Identifier
Mp00113:
Perfect matchings
—reverse⟶
Perfect matchings
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Images
=>
Cc0012;cc-rep-0Cc0012;cc-rep-1Cc0005;cc-rep-2Cc0021;cc-rep-3
[(1,2)]=>[(1,2)]=>[1,0]=>[[]]
[(1,2),(3,4)]=>[(1,2),(3,4)]=>[1,0,1,0]=>[[],[]]
[(1,3),(2,4)]=>[(1,3),(2,4)]=>[1,1,0,0]=>[[[]]]
[(1,4),(2,3)]=>[(1,4),(2,3)]=>[1,1,0,0]=>[[[]]]
[(1,2),(3,4),(5,6)]=>[(1,2),(3,4),(5,6)]=>[1,0,1,0,1,0]=>[[],[],[]]
[(1,3),(2,4),(5,6)]=>[(1,2),(3,5),(4,6)]=>[1,0,1,1,0,0]=>[[],[[]]]
[(1,4),(2,3),(5,6)]=>[(1,2),(3,6),(4,5)]=>[1,0,1,1,0,0]=>[[],[[]]]
[(1,5),(2,3),(4,6)]=>[(1,3),(2,6),(4,5)]=>[1,1,0,1,0,0]=>[[[],[]]]
[(1,6),(2,3),(4,5)]=>[(1,6),(2,3),(4,5)]=>[1,1,0,1,0,0]=>[[[],[]]]
[(1,6),(2,4),(3,5)]=>[(1,6),(2,4),(3,5)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,5),(2,4),(3,6)]=>[(1,4),(2,6),(3,5)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,4),(2,5),(3,6)]=>[(1,4),(2,5),(3,6)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,3),(2,5),(4,6)]=>[(1,3),(2,5),(4,6)]=>[1,1,0,1,0,0]=>[[[],[]]]
[(1,2),(3,5),(4,6)]=>[(1,3),(2,4),(5,6)]=>[1,1,0,0,1,0]=>[[[]],[]]
[(1,2),(3,6),(4,5)]=>[(1,4),(2,3),(5,6)]=>[1,1,0,0,1,0]=>[[[]],[]]
[(1,3),(2,6),(4,5)]=>[(1,5),(2,3),(4,6)]=>[1,1,0,1,0,0]=>[[[],[]]]
[(1,4),(2,6),(3,5)]=>[(1,5),(2,4),(3,6)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,5),(2,6),(3,4)]=>[(1,5),(2,6),(3,4)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,6),(2,5),(3,4)]=>[(1,6),(2,5),(3,4)]=>[1,1,1,0,0,0]=>[[[[]]]]
[(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[(1,3),(2,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,7),(6,8)]=>[1,0,1,0,1,1,0,0]=>[[],[],[[]]]
[(1,4),(2,3),(5,6),(7,8)]=>[(1,2),(3,4),(5,8),(6,7)]=>[1,0,1,0,1,1,0,0]=>[[],[],[[]]]
[(1,5),(2,3),(4,6),(7,8)]=>[(1,2),(3,5),(4,8),(6,7)]=>[1,0,1,1,0,1,0,0]=>[[],[[],[]]]
[(1,6),(2,3),(4,5),(7,8)]=>[(1,2),(3,8),(4,5),(6,7)]=>[1,0,1,1,0,1,0,0]=>[[],[[],[]]]
[(1,7),(2,3),(4,5),(6,8)]=>[(1,3),(2,8),(4,5),(6,7)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,8),(2,3),(4,5),(6,7)]=>[(1,8),(2,3),(4,5),(6,7)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,8),(2,4),(3,5),(6,7)]=>[(1,8),(2,3),(4,6),(5,7)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,7),(2,4),(3,5),(6,8)]=>[(1,3),(2,8),(4,6),(5,7)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,6),(2,4),(3,5),(7,8)]=>[(1,2),(3,8),(4,6),(5,7)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,5),(2,4),(3,6),(7,8)]=>[(1,2),(3,6),(4,8),(5,7)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,4),(2,5),(3,6),(7,8)]=>[(1,2),(3,6),(4,7),(5,8)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,3),(2,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,7),(6,8)]=>[1,0,1,1,0,1,0,0]=>[[],[[],[]]]
[(1,2),(3,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[1,0,1,1,0,0,1,0]=>[[],[[]],[]]
[(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,6),(4,5),(7,8)]=>[1,0,1,1,0,0,1,0]=>[[],[[]],[]]
[(1,3),(2,6),(4,5),(7,8)]=>[(1,2),(3,7),(4,5),(6,8)]=>[1,0,1,1,0,1,0,0]=>[[],[[],[]]]
[(1,4),(2,6),(3,5),(7,8)]=>[(1,2),(3,7),(4,6),(5,8)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,5),(2,6),(3,4),(7,8)]=>[(1,2),(3,7),(4,8),(5,6)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,6),(2,5),(3,4),(7,8)]=>[(1,2),(3,8),(4,7),(5,6)]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[(1,7),(2,5),(3,4),(6,8)]=>[(1,3),(2,8),(4,7),(5,6)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,8),(2,5),(3,4),(6,7)]=>[(1,8),(2,3),(4,7),(5,6)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,8),(2,6),(3,4),(5,7)]=>[(1,8),(2,4),(3,7),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,7),(2,6),(3,4),(5,8)]=>[(1,4),(2,8),(3,7),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,6),(2,7),(3,4),(5,8)]=>[(1,4),(2,7),(3,8),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,5),(2,7),(3,4),(6,8)]=>[(1,3),(2,7),(4,8),(5,6)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,4),(2,7),(3,5),(6,8)]=>[(1,3),(2,7),(4,6),(5,8)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,3),(2,7),(4,5),(6,8)]=>[(1,3),(2,7),(4,5),(6,8)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,2),(3,7),(4,5),(6,8)]=>[(1,3),(2,6),(4,5),(7,8)]=>[1,1,0,1,0,0,1,0]=>[[[],[]],[]]
[(1,2),(3,8),(4,5),(6,7)]=>[(1,6),(2,3),(4,5),(7,8)]=>[1,1,0,1,0,0,1,0]=>[[[],[]],[]]
[(1,3),(2,8),(4,5),(6,7)]=>[(1,7),(2,3),(4,5),(6,8)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,4),(2,8),(3,5),(6,7)]=>[(1,7),(2,3),(4,6),(5,8)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,5),(2,8),(3,4),(6,7)]=>[(1,7),(2,3),(4,8),(5,6)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,6),(2,8),(3,4),(5,7)]=>[(1,7),(2,4),(3,8),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,7),(2,8),(3,4),(5,6)]=>[(1,7),(2,8),(3,4),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,8),(2,7),(3,4),(5,6)]=>[(1,8),(2,7),(3,4),(5,6)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,8),(2,7),(3,5),(4,6)]=>[(1,8),(2,7),(3,5),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,8),(3,5),(4,6)]=>[(1,7),(2,8),(3,5),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,8),(3,5),(4,7)]=>[(1,7),(2,5),(3,8),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,5),(2,8),(3,6),(4,7)]=>[(1,7),(2,5),(3,6),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,4),(2,8),(3,6),(5,7)]=>[(1,7),(2,4),(3,6),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,3),(2,8),(4,6),(5,7)]=>[(1,7),(2,4),(3,5),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,2),(3,8),(4,6),(5,7)]=>[(1,6),(2,4),(3,5),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,2),(3,7),(4,6),(5,8)]=>[(1,4),(2,6),(3,5),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,3),(2,7),(4,6),(5,8)]=>[(1,4),(2,7),(3,5),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,4),(2,7),(3,6),(5,8)]=>[(1,4),(2,7),(3,6),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,5),(2,7),(3,6),(4,8)]=>[(1,5),(2,7),(3,6),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,7),(3,5),(4,8)]=>[(1,5),(2,7),(3,8),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,6),(3,5),(4,8)]=>[(1,5),(2,8),(3,7),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,8),(2,6),(3,5),(4,7)]=>[(1,8),(2,5),(3,7),(4,6)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,8),(2,5),(3,6),(4,7)]=>[(1,8),(2,5),(3,6),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,5),(3,6),(4,8)]=>[(1,5),(2,8),(3,6),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,5),(3,7),(4,8)]=>[(1,5),(2,6),(3,8),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,5),(2,6),(3,7),(4,8)]=>[(1,5),(2,6),(3,7),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,4),(2,6),(3,7),(5,8)]=>[(1,4),(2,6),(3,7),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,3),(2,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,7),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,2),(3,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,6),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,2),(3,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[1,1,0,1,0,0,1,0]=>[[[],[]],[]]
[(1,3),(2,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,7),(6,8)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,4),(2,5),(3,7),(6,8)]=>[(1,3),(2,6),(4,7),(5,8)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,5),(2,4),(3,7),(6,8)]=>[(1,3),(2,6),(4,8),(5,7)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,6),(2,4),(3,7),(5,8)]=>[(1,4),(2,6),(3,8),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,7),(2,4),(3,6),(5,8)]=>[(1,4),(2,8),(3,6),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,8),(2,4),(3,6),(5,7)]=>[(1,8),(2,4),(3,6),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,8),(2,3),(4,6),(5,7)]=>[(1,8),(2,4),(3,5),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,7),(2,3),(4,6),(5,8)]=>[(1,4),(2,8),(3,5),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,6),(2,3),(4,7),(5,8)]=>[(1,4),(2,5),(3,8),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,5),(2,3),(4,7),(6,8)]=>[(1,3),(2,5),(4,8),(6,7)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,4),(2,3),(5,7),(6,8)]=>[(1,3),(2,4),(5,8),(6,7)]=>[1,1,0,0,1,1,0,0]=>[[[]],[[]]]
