[]]],[]]]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[[]],[]]]]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[[],[]]]]]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[],[[],[[[]]]]]]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[[[]]]],[],[]]=>0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[[]]]],[[]]]=>0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[[[]]],[]],[]]=>0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[[[]]],[],[]]]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[[[]]],[[]]]]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[[[]],[]]],[]]=>0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[[[]],[]],[]]]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[[[]],[],[]]]]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[[[]],[[]]]]]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[]]]],[]]=>0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[]]],[]]]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[]],[]]]]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[]]]]]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[[]]]]]]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[[[[]]]]],[]]=>0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[[]]]],[]]]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[[[[]]],[]]]]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[],[[[[]],[]]]]]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[],[[[[],[]]]]]]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[[[[[]]]]]]]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[]]=>0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[[]]]=>0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[[]],[]]=>0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[[],[]]]=>0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[[[]]]]=>0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[]]],[[]],[],[]]=>0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[]]],[[]],[[]]]=>0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[]]],[[],[]],[]]=>0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[]]]=>0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[[]]],[[],[[]]]]=>0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[]]],[[[]]],[]]=>0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[]]],[[[]],[]]]=>0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[]]],[[[],[]]]]=>0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[]]],[[[[]]]]]=>0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[]]=>0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[]],[],[[]]]=>0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[]],[[]],[]]=>0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[]],[[],[]]]=>0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[]],[[[]]]]=>0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[]],[],[]]=>0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[]],[[]]]=>0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[]],[]]=>0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[]]]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[[]]]]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[[]]],[]]=>0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[[]],[]]]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[[],[]]]]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[[[]]]]]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[[]]],[],[]]=>0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[[]]],[[]]]=>0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[[]],[]],[]]=>0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[[]],[],[]]]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]],[[]]]]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[[],[]]],[]]=>0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[[],[]],[]]]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[]]]]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[[],[[]]]]]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[[[]]]],[]]=>0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[[[]]],[]]]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[[[]],[]]]]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[[]],[[[],[]]]]]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[]],[[[[]]]]]]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[]]=>0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[]]],[],[[]]]=>0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[]]],[[]],[]]=>0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]]],[[],[]]]=>0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[],[]]],[[[]]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[]],[]],[],[]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[]],[]],[[]]]=>0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[]],[]]=>0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[]]]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[[]]]]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[]],[[]]],[]]=>0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[]],[[]],[]]]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]]]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[]],[[[]]]]]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[]]],[],[]]=>0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[]]],[[]]]=>0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[]],[]],[]]=>0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[]],[],[]]]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[]],[[]]]]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[]]],[]]=>0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[]],[]]]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[]]]]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[[]]]]]=>2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[[]]]],[]]=>0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[[]]],[]]]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[[]],[]]]]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[[],[]]]]]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[[[]]]]]]=>2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[]]]],[],[]]=>0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[[]]]],[[]]]=>0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[[]]],[]],[]]=>0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[[]]],[],[]]]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[]]],[[]]]]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[[]],[]]],[]]=>0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[[]],[]],[]]]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[[]],[],[]]]]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[[]],[[]]]]]=>2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[]]]],[]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[]]]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[]],[]]]]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[]]]]]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[[]]]]]]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[[[]]]]],[]]=>0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[[]]]],[]]]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[[[]]],[]]]]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[[[]],[]]]]]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[[[],[]]]]]]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[[[[]]]]]]]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[]]=>0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[]]]],[],[[]]]=>0