Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0021;cc-rep-3
[1,0]=>[1,0]=>[1,0]=>[[]]
[1,0,1,0]=>[1,0,1,0]=>[1,0,1,0]=>[[],[]]
[1,1,0,0]=>[1,1,0,0]=>[1,0,1,0]=>[[],[]]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[],[],[]]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[1,0,1,0,1,0]=>[[],[],[]]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,0,1,0,1,0]=>[[],[],[]]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[[],[],[]]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[[],[],[]]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0]=>[[],[[]],[]]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.
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.
searching the database
Sorry, this map was not found in the database.