[(1,3),(2,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,7),(6,8)]=>[1,1,0,0,1,1,0,0]=>[[[]],[[]]]
[(1,2),(3,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[1,1,0,0,1,0,1,0]=>[[[]],[],[]]
[(1,2),(3,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,6),(7,8)]=>[1,1,0,0,1,0,1,0]=>[[[]],[],[]]
[(1,3),(2,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,7),(6,8)]=>[1,1,0,0,1,1,0,0]=>[[[]],[[]]]
[(1,4),(2,3),(5,8),(6,7)]=>[(1,4),(2,3),(5,8),(6,7)]=>[1,1,0,0,1,1,0,0]=>[[[]],[[]]]
[(1,5),(2,3),(4,8),(6,7)]=>[(1,5),(2,3),(4,8),(6,7)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,6),(2,3),(4,8),(5,7)]=>[(1,5),(2,4),(3,8),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,7),(2,3),(4,8),(5,6)]=>[(1,5),(2,8),(3,4),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,8),(2,3),(4,7),(5,6)]=>[(1,8),(2,5),(3,4),(6,7)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,8),(2,4),(3,7),(5,6)]=>[(1,8),(2,6),(3,4),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,7),(2,4),(3,8),(5,6)]=>[(1,6),(2,8),(3,4),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,6),(2,4),(3,8),(5,7)]=>[(1,6),(2,4),(3,8),(5,7)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,5),(2,4),(3,8),(6,7)]=>[(1,6),(2,3),(4,8),(5,7)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,4),(2,5),(3,8),(6,7)]=>[(1,6),(2,3),(4,7),(5,8)]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[(1,3),(2,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,7),(6,8)]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[(1,2),(3,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,6),(7,8)]=>[1,1,0,1,0,0,1,0]=>[[[],[]],[]]
[(1,2),(3,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,6),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,3),(2,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,7),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,4),(2,6),(3,8),(5,7)]=>[(1,6),(2,4),(3,7),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,5),(2,6),(3,8),(4,7)]=>[(1,6),(2,5),(3,7),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,5),(3,8),(4,7)]=>[(1,6),(2,5),(3,8),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,5),(3,8),(4,6)]=>[(1,6),(2,8),(3,5),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,8),(2,5),(3,7),(4,6)]=>[(1,8),(2,6),(3,5),(4,7)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,8),(2,6),(3,7),(4,5)]=>[(1,8),(2,6),(3,7),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,6),(3,8),(4,5)]=>[(1,6),(2,8),(3,7),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,7),(3,8),(4,5)]=>[(1,6),(2,7),(3,8),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,5),(2,7),(3,8),(4,6)]=>[(1,6),(2,7),(3,5),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,4),(2,7),(3,8),(5,6)]=>[(1,6),(2,7),(3,4),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,3),(2,7),(4,8),(5,6)]=>[(1,5),(2,7),(3,4),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,2),(3,7),(4,8),(5,6)]=>[(1,5),(2,6),(3,4),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,2),(3,8),(4,7),(5,6)]=>[(1,6),(2,5),(3,4),(7,8)]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[(1,3),(2,8),(4,7),(5,6)]=>[(1,7),(2,5),(3,4),(6,8)]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[(1,4),(2,8),(3,7),(5,6)]=>[(1,7),(2,6),(3,4),(5,8)]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[(1,5),(2,8),(3,7),(4,6)]=>[(1,7),(2,6),(3,5),(4,8)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,6),(2,8),(3,7),(4,5)]=>[(1,7),(2,6),(3,8),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,7),(2,8),(3,6),(4,5)]=>[(1,7),(2,8),(3,6),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,8),(2,7),(3,6),(4,5)]=>[(1,8),(2,7),(3,6),(4,5)]=>[1,1,1,1,0,0,0,0]=>[[[[[]]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]
[(1,3),(2,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,9),(8,10)]=>[1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[[]]]
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[[]]]
[(1,5),(2,3),(4,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,7),(6,10),(8,9)]=>[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]
[(1,7),(2,3),(4,5),(6,8),(9,10)]=>[(1,2),(3,5),(4,10),(6,7),(8,9)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,9),(2,3),(4,5),(6,7),(8,10)]=>[(1,3),(2,10),(4,5),(6,7),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,10),(2,4),(3,5),(6,7),(8,9)]=>[(1,10),(2,3),(4,5),(6,8),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,9),(2,4),(3,5),(6,7),(8,10)]=>[(1,3),(2,10),(4,5),(6,8),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,8),(2,4),(3,5),(6,7),(9,10)]=>[(1,2),(3,10),(4,5),(6,8),(7,9)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,7),(2,4),(3,5),(6,8),(9,10)]=>[(1,2),(3,5),(4,10),(6,8),(7,9)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,6),(2,4),(3,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,10),(6,8),(7,9)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,5),(2,4),(3,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,10),(7,9)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,9),(7,10)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,7),(6,9),(8,10)]=>[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]
[(1,2),(3,5),(4,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,7),(6,8),(9,10)]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[(1,3),(2,6),(4,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,9),(6,7),(8,10)]=>[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]
[(1,4),(2,6),(3,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,9),(6,8),(7,10)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,5),(2,6),(3,4),(7,8),(9,10)]=>[(1,2),(3,4),(5,9),(6,10),(7,8)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[(1,7),(2,5),(3,4),(6,8),(9,10)]=>[(1,2),(3,5),(4,10),(6,9),(7,8)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,9),(2,5),(3,4),(6,7),(8,10)]=>[(1,3),(2,10),(4,5),(6,9),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,10),(2,6),(3,4),(5,7),(8,9)]=>[(1,10),(2,3),(4,6),(5,9),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,9),(2,6),(3,4),(5,7),(8,10)]=>[(1,3),(2,10),(4,6),(5,9),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,6),(3,4),(5,7),(9,10)]=>[(1,2),(3,10),(4,6),(5,9),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,7),(2,6),(3,4),(5,8),(9,10)]=>[(1,2),(3,6),(4,10),(5,9),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,6),(2,7),(3,4),(5,8),(9,10)]=>[(1,2),(3,6),(4,9),(5,10),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,5),(2,7),(3,4),(6,8),(9,10)]=>[(1,2),(3,5),(4,9),(6,10),(7,8)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,4),(2,7),(3,5),(6,8),(9,10)]=>[(1,2),(3,5),(4,9),(6,8),(7,10)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,3),(2,7),(4,5),(6,8),(9,10)]=>[(1,2),(3,5),(4,9),(6,7),(8,10)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,2),(3,7),(4,5),(6,8),(9,10)]=>[(1,2),(3,5),(4,8),(6,7),(9,10)]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[(1,3),(2,8),(4,5),(6,7),(9,10)]=>[(1,2),(3,9),(4,5),(6,7),(8,10)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,4),(2,8),(3,5),(6,7),(9,10)]=>[(1,2),(3,9),(4,5),(6,8),(7,10)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,5),(2,8),(3,4),(6,7),(9,10)]=>[(1,2),(3,9),(4,5),(6,10),(7,8)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,6),(2,8),(3,4),(5,7),(9,10)]=>[(1,2),(3,9),(4,6),(5,10),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,7),(2,8),(3,4),(5,6),(9,10)]=>[