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[]]]],[[]],[]]=>0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[]]]],[[],[]]]=>0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[]]]],[[[]]]]=>0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[]]],[]],[],[]]=>0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[]]],[]],[[]]]=>0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[]],[]]=>0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[]]]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[[]]]]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[]]],[[]]],[]]=>0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[]]],[[]],[]]]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[]]],[[],[]]]]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[]]],[[[]]]]]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[]],[]]],[],[]]=>0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[]],[]]],[[]]]=>0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[]],[]],[]],[]]=>0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[]],[],[]]]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[]],[]],[[]]]]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[]]],[]]=>0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[]],[]]]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[]]]]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[[]]]]]=>2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[]],[[]]]],[]]=>0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[]],[[]]],[]]]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[]],[[]],[]]]]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[]],[[],[]]]]]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[]],[[[]]]]]]=>2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[]]]],[],[]]=>0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[]]]],[[]]]=>0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[]]],[]],[]]=>0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]]],[],[]]]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[]]],[[]]]]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[]],[]]],[]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]]]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[]],[],[]]]]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]],[[]]]]]=>2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[]]]],[]]=>0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[]]],[]]]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[]],[]]]]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[]]]]]=>3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[[]]]]]]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[[]]]]],[]]=>0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[]]]],[]]]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[[]]],[]]]]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[[]],[]]]]]=>3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[[],[]]]]]]=>3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[[[]]]]]]]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[[]]]]],[],[]]=>0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[[]]]]],[[]]]=>0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[[]]]],[]],[]]=>0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[[]]]],[],[]]]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[[]]]],[[]]]]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]]],[]]],[]]=>0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[]]],[]],[]]]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[[]]],[],[]]]]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[]]],[[]]]]]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]],[]]]],[]]=>0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[]]],[]]]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[]],[]],[]]]]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[]]]]]=>3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[]],[[]]]]]]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[]]]]],[]]=>0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[]]]],[]]]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[]]],[]]]]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[]],[]]]]]=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[]]]]]]=>4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[[]]]]]]]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[]]]]]],[]]=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[[]]]]],[]]]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[[]]]],[]]]]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[[]]],[]]]]]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[[]],[]]]]]]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[]]]]]]]=>5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]]]]]]]]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[],[[]]]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[],[[],[]]]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[[[]]]]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[],[[]],[[]]]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[]]]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[[]]]]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[],[[[]],[]]]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[],[[[],[]]]]=>0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[],[[[[]]]]]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[],[[]],[],[[]]]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[],[[]],[[],[]]]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[],[[]],[[[]]]]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[],[[],[]],[[]]]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[]]]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[[]]]]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[],[[],[[]],[]]]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[],[[],[[],[]]]]=>0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[],[[],[[[]]]]]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[],[[[]]],[[]]]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[],[[[]],[],[]]]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[],[[[]],[[]]]]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[],[[[],[]],[]]]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[],[[[],[],[]]]]=>0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[],[[[],[[]]]]]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[[[]]],[]]]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[],[[[[]],[]]]]=>0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[],[[[[],[]]]]]=>0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[],[[[[[]]]]]]=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[],[[]],[],[],[[]]]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[],[[]],[],[[],[]]]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[],[[]],[],[[[]]]]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]],[[]]]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[],[[]],[[],[],[]]]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[],[[]],[[],[[]]]]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[[]],[[[]],[]]]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[],[],[[]],[[[],[]]]]=>0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[],[],[[]],[[[[]]]]]=>0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[[]]]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[],[[],[]],[[],[]]]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[],[[],[]],[[[]]]]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