(1,2),(3,9),(4,10),(5,6),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,9),(2,7),(3,4),(5,6),(8,10)]=>[(1,3),(2,10),(4,9),(5,6),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,10),(2,8),(3,4),(5,6),(7,9)]=>[(1,10),(2,4),(3,9),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,8),(3,4),(5,6),(7,10)]=>[(1,4),(2,10),(3,9),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,8),(2,9),(3,4),(5,6),(7,10)]=>[(1,4),(2,9),(3,10),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,9),(3,4),(5,6),(8,10)]=>[(1,3),(2,9),(4,10),(5,6),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,6),(2,9),(3,4),(5,7),(8,10)]=>[(1,3),(2,9),(4,6),(5,10),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,9),(3,4),(6,7),(8,10)]=>[(1,3),(2,9),(4,5),(6,10),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,4),(2,9),(3,5),(6,7),(8,10)]=>[(1,3),(2,9),(4,5),(6,8),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,3),(2,9),(4,5),(6,7),(8,10)]=>[(1,3),(2,9),(4,5),(6,7),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,2),(3,9),(4,5),(6,7),(8,10)]=>[(1,3),(2,8),(4,5),(6,7),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,3),(2,10),(4,5),(6,7),(8,9)]=>[(1,9),(2,3),(4,5),(6,7),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,10),(3,5),(6,7),(8,9)]=>[(1,9),(2,3),(4,5),(6,8),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,5),(2,10),(3,4),(6,7),(8,9)]=>[(1,9),(2,3),(4,5),(6,10),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,10),(3,4),(5,7),(8,9)]=>[(1,9),(2,3),(4,6),(5,10),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,7),(2,10),(3,4),(5,6),(8,9)]=>[(1,9),(2,3),(4,10),(5,6),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,10),(3,4),(5,6),(7,9)]=>[(1,9),(2,4),(3,10),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,10),(3,4),(5,6),(7,8)]=>[(1,9),(2,10),(3,4),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,9),(3,5),(4,6),(7,8)]=>[(1,10),(2,9),(3,4),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,10),(3,5),(4,6),(7,8)]=>[(1,9),(2,10),(3,4),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,10),(3,5),(4,6),(7,9)]=>[(1,9),(2,4),(3,10),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,10),(3,5),(4,6),(8,9)]=>[(1,9),(2,3),(4,10),(5,7),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,10),(3,5),(4,7),(8,9)]=>[(1,9),(2,3),(4,7),(5,10),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,10),(3,6),(4,7),(8,9)]=>[(1,9),(2,3),(4,7),(5,8),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,10),(3,6),(5,7),(8,9)]=>[(1,9),(2,3),(4,6),(5,8),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,10),(4,6),(5,7),(8,9)]=>[(1,9),(2,3),(4,6),(5,7),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,10),(4,6),(5,7),(8,9)]=>[(1,8),(2,3),(4,6),(5,7),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,9),(4,6),(5,7),(8,10)]=>[(1,3),(2,8),(4,6),(5,7),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,9),(4,6),(5,7),(8,10)]=>[(1,3),(2,9),(4,6),(5,7),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,9),(3,6),(5,7),(8,10)]=>[(1,3),(2,9),(4,6),(5,8),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,9),(3,6),(4,7),(8,10)]=>[(1,3),(2,9),(4,7),(5,8),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,9),(3,5),(4,7),(8,10)]=>[(1,3),(2,9),(4,7),(5,10),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,9),(3,5),(4,6),(8,10)]=>[(1,3),(2,9),(4,10),(5,7),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>[(1,4),(2,9),(3,10),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,8),(3,5),(4,6),(7,10)]=>[(1,4),(2,10),(3,9),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,8),(3,5),(4,6),(7,9)]=>[(1,10),(2,4),(3,9),(5,7),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,7),(3,5),(4,6),(8,9)]=>[(1,10),(2,3),(4,9),(5,7),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,9),(2,7),(3,5),(4,6),(8,10)]=>[(1,3),(2,10),(4,9),(5,7),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,7),(3,5),(4,6),(9,10)]=>[(1,2),(3,10),(4,9),(5,7),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,8),(3,5),(4,6),(9,10)]=>[(1,2),(3,9),(4,10),(5,7),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,8),(3,5),(4,7),(9,10)]=>[(1,2),(3,9),(4,7),(5,10),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,5),(2,8),(3,6),(4,7),(9,10)]=>[(1,2),(3,9),(4,7),(5,8),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,4),(2,8),(3,6),(5,7),(9,10)]=>[(1,2),(3,9),(4,6),(5,8),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,3),(2,8),(4,6),(5,7),(9,10)]=>[(1,2),(3,9),(4,6),(5,7),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,2),(3,8),(4,6),(5,7),(9,10)]=>[(1,2),(3,8),(4,6),(5,7),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,2),(3,7),(4,6),(5,8),(9,10)]=>[(1,2),(3,6),(4,8),(5,7),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,3),(2,7),(4,6),(5,8),(9,10)]=>[(1,2),(3,6),(4,9),(5,7),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,4),(2,7),(3,6),(5,8),(9,10)]=>[(1,2),(3,6),(4,9),(5,8),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,5),(2,7),(3,6),(4,8),(9,10)]=>[(1,2),(3,7),(4,9),(5,8),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,7),(3,5),(4,8),(9,10)]=>[(1,2),(3,7),(4,9),(5,10),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,6),(3,5),(4,8),(9,10)]=>[(1,2),(3,7),(4,10),(5,9),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,8),(2,6),(3,5),(4,7),(9,10)]=>[(1,2),(3,10),(4,7),(5,9),(6,8)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,9),(2,6),(3,5),(4,7),(8,10)]=>[(1,3),(2,10),(4,7),(5,9),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,6),(3,5),(4,7),(8,9)]=>[(1,10),(2,3),(4,7),(5,9),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,5),(3,6),(4,7),(8,9)]=>[(1,10),(2,3),(4,7),(5,8),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,9),(2,5),(3,6),(4,7),(8,10)]=>[(1,3),(2,10),(4,7),(5,8),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,5),(3,6),(4,7),(9,10)]=>[(1,2),(3,10),(4,7),(5,8),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,5),(3,6),(4,8),(9,10)]=>[(1,2),(3,7),(4,10),(5,8),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,5),(3,7),(4,8),(9,10)]=>[(1,2),(3,7),(4,8),(5,10),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>[(1,2),(3,7),(4,8),(5,9),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>[(1,2),(3,6),(4,8),(5,9),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>[(1,2),(3,6),(4,7),(5,9),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>[(1,2),(3,6),(4,7),(5,8),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,7),(6,8),(9,10)]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,7),(6,9),(8,10)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,8),(6,9),(7,10)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,5),(2,4),(3,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,8),(6,10),(7,9)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,6),(2,4),(3,7),(5,8),(9,10)]=>[(1,2),(3,6),(4,8),(5,10),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,7),(2,4),(3,6),(5,8),(9,10)]=>[(1,2),(3,6),(4,10),(5,8),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,8),(2,4),(3,6),(5,7),(9,10)]=>[(1,2),(3,10),(4,6),(5,8),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,9),(2,4),(3,6),(5,7),(8,10)]=>[(1,3),(2,10),(4,6),(5,8),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,10),(2,4),(3,6),(5,7),(8,9)]=>[(1,10),(2,3),(4,6),(5,8),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,10),(2,3),(4,6),(5,7),(8,9)]=>[(1,10),(2,3),(4,6),(5,7),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,9),(2,3),(4,6),(5,7),(8,10)]=>[(1,3),(2,10),(4,6),(5,7),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,8),(2,3),(4,6),(5,7),(9,10)]=>[(1,2),(3,10),(4,6),(5,7),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,7),(2,3),(4,6),(5,8),(9,10)]=>[(1,2),(3,6),(4,10),(5,7),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,6),(2,3),(4,7),(5,8),(9,10)]=>[(1,2),(3,6),(4,7),(5,10),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,5),(2,3),(4,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,7),(6,10),(8,9)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,4),(2,3),(5,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,6),(7,10),(8,9)]=>[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]
[(1,3),(2,4),(5,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,6),(7,9),(8,10)]=>[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]
[(1,2),(3,4),(5,7),(6,8),(9,10)]=>[(1,2),(3,5),(4,6),(7,8),(9,10)]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[(1,3),(2,4),(5,8),(6,7),(9,10)]=>[(1,2),(3,6),(4,5),(7,9),(8,10)]=>[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]
[(1,5),(2,3),(4,8),(6,7),(9,10)]=>[(1,2),(3,7),(4,5),(6,10),(8,9)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,6),(2,3),(4,8),(5,7),(9,10)]=>[(1,2),(3,7),(4,6),(5,10),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,7),(2,3),(4,8),(5,6),(9,10)]=>[(1,2),(3,7),(4,10),(5,6),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,9),(2,3),(4,7),(5,6),(8,10)]=>[(1,3),(2,10),(4,7),(5,6),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,10),(2,4),(3,7),(5,6),(8,9)]=>[(1,10),(2,3),(4,8),(5,6),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,9),(2,4),(3,7),(5,6),(8,10)]=>[(1,3),(2,10),(4,8),(5,6),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,4),(3,7),(5,6),(9,10)]=>[(1,2),(3,10),(4,8),(5,6),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,7),(2,4),(3,8),(5,6),(9,10)]=>[(1,2),(3,8),(4,10),(5,6),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,6),(2,4),(3,8),(5,7),(9,10)]=>[(1,2),(3,8),(4,6),(5,10),(7,9)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,5),(2,4),(3,8),(6,7),(9,10)]=>[(1,2),(3,8),(4,5),(6,10),(7,9)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,4),(2,5),(3,8),(6,7),(9,10)]=>[(1,2),(3,8),(4,5),(6,9),(7,10)]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[(1,3),(2,5),(4,8),(6,7),(9,10)]=>[(1,2),(3,7),(4,5),(6,9),(8,10)]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[(1,2),(3,5),(4,8),(6,7),(9,10)]=>[(1,2),(3,7),(4,5),(6,8),(9,10)]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[(1,2),(3,6),(4,8),(5,7),(9,10)]=>[(1,2),(3,7),(4,6),(5,8),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,3),(2,6),(4,8),(5,7),(9,10)]=>[(1,2),(3,7),(4,6),(5,9),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,4),(2,6),(3,8),(5,7),(9,10)]=>[(1,2),(3,8),(4,6),(5,9),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,5),(2,6),(3,8),(4,7),(9,10)]=>[(1,2),(3,8),(4,7),(5,9),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,5),(3,8),(4,7),(9,10)]=>[(1,2),(3,8),(4,7),(5,10),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,5),(3,8),(4,6),(9,10)]=>[(1,2),(3,8),(4,10),(5,7),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,8),(2,5),(3,7),(4,6),(9,10)]=>[(1,2),(3,10),(4,8),(5,7),(6,9)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,9),(2,5),(3,7),(4,6),(8,10)]=>[(1,3),(2,10),(4,8),(5,7),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,5),(3,7),(4,6),(8,9)]=>[(1,10),(2,3),(4,8),(5,7),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,6),(3,7),(4,5),(8,9)]=>[(1,10),(2,3),(4,8),(5,9),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,9),(2,6),(3,7),(4,5),(8,10)]=>[(1,3),(2,10),(4,8),(5,9),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,6),(3,7),(4,5),(9,10)]=>[(1,2),(3,10),(4,8),(5,9),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,6),(3,8),(4,5),(9,10)]=>[(1,2),(3,8),(4,10),(5,9),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,7),(3,8),(4,5),(9,10)]=>[(1,2),(3,8),(4,9),(5,10),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,5),(2,7),(3,8),(4,6),(9,10)]=>[(1,2),(3,8),(4,9),(5,7),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,4),(2,7),(3,8),(5,6),(9,10)]=>[(1,2),(3,8),(4,9),(5,6),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,3),(2,7),(4,8),(5,6),(9,10)]=>[(1,2),(3,7),(4,9),(5,6),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,2),(3,7),(4,8),(5,6),(9,10)]=>[(1,2),(3,7),(4,8),(5,6),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[(1,3),(2,8),(4,7),(5,6),(9,10)]=>[(1,2),(3,9),(4,7),(5,6),(8,10)]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[(1,4),(2,8),(3,7),(5,6),(9,10)]=>[(1,2),(3,9),(4,8),(5,6),(7,10)]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[(1,5),(2,8),(3,7),(4,6),(9,10)]=>[(1,2),(3,9),(4,8),(5,7),(6,10)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,6),(2,8),(3,7),(4,5),(9,10)]=>[(1,2),(3,9),(4,8),(5,10),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,7),(2,8),(3,6),(4,5),(9,10)]=>[(1,2),(3,9),(4,10),(5,8),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[(1,9),(2,7),(3,6),(4,5),(8,10)]=>[(1,3),(2,10),(4,9),(5,8),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,10),(2,8),(3,6),(4,5),(7,9)]=>[(1,10),(2,4),(3,9),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,8),(3,6),(4,5),(7,10)]=>[(1,4),(2,10),(3,9),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,9),(3,6),(4,5),(7,10)]=>[(1,4),(2,9),(3,10),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,9),(3,6),(4,5),(8,10)]=>[(1,3),(2,9),(4,10),(5,8),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,9),(3,7),(4,5),(8,10)]=>[(1,3),(2,9),(4,8),(5,10),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,9),(3,7),(4,6),(8,10)]=>[(1,3),(2,9),(4,8),(5,7),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,9),(3,7),(5,6),(8,10)]=>[(1,3),(2,9),(4,8),(5,6),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,9),(4,7),(5,6),(8,10)]=>[(1,3),(2,9),(4,7),(5,6),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,9),(4,7),(5,6),(8,10)]=>[(1,3),(2,8),(4,7),(5,6),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,10),(4,7),(5,6),(8,9)]=>[(1,9),(2,3),(4,7),(5,6),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,10),(3,7),(5,6),(8,9)]=>[(1,9),(2,3),(4,8),(5,6),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,10),(3,7),(4,6),(8,9)]=>[(1,9),(2,3),(4,8),(5,7),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,10),(3,7),(4,5),(8,9)]=>[(1,9),(2,3),(4,8),(5,10),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,10),(3,6),(4,5),(8,9)]=>[(1,9),(2,3),(4,10),(5,8),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,10),(3,6),(4,5),(7,9)]=>[(1,9),(2,4),(3,10),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,10),(3,6),(4,5),(7,8)]=>[(1,9),(2,10),(3,4),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,9),(3,7),(4,5),(6,8)]=>[(1,10),(2,9),(3,5),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,10),(3,7),(4,5),(6,8)]=>[(1,9),(2,10),(3,5),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,10),(3,7),(4,5),(6,9)]=>[(1,9),(2,5),(3,10),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,10),(3,8),(4,5),(6,9)]=>[(1,9),(2,5),(3,8),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,10),(3,8),(4,5),(7,9)]=>[(1,9),(2,4),(3,8),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,10),(3,8),(4,6),(7,9)]=>[(1,9),(2,4),(3,8),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,10),(3,8),(5,6),(7,9)]=>[(1,9),(2,4),(3,8),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,10),(4,8),(5,6),(7,9)]=>[(1,9),(2,4),(3,7),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,10),(4,8),(5,6),(7,9)]=>[(1,8),(2,4),(3,7),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,9),(4,8),(5,6),(7,10)]=>[(1,4),(2,8),(3,7),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,9),(4,8),(5,6),(7,10)]=>[(1,4),(2,9),(3,7),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,9),(3,8),(5,6),(7,10)]=>[(1,4),(2,9),(3,8),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,9),(3,8),(4,6),(7,10)]=>[(1,4),(2,9),(3,8