[],[]],[[]]]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[]]]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[[]]]]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[],[[]],[]]]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[],[[],[]]]]=>0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[],[[[]]]]]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[],[[],[[]]],[[]]]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[],[[],[[]],[],[]]]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[],[[],[[]],[[]]]]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[],[[],[[],[]],[]]]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[],[[],[],[]]]]=>0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[],[[],[[],[[]]]]]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[],[[],[[[]]],[]]]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[[[]],[]]]]=>0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[[],[[[],[]]]]]=>0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[],[[],[[[[]]]]]]=>0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[],[[[]]],[],[[]]]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[],[[[]]],[[],[]]]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[],[[[]]],[[[]]]]=>0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[],[[[]],[]],[[]]]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[],[[[]],[],[],[]]]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[],[[[]],[],[[]]]]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[],[[[]],[[]],[]]]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[],[[[]],[[],[]]]]=>0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[],[[[]],[[[]]]]]=>0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[],[[[],[]]],[[]]]=>0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[[],[]],[],[]]]=>0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[],[[[],[]],[[]]]]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[],[[[],[],[]],[]]]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[],[]]]]=>0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[],[[[],[],[[]]]]]=>0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[],[[[],[[]]],[]]]=>0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[],[[[],[[]],[]]]]=>0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[],[[[],[[],[]]]]]=>0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[],[[[],[[[]]]]]]=>0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[],[[[[]]]],[[]]]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[],[[[[]]],[],[]]]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[],[[[[]]],[[]]]]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[],[[[[]],[]],[]]]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[],[[[[]],[],[]]]]=>0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[],[[[[]],[[]]]]]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[],[[[[],[]]],[]]]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[],[[[[],[]],[]]]]=>0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[],[[[[],[],[]]]]]=>0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[],[[[[],[[]]]]]]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[[[[]]]],[]]]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[[]]],[]]]]=>0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[],[[[[[]],[]]]]]=>0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[],[[[[[],[]]]]]]=>0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[],[[[[[[]]]]]]]=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[],[[]]]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[],[[],[]]]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[],[[[]]]]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[],[[]],[[]]]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[],[[]],[],[[],[],[]]]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[[],[[]]]]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[],[[]],[],[[[]],[]]]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[],[[]],[],[[[],[]]]]=>0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[],[[]],[],[[[[]]]]]=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[[]],[],[[]]]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[]]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[],[]]]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[]],[[[]]]]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[]],[[],[]],[[]]]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[],[]]]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[]],[[],[],[[]]]]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[]],[[],[[]],[]]]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[]],[[],[[],[]]]]=>0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[]],[[],[[[]]]]]=>0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>0
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[]],[[[]]],[[]]]=>0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]=>0
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[]],[[[]],[],[]]]=>0
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[[]],[[]]]]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[[],[]],[]]]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[]],[[[],[],[]]]]=>0
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[]],[[[],[[]]]]]=>0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]=>0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[]],[[[[]]],[]]]=>0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[]],[[[[]],[]]]]=>0
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[]],[[[[],[]]]]]=>0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[]],[[[[[]]]]]]=>0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[],[]],[],[],[[]]]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[],[]],[],[[],[]]]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[]],[],[[[]]]]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[]],[[]],[[]]]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[],[]],[[],[],[]]]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[],[]],[[],[[]]]]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[],[]],[[[]],[]]]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[],[[],[]],[[[],[]]]]=>0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[],[[],[]],[[[[]]]]]=>0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[],[]],[],[[]]]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[],[]],[[],[]]]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[],[]],[[[]]]]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[],[]],[[]]]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[]]]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[[]]]]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[],[[]],[]]]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[],[[],[]]]]=>0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[],[[[]]]]]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[],[[]]],[[]]]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[],[[]],[],[]]]=>0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[],[[]],[[]]]]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[],[[],[]],[]]]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[],[[],[],[]]]]=>0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[],[[],[[]]]]]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[],[[[]]],[]]]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[],[[[]],[]]]]=>0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[],[[[],[]]]]]=>0