),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,9),(3,8),(4,5),(7,10)]=>[(1,4),(2,9),(3,8),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,9),(3,8),(4,5),(6,10)]=>[(1,5),(2,9),(3,8),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,9),(3,7),(4,5),(6,10)]=>[(1,5),(2,9),(3,10),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,8),(3,7),(4,5),(6,10)]=>[(1,5),(2,10),(3,9),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,8),(3,7),(4,5),(6,9)]=>[(1,10),(2,5),(3,9),(4,8),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,7),(3,8),(4,5),(6,9)]=>[(1,10),(2,5),(3,8),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,7),(3,8),(4,5),(6,10)]=>[(1,5),(2,10),(3,8),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,7),(3,9),(4,5),(6,10)]=>[(1,5),(2,8),(3,10),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,8),(3,9),(4,5),(6,10)]=>[(1,5),(2,8),(3,9),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,8),(3,9),(4,5),(7,10)]=>[(1,4),(2,8),(3,9),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,8),(3,9),(4,6),(7,10)]=>[(1,4),(2,8),(3,9),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,8),(3,9),(5,6),(7,10)]=>[(1,4),(2,8),(3,9),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,8),(4,9),(5,6),(7,10)]=>[(1,4),(2,7),(3,9),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,8),(4,9),(5,6),(7,10)]=>[(1,4),(2,7),(3,8),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,7),(4,9),(5,6),(8,10)]=>[(1,3),(2,7),(4,8),(5,6),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,7),(4,9),(5,6),(8,10)]=>[(1,3),(2,7),(4,9),(5,6),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,7),(3,9),(5,6),(8,10)]=>[(1,3),(2,8),(4,9),(5,6),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,7),(3,9),(4,6),(8,10)]=>[(1,3),(2,8),(4,9),(5,7),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,7),(3,9),(4,5),(8,10)]=>[(1,3),(2,8),(4,9),(5,10),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,6),(3,9),(4,5),(8,10)]=>[(1,3),(2,8),(4,10),(5,9),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,6),(3,9),(4,5),(7,10)]=>[(1,4),(2,8),(3,10),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,6),(3,8),(4,5),(7,10)]=>[(1,4),(2,10),(3,8),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,6),(3,8),(4,5),(7,9)]=>[(1,10),(2,4),(3,8),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,5),(3,8),(4,6),(7,9)]=>[(1,10),(2,4),(3,8),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,5),(3,8),(4,6),(7,10)]=>[(1,4),(2,10),(3,8),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,5),(3,9),(4,6),(7,10)]=>[(1,4),(2,8),(3,10),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,5),(3,9),(4,6),(8,10)]=>[(1,3),(2,8),(4,10),(5,7),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,5),(3,9),(4,7),(8,10)]=>[(1,3),(2,8),(4,7),(5,10),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,6),(3,9),(4,7),(8,10)]=>[(1,3),(2,8),(4,7),(5,9),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,6),(3,9),(5,7),(8,10)]=>[(1,3),(2,8),(4,6),(5,9),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,6),(4,9),(5,7),(8,10)]=>[(1,3),(2,7),(4,6),(5,9),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,6),(4,9),(5,7),(8,10)]=>[(1,3),(2,7),(4,6),(5,8),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,5),(4,9),(6,7),(8,10)]=>[(1,3),(2,7),(4,5),(6,8),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,3),(2,5),(4,9),(6,7),(8,10)]=>[(1,3),(2,7),(4,5),(6,9),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,5),(3,9),(6,7),(8,10)]=>[(1,3),(2,8),(4,5),(6,9),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,5),(2,4),(3,9),(6,7),(8,10)]=>[(1,3),(2,8),(4,5),(6,10),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,4),(3,9),(5,7),(8,10)]=>[(1,3),(2,8),(4,6),(5,10),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,7),(2,4),(3,9),(5,6),(8,10)]=>[(1,3),(2,8),(4,10),(5,6),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,4),(3,9),(5,6),(7,10)]=>[(1,4),(2,8),(3,10),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,4),(3,8),(5,6),(7,10)]=>[(1,4),(2,10),(3,8),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,4),(3,8),(5,6),(7,9)]=>[(1,10),(2,4),(3,8),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,3),(4,8),(5,6),(7,9)]=>[(1,10),(2,4),(3,7),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,9),(2,3),(4,8),(5,6),(7,10)]=>[(1,4),(2,10),(3,7),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,8),(2,3),(4,9),(5,6),(7,10)]=>[(1,4),(2,7),(3,10),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,7),(2,3),(4,9),(5,6),(8,10)]=>[(1,3),(2,7),(4,10),(5,6),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,6),(2,3),(4,9),(5,7),(8,10)]=>[(1,3),(2,7),(4,6),(5,10),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,5),(2,3),(4,9),(6,7),(8,10)]=>[(1,3),(2,7),(4,5),(6,10),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,3),(5,9),(6,7),(8,10)]=>[(1,3),(2,6),(4,5),(7,10),(8,9)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,3),(2,4),(5,9),(6,7),(8,10)]=>[(1,3),(2,6),(4,5),(7,9),(8,10)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,2),(3,4),(5,9),(6,7),(8,10)]=>[(1,3),(2,6),(4,5),(7,8),(9,10)]=>[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]
[(1,3),(2,4),(5,10),(6,7),(8,9)]=>[(1,6),(2,3),(4,5),(7,9),(8,10)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,5),(2,3),(4,10),(6,7),(8,9)]=>[(1,7),(2,3),(4,5),(6,10),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,6),(2,3),(4,10),(5,7),(8,9)]=>[(1,7),(2,3),(4,6),(5,10),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,7),(2,3),(4,10),(5,6),(8,9)]=>[(1,7),(2,3),(4,10),(5,6),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,8),(2,3),(4,10),(5,6),(7,9)]=>[(1,7),(2,4),(3,10),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,9),(2,3),(4,10),(5,6),(7,8)]=>[(1,7),(2,10),(3,4),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,10),(2,4),(3,9),(5,6),(7,8)]=>[(1,10),(2,8),(3,4),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,4),(3,10),(5,6),(7,8)]=>[(1,8),(2,10),(3,4),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,8),(2,4),(3,10),(5,6),(7,9)]=>[(1,8),(2,4),(3,10),(5,6),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,4),(3,10),(5,6),(8,9)]=>[(1,8),(2,3),(4,10),(5,6),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,6),(2,4),(3,10),(5,7),(8,9)]=>[(1,8),(2,3),(4,6),(5,10),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,4),(3,10),(6,7),(8,9)]=>[(1,8),(2,3),(4,5),(6,10),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,4),(2,5),(3,10),(6,7),(8,9)]=>[(1,8),(2,3),(4,5),(6,9),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,3),(2,5),(4,10),(6,7),(8,9)]=>[(1,7),(2,3),(4,5),(6,9),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,2),(3,5),(4,10),(6,7),(8,9)]=>[(1,7),(2,3),(4,5),(6,8),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,2),(3,6),(4,10),(5,7),(8,9)]=>[(1,7),(2,3),(4,6),(5,8),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,6),(4,10),(5,7),(8,9)]=>[(1,7),(2,3),(4,6),(5,9),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,6),(3,10),(5,7),(8,9)]=>[(1,8),(2,3),(4,6),(5,9),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,6),(3,10),(4,7),(8,9)]=>[(1,8),(2,3),(4,7),(5,9),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,5),(3,10),(4,7),(8,9)]=>[(1,8),(2,3),(4,7),(5,10),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,5),(3,10),(4,6),(8,9)]=>[(1,8),(2,3),(4,10),(5,7),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,5),(3,10),(4,6),(7,9)]=>[(1,8),(2,4),(3,10),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,5),(3,10),(4,6),(7,8)]=>[(1,8),(2,10),(3,4),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,5),(3,9),(4,6),(7,8)]=>[(1,10),(2,8),(3,4),(5,7),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,6),(3,9),(4,5),(7,8)]=>[(1,10),(2,8),(3,4),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,6),(3,10),(4,5),(7,8)]=>[(1,8),(2,10),(3,4),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,6),(3,10),(4,5),(7,9)]=>[(1,8),(2,4),(3,10),(5,9),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,6),(3,10),(4,5),(8,9)]=>[(1,8),(2,3),(4,10),(5,9),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,7),(3,10),(4,5),(8,9)]=>[(1,8),(2,3),(4,9),(5,10),(6,7)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,7),(3,10),(4,6),(8,9)]=>[(1,8),(2,3),(4,9),(5,7),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,7),(3,10),(5,6),(8,9)]=>[(1,8),(2,3),(4,9),(5,6),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,7),(4,10),(5,6),(8,9)]=>[(1,7),(2,3),(4,9),(5,6),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,7),(4,10),(5,6),(8,9)]=>[(1,7),(2,3),(4,8),(5,6),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,8),(4,10),(5,6),(7,9)]=>[(1,7),(2,4),(3,8),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,8),(4,10),(5,6),(7,9)]=>[(1,7),(2,4),(3,9),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,8),(3,10),(5,6),(7,9)]=>[(1,8),(2,4),(3,9),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,8),(3,10),(4,6),(7,9)]=>[(1,8),(2,4),(3,9),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,8),(3,10),(4,5),(7,9)]=>[(1,8),(2,4),(3,9),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,8),(3,10),(4,5),(6,9)]=>[(1,8),(2,5),(3,9),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,7),(3,10),(4,5),(6,9)]=>[(1,8),(2,5),(3,10),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,7),(3,10),(4,5),(6,8)]=>[(1,8),(2,10),(3,5),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,7),(3,9),(4,5),(6,8)]=>[(1,10),(2,8),(3,5),(4,9),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,8),(3,9),(4,5),(6,7)]=>[(1,10),(2,8),(3,9),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,8),(3,10),(4,5),(6,7)]=>[(1,8),(2,10),(3,9),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,9),(3,10),(4,5),(6,7)]=>[(1,8),(2,9),(3,10),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,9),(3,10),(4,5),(6,8)]=>[(1,8),(2,9),(3,5),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,9),(3,10),(4,5),(7,8)]=>[(1,8),(2,9),(3,4),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,9),(3,10),(4,6),(7,8)]=>[(1,8),(2,9),(3,4),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,9),(3,10),(5,6),(7,8)]=>[(1,8),(2,9),(3,4),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,9),(4,10),(5,6),(7,8)]=>[(1,7),(2,9),(3,4),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,9),(4,10),(5,6),(7,8)]=>[(1,7),(2,8),(3,4),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,10),(4,9),(5,6),(7,8)]=>[(1,9),(2,7),(3,4),(5,6),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,10),(3,9),(5,6),(7,8)]=>[(1,9),(2,8),(3,4),(5,6),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,10),(3,9),(4,6),(7,8)]=>[(1,9),(2,8),(3,4),(5,7),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,10),(3,9),(4,5),(7,8)]=>[(1,9),(2,8),(3,4),(5,10),(6,7)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,10),(3,9),(4,5),(6,8)]=>[(1,9),(2,8),(3,5),(4,10),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,10),(3,9),(4,5),(6,7)]=>[(1,9),(2,8),(3,10),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,10),(3,8),(4,5),(6,7)]=>[(1,9),(2,10),(3,8),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>[(1,10),(2,9),(3,8),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,8),(4,6),(5,7)]=>[(1,9),(2,10),(3,8),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,9),(4,6),(5,7)]=>[(1,9),(2,8),(3,10),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,9),(4,6),(5,8)]=>[(1,9),(2,8),(3,6),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,10),(3,9),(4,7),(5,8)]=>[(1,9),(2,8),(3,6),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,10),(3,9),(4,7),(6,8)]=>[(1,9),(2,8),(3,5),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,10),(3,9),(5,7),(6,8)]=>[(1,9),(2,8),(3,5),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,10),(4,9),(5,7),(6,8)]=>[(1,9),(2,7),(3,5),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,10),(4,9),(5,7),(6,8)]=>[(1,8),(2,7),(3,5),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,9),(4,10),(5,7),(6,8)]=>[(1,7),(2,8),(3,5),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,9),(4,10),(5,7),(6,8)]=>[(1,7),(2,9),(3,5),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,9),(3,10),(5,7),(6,8)]=>[(1,8),(2,9),(3,5),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,9),(3,10),(4,7),(6,8)]=>[(1,8),(2,9),(3,5),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,9),(3,10),(4,7),(5,8)]=>[(1,8),(2,9),(3,6),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,10),(4,6),(5,8)]=>[(1,8),(2,9),(3,6),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,10),(4,6),(5,7)]=>[(1,8),(2,9),(3,10),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,10),(4,6),(5,7)]=>[(1,8),(2,10),(3,9),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>[(1,10),(2,8),(3,9),(4,6),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,9),(4,6),(5,8)]=>[(1,10),(2,8),(3,6),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,10),(4,6),(5,8)]=>[(1,8),(2,10),(3,6),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,10),(4,6),(5,9)]=>[(1,8),(2,6),(3,10),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,10),(4,6),(5,9)]=>[(1,8),(2,6),(3,9),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,8),(3,10),(4,7),(5,9)]=>[(1,8),(2,6),(3,9),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,8),(3,10),(4,7),(6,9)]=>[(1,8),(2,5),(3,9),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,8),(3,10),(5,7),(6,9)]=>[(1,8),(2,5),(3,9),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,8),(4,10),(5,7),(6,9)]=>[(1,7),(2,5),(3,9),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,8),(4,10),(5,7),(6,9)]=>[(1,7),(2,5),(3,8),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,7),(4,10),(5,8),(6,9)]=>[(1,7),(2,5),(3,6),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,7),(4,10),(5,8),(6,9)]=>[(1,7),(2,5),(3,6),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,7),(3,10),(5,8),(6,9)]=>[(1,8),(2,5),(3,6),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,7),(3,10),(4,8),(6,9)]=>[(1,8),(2,5),(3,7),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,7),(3,10),(4,8),(5,9)]=>[(1,8),(2,6),(3,7),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,10),(4,8),(5,9)]=>[(1,8),(2,6),(3,7),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,10),(4,7),(5,9)]=>[(1,8),(2,6),(3,10),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,10),(4,7),(5,8)]=>[(1,8),(2,10),(3,6),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,6),(3,9),(4,7),(5,8)]=>[(1,10),(2,8),(3,6),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,5),(3,9),(4,7),(6,8)]=>[(1,10),(2,8),(3,5),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,10),(4,7),(6,8)]=>[(1,8),(2,10),(3,5),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,10),(4,7),(6,9)]=>[(1,8),(2,5),(3,10),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,5),(3,10),(4,8),(6,9)]=>[(1,8),(2,5),(3,7),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,5),(3,10),(4,8),(7,9)]=>[(1,8),(2,4),(3,7),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,6),(3,10),(4,8),(7,9)]=>[(1,8),(2,4),(3,7),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,6),(3,10),(5,8),(7,9)]=>[(1,8),(2,4),(3,6),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,6),(4,10),(5,8),(7,9)]=>[(1,7),(2,4),(3,6),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,6),(4,10),(5,8),(7,9)]=>[(1,7),(2,4),(3,6),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,5),(4,10),(6,8),(7,9)]=>[(1,7),(2,4),(3,5),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,5),(4,10),(6,8),(7,9)]=>[(1,7),(2,4),(3,5),