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[],[[[[]]]]]]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[]]],[],[[]]]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[],[[]]],[[],[]]]=>0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[],[[]]],[[[]]]]=>0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[],[[]],[]],[[]]]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[],[[]],[],[],[]]]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[],[[]],[],[[]]]]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[[]],[]]]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[],[[]],[[],[]]]]=>0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[],[[]],[[[]]]]]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[],[[],[]]],[[]]]=>0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]=>0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[],[[],[]],[],[]]]=>0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[],[[],[]],[[]]]]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[],[[],[],[]],[]]]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[],[]]]]=>0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[],[[]]]]]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[],[[],[[]]],[]]]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[[],[[]],[]]]]=>0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[],[[],[[],[]]]]]=>0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[],[[],[[[]]]]]]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[],[[[]]]],[[]]]=>0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]=>0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[],[[[]]],[],[]]]=>0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[],[[[]]],[[]]]]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[],[[[]],[]],[]]]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[],[[[]],[],[]]]]=>0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[]],[[]]]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[]]],[]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[],[[[],[]],[]]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[],[[[],[],[]]]]]=>0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[],[[[],[[]]]]]]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[],[[[[]]]],[]]]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[],[[[[]]],[]]]]=>0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[],[[[[]],[]]]]]=>0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[],[[[[],[]]]]]]=>0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[],[[[[[]]]]]]]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[],[[[]]],[],[],[[]]]=>0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]=>0
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[],[[[]]],[],[[],[]]]=>0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[],[[[]]],[],[[[]]]]=>0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>0
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[],[[[]]],[[]],[[]]]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[[]]],[[],[],[]]]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[],[[[]]],[[],[[]]]]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[],[[[]]],[[[]],[]]]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[[]]],[[[],[]]]]=>0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[],[[[]]],[[[[]]]]]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[],[[[]],[]],[],[[]]]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[],[[[]],[]],[[],[]]]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[],[[[]],[]],[[[]]]]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[],[[[]],[],[]],[[]]]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[],[]]]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[],[[]]]]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[],[[[]],[],[[]],[]]]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[],[[[]],[],[[],[]]]]=>0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[],[[[]],[],[[[]]]]]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[[]],[[]]],[[]]]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[[]],[],[]]]=>0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]],[[]]]]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[],[[[]],[[],[]],[]]]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[],[[[]],[[],[],[]]]]=>0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[],[[[]],[[],[[]]]]]=>0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]=>0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[[[]],[[[]]],[]]]=>0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[],[[[]],[[[]],[]]]]=>0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[],[[[]],[[[],[]]]]]=>0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[],[[[]],[[[[]]]]]]=>0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[[],[]]],[],[[]]]=>0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]=>0
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[],[]]]=>0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[],[[[],[]]],[[[]]]]=>0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>0
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[],[[[],[]],[]],[[]]]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[],[[[],[]],[],[],[]]]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[[],[]],[],[[]]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[],[[[],[]],[[]],[]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[],[]],[[],[]]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[],[[[],[]],[[[]]]]]=>0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>0
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[],[]]],[[]]]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[],[]],[],[]]]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[]],[[]]]]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[],[]],[]]]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[],[]]]]=>0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[],[[]]]]]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[],[[]]],[]]]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[],[[]],[]]]]=>0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[],[[],[]]]]]=>0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[],[[[]]]]]]=>0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>0
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[],[[[],[[]]]],[[]]]=>0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]=>0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[],[[[],[[]]],[],[]]]=>0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[]]],[[]]]]=>0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]=>0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[],[[[],[[]],[]],[]]]=>0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[],[[[],[[]],[],[]]]]=>0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[[],[[]],[[]]]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[],[[],[]]],[]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[],[[[],[[],[]],[]]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[],[[[],[[],[],[]]]]]=>0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[],[[[],[[],[[]]]]]]=>0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]=>0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[[[],[[[]]]],[]]]=>0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[],[[[],[[[]]],[]]]]=>0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[],[[[],[[[]],[]]]]]=>0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[],[[[],[[[],[]]]]]]=>0