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,5),(3,10),(6,8),(7,9)]=>[(1,8),(2,4),(3,5),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,4),(3,10),(6,8),(7,9)]=>[(1,8),(2,4),(3,5),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,4),(3,10),(5,8),(7,9)]=>[(1,8),(2,4),(3,6),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,4),(3,10),(5,8),(6,9)]=>[(1,8),(2,5),(3,6),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,10),(5,7),(6,9)]=>[(1,8),(2,5),(3,10),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,10),(5,7),(6,8)]=>[(1,8),(2,10),(3,5),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,4),(3,9),(5,7),(6,8)]=>[(1,10),(2,8),(3,5),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,3),(4,9),(5,7),(6,8)]=>[(1,10),(2,7),(3,5),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,10),(5,7),(6,8)]=>[(1,7),(2,10),(3,5),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,10),(5,7),(6,9)]=>[(1,7),(2,5),(3,10),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,7),(2,3),(4,10),(5,8),(6,9)]=>[(1,7),(2,5),(3,6),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,6),(2,3),(4,10),(5,8),(7,9)]=>[(1,7),(2,4),(3,6),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,5),(2,3),(4,10),(6,8),(7,9)]=>[(1,7),(2,4),(3,5),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,3),(5,10),(6,8),(7,9)]=>[(1,6),(2,4),(3,5),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,3),(2,4),(5,10),(6,8),(7,9)]=>[(1,6),(2,4),(3,5),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,2),(3,4),(5,10),(6,8),(7,9)]=>[(1,6),(2,4),(3,5),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,2),(3,4),(5,9),(6,8),(7,10)]=>[(1,4),(2,6),(3,5),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,3),(2,4),(5,9),(6,8),(7,10)]=>[(1,4),(2,6),(3,5),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,4),(2,3),(5,9),(6,8),(7,10)]=>[(1,4),(2,6),(3,5),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,5),(2,3),(4,9),(6,8),(7,10)]=>[(1,4),(2,7),(3,5),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,6),(2,3),(4,9),(5,8),(7,10)]=>[(1,4),(2,7),(3,6),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,7),(2,3),(4,9),(5,8),(6,10)]=>[(1,5),(2,7),(3,6),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,9),(5,7),(6,10)]=>[(1,5),(2,7),(3,10),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,8),(5,7),(6,10)]=>[(1,5),(2,10),(3,7),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,3),(4,8),(5,7),(6,9)]=>[(1,10),(2,5),(3,7),(4,6),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,4),(3,8),(5,7),(6,9)]=>[(1,10),(2,5),(3,8),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,8),(5,7),(6,10)]=>[(1,5),(2,10),(3,8),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,9),(5,7),(6,10)]=>[(1,5),(2,8),(3,10),(4,6),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,4),(3,9),(5,8),(6,10)]=>[(1,5),(2,8),(3,6),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,4),(3,9),(5,8),(7,10)]=>[(1,4),(2,8),(3,6),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,4),(3,9),(6,8),(7,10)]=>[(1,4),(2,8),(3,5),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,5),(3,9),(6,8),(7,10)]=>[(1,4),(2,8),(3,5),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,5),(4,9),(6,8),(7,10)]=>[(1,4),(2,7),(3,5),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,5),(4,9),(6,8),(7,10)]=>[(1,4),(2,7),(3,5),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,6),(4,9),(5,8),(7,10)]=>[(1,4),(2,7),(3,6),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,6),(4,9),(5,8),(7,10)]=>[(1,4),(2,7),(3,6),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,6),(3,9),(5,8),(7,10)]=>[(1,4),(2,8),(3,6),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,6),(3,9),(4,8),(7,10)]=>[(1,4),(2,8),(3,7),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,5),(3,9),(4,8),(7,10)]=>[(1,4),(2,8),(3,7),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,5),(3,9),(4,8),(6,10)]=>[(1,5),(2,8),(3,7),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,9),(4,7),(6,10)]=>[(1,5),(2,8),(3,10),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,8),(4,7),(6,10)]=>[(1,5),(2,10),(3,8),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,5),(3,8),(4,7),(6,9)]=>[(1,10),(2,5),(3,8),(4,7),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,6),(3,8),(4,7),(5,9)]=>[(1,10),(2,6),(3,8),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,8),(4,7),(5,10)]=>[(1,6),(2,10),(3,8),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,9),(4,7),(5,10)]=>[(1,6),(2,8),(3,10),(4,7),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,9),(4,8),(5,10)]=>[(1,6),(2,8),(3,7),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,7),(3,9),(4,8),(5,10)]=>[(1,6),(2,8),(3,7),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,7),(3,9),(4,8),(6,10)]=>[(1,5),(2,8),(3,7),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,7),(3,9),(5,8),(6,10)]=>[(1,5),(2,8),(3,6),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,7),(4,9),(5,8),(6,10)]=>[(1,5),(2,7),(3,6),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,7),(4,9),(5,8),(6,10)]=>[(1,5),(2,7),(3,6),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,8),(4,9),(5,7),(6,10)]=>[(1,5),(2,7),(3,8),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,8),(4,9),(5,7),(6,10)]=>[(1,5),(2,7),(3,9),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,8),(3,9),(5,7),(6,10)]=>[(1,5),(2,8),(3,9),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,8),(3,9),(4,7),(6,10)]=>[(1,5),(2,8),(3,9),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,8),(3,9),(4,7),(5,10)]=>[(1,6),(2,8),(3,9),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,9),(4,6),(5,10)]=>[(1,6),(2,8),(3,9),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,9),(4,6),(5,10)]=>[(1,6),(2,8),(3,10),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,8),(4,6),(5,10)]=>[(1,6),(2,10),(3,8),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,8),(4,6),(5,9)]=>[(1,10),(2,6),(3,8),(4,9),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,7),(4,6),(5,9)]=>[(1,10),(2,6),(3,9),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,7),(4,6),(5,10)]=>[(1,6),(2,10),(3,9),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,7),(4,6),(5,10)]=>[(1,6),(2,9),(3,10),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,8),(4,6),(5,10)]=>[(1,6),(2,9),(3,8),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,9),(3,8),(4,7),(5,10)]=>[(1,6),(2,9),(3,8),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,9),(3,8),(4,7),(6,10)]=>[(1,5),(2,9),(3,8),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,9),(3,8),(5,7),(6,10)]=>[(1,5),(2,9),(3,8),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,9),(4,8),(5,7),(6,10)]=>[(1,5),(2,9),(3,7),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,9),(4,8),(5,7),(6,10)]=>[(1,5),(2,8),(3,7),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,10),(4,8),(5,7),(6,9)]=>[(1,8),(2,5),(3,7),(4,6),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,10),(4,8),(5,7),(6,9)]=>[(1,9),(2,5),(3,7),(4,6),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,10),(3,8),(5,7),(6,9)]=>[(1,9),(2,5),(3,8),(4,6),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,10),(3,8),(4,7),(6,9)]=>[(1,9),(2,5),(3,8),(4,7),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,10),(3,8),(4,7),(5,9)]=>[(1,9),(2,6),(3,8),(4,7),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,8),(4,6),(5,9)]=>[(1,9),(2,6),(3,8),(4,10),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,7),(4,6),(5,9)]=>[(1,9),(2,6),(3,10),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,7),(4,6),(5,8)]=>[(1,9),(2,10),(3,6),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,9),(3,7),(4,6),(5,8)]=>[(1,10),(2,9),(3,6),(4,8),(5,7)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,9),(3,6),(4,7),(5,8)]=>[