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[],[[[],[[[[]]]]]]]=>0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[[[]]]],[],[[]]]=>0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]=>0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[[]]]],[[],[]]]=>0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[],[[[[]]]],[[[]]]]=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[],[[[[]]],[]],[[]]]=>0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]=>0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[],[[[[]]],[],[],[]]]=>0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[],[[[[]]],[],[[]]]]=>0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]=>0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[[[[]]],[[]],[]]]=>0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[]]],[[],[]]]]=>0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[],[[[[]]],[[[]]]]]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[],[[[[]],[]]],[[]]]=>0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]=>0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[],[[[[]],[]],[],[]]]=>0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[]],[]],[[]]]]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[],[[[[]],[],[]],[]]]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[],[[[[]],[],[],[]]]]=>0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[[]],[],[[]]]]]=>0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]=>0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[[[[]],[[]]],[]]]=>0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[],[[[[]],[[]],[]]]]=>0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[[[]],[[],[]]]]]=>0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[],[[[[]],[[[]]]]]]=>0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[],[[[[],[]]]],[[]]]=>0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]=>0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[],[[[[],[]]],[],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[]]],[[]]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[],[]],[]],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[],[[[[],[]],[],[]]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[[[],[]],[[]]]]]=>0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]=>0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[],[]],[]]]]=>0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[],[]]]]]=>0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[[]]]]]]=>0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]=>0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[],[[[[],[[]]]],[]]]=>0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[[[],[[]]],[]]]]=>0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[[[],[[]],[]]]]]=>0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[[[],[[],[]]]]]]=>0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[],[[[[],[[[]]]]]]]=>0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[],[[[[[]]]]],[[]]]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[],[[[[[]]]],[],[]]]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[],[[[[[]]]],[[]]]]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[]]],[]],[]]]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[[[]]],[],[]]]]=>0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[[[]]],[[]]]]]=>0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]=>0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[[]],[]]],[]]]=>0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[[[[]],[]],[]]]]=>0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[]]]]]=>0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[],[[[[[]],[[]]]]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[[],[]]]],[]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[[],[]]],[]]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[]],[]]]]]=>0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[]]]]]]=>0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[[],[[]]]]]]]=>0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]=>0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[],[[[[[[]]]]],[]]]=>0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[],[[[[[[]]]],[]]]]=>0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[],[[[[[[]]],[]]]]]=>0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[],[[[[[[]],[]]]]]]=>0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[]]]]]]]=>0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[[]]]]]]]]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[],[]]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[],[[]]]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[],[[]],[]]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[],[[],[]]]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[],[[[]]]]=>0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[],[[]],[],[]]=>0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[],[[]],[[]]]=>0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[],[[],[]],[]]=>0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[],[[],[],[]]]=>0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[],[[],[[]]]]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[],[[[]]],[]]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[],[[[]],[]]]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[],[[[],[]]]]=>0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[],[[[[]]]]]=>0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[[]],[],[],[]]=>0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]],[],[[]]]=>0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[],[[]],[[]],[]]=>0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[],[[]],[[],[]]]=>0
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[],[[]],[[[]]]]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[],[[],[]],[],[]]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[],[[],[]],[[]]]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[],[[],[],[]],[]]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[],[]]]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[],[[],[],[[]]]]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[],[[],[[]]],[]]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[],[[],[[]],[]]]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[],[[],[[],[]]]]=>0
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[],[[],[[[]]]]]=>0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[],[[[]]],[],[]]=>0
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[],[[[]]],[[]]]=>0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[],[[[]],[]],[]]=>0
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[],[[[]],[],[]]]=>0
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[],[[[]],[[]]]]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[],[[[],[]]],[]]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[],[[[],[]],[]]]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[],[[[],[],[]]]]=>0
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[],[[[],[[]]]]]=>0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[],[[[[]]]],[]]=>0
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[],[[[[]]],[]]]=>0
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[]],[]]]]=>0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[],[[[[],[]]]]]=>0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[],[[[[[]]]]]]=>0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[],[]]=>0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[[]],[],[],[[]]]=>0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[[]],[],[[]],[]]=>0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[[]],[],[[],[]]]=>0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[[]],[],[[[]]]]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[[]],[],[]]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[]]]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[]],[[],[]],[]]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[]],[[],[],[]]]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[]],[[],[[]]]]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[]],[[[]]],[]]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[]]]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[]],[[[],[]]]]=>0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[]],[[[[]]]]]=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[]],[[],[]],[],[],[]]=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[]],[[],[]],[],[[]]]=>0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[],[]],[[]],[]]=>0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]],[[],[]]]=>0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[]],[[],[]],[[[]]]]=>0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[],[]],[],[]]=>0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[],[]],[[]]]=>0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[]],[]]=>0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[],[]]]=>0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[],[[]]]]=>0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[],[[]]],[]]=>0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[],[[]],[]]]=>0
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[],[[],[]]]]=>0
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[],[[[]]]]]=>0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[]],[[],[[]]],[],[]]=>0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[]],[[],[[]]],[[]]]=>0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[]],[[],[[]],[]],[]]=>0
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[]],[[],[[]],[],[]]]=>0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[[]],[[]]]]=>0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[]],[[],[[],[]]],[]]=>0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[]],[[],[[],[]],[]]]=>0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[]],[[],[[],[],[]]]]=>0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[]],[[],[[],[[]]]]]=>0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[]],[[],[[[]]]],[]]=>0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[]],[[],[[[]]],[]]]=>0
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[]],[[],[[[]],[]]]]=>0
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[]],[[],[[[],[]]]]]=>0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[]],[[],[[[[]]]]]]=>0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[]],[[[]]],[],[],[]]=>0
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[]],[[[]]],[],[[]]]=>0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[]],[[[]]],[[]],[]]=>0
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[]],[[[]]],[[],[]]]=>0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[[]]],[[[]]]]=>0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[]],[[[]],[]],[],[]]=>0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]]]=>0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[]],[]]=>0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[]],[[[]],[],[],[]]]=>0
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[]],[[[]],[],[[]]]]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[]],[[[]],[[]]],[]]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[]]]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[]],[[[]],[[],[]]]]=>0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[]],[[[]],[[[]]]]]=>0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[]],[[[],[]]],[],[]]=>0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[]],[[[],[]]],[[]]]=>0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[]],[[[],[]],[]],[]]=>0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[]],[[[],[]],[],[]]]=>0
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[]],[[[],[]],[[]]]]=>0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[]],[[[],[],[]]],[]]=>0
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[]],[[[],[],[]],[]]]=>0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[],[]]]]=>0
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[]],[[[],[],[[]]]]]=>0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[]],[[[],[[]]]],[]]=>0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[]],[[[],[[]]],[]]]=>0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[]],[[[],[[]],[]]]]=>0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[]],[[[],[[],[]]]]]=>0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[]],[[[],[[[]]]]]]=>0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[]],[[[[]]]],[],[]]=>0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[]],[[[[]]]],[[]]]=>0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[]],[[[[]]],[]],[]]=>0
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[]],[[[[]]],[],[]]]=>0
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[]],[[[[]]],[[]]]]=>0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[]],[[[[]],[]]],[]]=>0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[]]]=>0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[]],[[[[]],[],[]]]]=>0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[]],[[[[]],[[]]]]]=>0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[]],[[[[],[]]]],[]]=>0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[]]],[]]]=>0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[]],[[[[],[]],[]]]]=>0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[[[],[],[]]]]]=>0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[]],[[[[],[[]]]]]]=>0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[]],[[[[[]]]]],[]]=>0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[]],[[[[[]]]],[]]]=>0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[]],[[[[[]]],[]]]]=>0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[]],[[[[[]],[]]]]]=>0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[]],[[[[[],[]]]]]]=>0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[]],[[[[[[]]]]]]]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[]]=>0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[],[[]]]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[],[[]],[]]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[],[[],[]]]=>0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[],[[[]]]]=>0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[],[]],[],[[]],[],[]]=>0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[],[]],[],[[]],[[]]]=>0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[]],[[],[[],[]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[[],[]],[]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[],[]]]=>0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[],[[],[[],[]]]],[]]=>0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[],[[[],[]],[]]],[]]=>0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[]]=>0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[],[[]]]=>0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[],[[]],[]]=>0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[],[[],[]]]=>0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[],[[[]]]]=>0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[]]],[],[[]],[],[]]=>0
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[]]],[],[[]],[[]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[],[]]]=>0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]],[[],[]]],[]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[],[[],[]]],[]],[]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[]],[]],[]],[]]=>0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[],[[[]]]]]],[]]=>0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[]]]]],[]]=>0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[]]]]]],[]]=>0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]]],[]]]],[]]=>0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[]]]]],[]]=>0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[]]]]]],[]]=>0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[]]]]]]],[]]=>0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[]]]]]]]],[]]=>0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[]]]]]]]]]=>0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[]]]]]]]]],[]]=>0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[],[]]]]]]],[]]=>0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[[],[]]]]]]]]=>0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[]]]]]]]]]]=>0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[[]]]]]]]]]],[]]=>0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[],[]]]]]]]],[]]=>0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[[]],[]]]]]],[]]=>0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[],[[]]]]]]],[]]=>0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[],[[[[[[[]],[]]]]]]]=>0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[],[[]]]]]]]]=>0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[],[]]]]]]]]]=>0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[[]]]]]]]]]]]=>0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[],[[],[[],[]]]]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[]],[[],[]]]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[]],[[],[[],[]]]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[],[]]],[[],[]]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[]],[]],[[],[]]]]=>0
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[],[[],[]]]],[]]]=>0
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[],[]],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]],[[],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[],[]]],[]],[]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[],[]],[]],[]],[]]]=>0
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[],[[],[[],[]]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[],[]],[[],[]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[[[],[[],[]]],[]]]=>0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[],[]],[]],[]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]],[[],[[],[]]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]]],[[[],[]],[]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[]],[[],[[],[]]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]],[[[],[]],[]]]=>0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[],[]]]],[[],[]]]=>0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[]],[]]],[[],[]]]=>0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[],[]]],[[],[]]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[]],[[],[]]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[]],[[],[]]]=>0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[],[]],[]],[]],[]],[]]=>0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[],[[],[[],[[],[[],[[],[]]]]]]]=>0
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[],[[[],[]],[[],[]]]]]]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[[],[]],[[],[[],[]]]]]]=>0
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[[],[]]],[[],[]]]]]=>0
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[[],[]],[]],[[],[]]]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[[],[]],[[],[[],[[],[]]]]]]=>0
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[[],[]],[[[],[]],[[],[]]]]]=>0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]],[[],[[],[]]]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[[],[]],[]],[[],[[],[]]]]]=>0
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[],[[],[]]]],[[],[]]]]=>0
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[[],[]],[]]],[[],[]]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[]],[[],[]]],[[],[]]]]=>0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[[],[]]],[]],[[],[]]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[[],[]],[]],[]],[[],[]]]]=>0
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[],[[[],[[],[[],[[],[]]]]],[]]]=>0
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[],[[[],[]],[]]]],[]]]=>0
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[[],[]],[[],[]]]],[]]]=>0
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[],[[],[]]],[]]],[]]]=>0
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[[],[]],[]],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[],[]],[[],[[],[]]]],[]]]=>0
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[],[]],[[[],[]],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[[],[]]],[[],[]]],[]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>0
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[],[[],[]]]],[]],[]]]=>0
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[[],[]],[]]],[]],[]]]=>0
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>0
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>0
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>0
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[]],[[],[[],[[],[[],[]]]]]]=>0
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[],[[[],[]],[[],[]]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[[],[]],[[],[[],[]]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[],[[],[]]],[[],[]]]]=>0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[[],[]],[]],[[],[]]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[]],[[[],[[],[[],[]]]],[]]]=>0
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[],[]],[[[],[[[],[]],[]]],[]]]=>0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[[[[],[]],[[],[]]],[]]]=>0
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[],[[],[]]],[]],[]]]=>0
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[[],[]],[]],[]],[]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[]]],[[],[[],[[],[]]]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[[],[]]],[[[],[]],[[],[]]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[]]],[[[],[[],[]]],[]]]=>0
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[[],[]]],[[[[],[]],[]],[]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>0
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>0
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>0
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>0
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>0
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>0
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>0
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>0
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Description
The length of the trunk of an ordered tree.
This is the length of the path from the root to the first vertex which has not exactly one child.
This is the length of the path from the root to the first vertex which has not exactly one child.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
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