(1,10),(2,9),(3,6),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,6),(4,7),(5,8)]=>[(1,9),(2,10),(3,6),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,6),(4,7),(5,9)]=>[(1,9),(2,6),(3,10),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,6),(4,8),(5,9)]=>[(1,9),(2,6),(3,7),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,10),(3,7),(4,8),(5,9)]=>[(1,9),(2,6),(3,7),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,10),(3,7),(4,8),(6,9)]=>[(1,9),(2,5),(3,7),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,10),(3,7),(5,8),(6,9)]=>[(1,9),(2,5),(3,6),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,10),(4,7),(5,8),(6,9)]=>[(1,9),(2,5),(3,6),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,10),(4,7),(5,8),(6,9)]=>[(1,8),(2,5),(3,6),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,9),(4,7),(5,8),(6,10)]=>[(1,5),(2,8),(3,6),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,9),(4,7),(5,8),(6,10)]=>[(1,5),(2,9),(3,6),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,9),(3,7),(5,8),(6,10)]=>[(1,5),(2,9),(3,6),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,9),(3,7),(4,8),(6,10)]=>[(1,5),(2,9),(3,7),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,9),(3,7),(4,8),(5,10)]=>[(1,6),(2,9),(3,7),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,6),(4,8),(5,10)]=>[(1,6),(2,9),(3,7),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,6),(4,7),(5,10)]=>[(1,6),(2,9),(3,10),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,6),(4,7),(5,10)]=>[(1,6),(2,10),(3,9),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,6),(4,7),(5,9)]=>[(1,10),(2,6),(3,9),(4,7),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,6),(4,8),(5,9)]=>[(1,10),(2,6),(3,7),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,6),(4,8),(5,10)]=>[(1,6),(2,10),(3,7),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,6),(4,9),(5,10)]=>[(1,6),(2,7),(3,10),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,6),(4,9),(5,10)]=>[(1,6),(2,7),(3,9),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,8),(3,7),(4,9),(5,10)]=>[(1,6),(2,7),(3,9),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,8),(3,7),(4,9),(6,10)]=>[(1,5),(2,7),(3,9),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,8),(3,7),(5,9),(6,10)]=>[(1,5),(2,6),(3,9),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,8),(4,7),(5,9),(6,10)]=>[(1,5),(2,6),(3,9),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,8),(4,7),(5,9),(6,10)]=>[(1,5),(2,6),(3,8),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,7),(4,8),(5,9),(6,10)]=>[(1,5),(2,6),(3,7),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,7),(4,8),(5,9),(6,10)]=>[(1,5),(2,6),(3,7),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,7),(3,8),(5,9),(6,10)]=>[(1,5),(2,6),(3,8),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>[(1,5),(2,7),(3,8),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>[(1,6),(2,7),(3,8),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,8),(4,9),(5,10)]=>[(1,6),(2,7),(3,8),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,7),(4,9),(5,10)]=>[(1,6),(2,7),(3,10),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,7),(4,8),(5,10)]=>[(1,6),(2,10),(3,7),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,6),(3,7),(4,8),(5,9)]=>[(1,10),(2,6),(3,7),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,5),(3,7),(4,8),(6,9)]=>[(1,10),(2,5),(3,7),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,7),(4,8),(6,10)]=>[(1,5),(2,10),(3,7),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,7),(4,9),(6,10)]=>[(1,5),(2,7),(3,10),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,5),(3,8),(4,9),(6,10)]=>[(1,5),(2,7),(3,8),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,5),(3,8),(4,9),(7,10)]=>[(1,4),(2,7),(3,8),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>[(1,4),(2,7),(3,8),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>[(1,4),(2,6),(3,8),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>[(1,4),(2,6),(3,7),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>[(1,4),(2,6),(3,7),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,7),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,7),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,8),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,4),(3,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,8),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,4),(3,8),(5,9),(7,10)]=>[(1,4),(2,6),(3,8),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,4),(3,8),(5,9),(6,10)]=>[(1,5),(2,6),(3,8),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,7),(5,9),(6,10)]=>[(1,5),(2,6),(3,10),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,7),(5,8),(6,10)]=>[(1,5),(2,10),(3,6),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,4),(3,7),(5,8),(6,9)]=>[(1,10),(2,5),(3,6),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,3),(4,7),(5,8),(6,9)]=>[(1,10),(2,5),(3,6),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,7),(5,8),(6,10)]=>[(1,5),(2,10),(3,6),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,7),(5,9),(6,10)]=>[(1,5),(2,6),(3,10),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>[(1,5),(2,6),(3,7),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,6),(2,3),(4,8),(5,9),(7,10)]=>[(1,4),(2,6),(3,7),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,5),(2,3),(4,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,7),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,3),(5,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,6),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,6),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>[(1,4),(2,5),(3,6),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,6),(7,8),(9,10)]=>[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,6),(7,9),(8,10)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,4),(2,3),(5,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,6),(7,10),(8,9)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,5),(2,3),(4,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,7),(6,10),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,6),(2,3),(4,7),(5,9),(8,10)]=>[(1,3),(2,6),(4,7),(5,10),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,7),(2,3),(4,6),(5,9),(8,10)]=>[(1,3),(2,6),(4,10),(5,7),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,8),(2,3),(4,6),(5,9),(7,10)]=>[(1,4),(2,6),(3,10),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,9),(2,3),(4,6),(5,8),(7,10)]=>[(1,4),(2,10),(3,6),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,10),(2,3),(4,6),(5,8),(7,9)]=>[(1,10),(2,4),(3,6),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,10),(2,4),(3,6),(5,8),(7,9)]=>[(1,10),(2,4),(3,6),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,4),(3,6),(5,8),(7,10)]=>[(1,4),(2,10),(3,6),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,8),(2,4),(3,6),(5,9),(7,10)]=>[(1,4),(2,6),(3,10),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,4),(3,6),(5,9),(8,10)]=>[(1,3),(2,6),(4,10),(5,8),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,6),(2,4),(3,7),(5,9),(8,10)]=>[(1,3),(2,6),(4,8),(5,10),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,4),(3,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,8),(6,10),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,8),(6,9),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,7),(6,9),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>[(1,3),(2,5),(4,7),(6,8),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>[(1,3),(2,6),(4,7),(5,8),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>[(1,3),(2,6),(4,7),(5,9),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>[(1,3),(2,6),(4,8),(5,9),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>[(1,3),(2,7),(4,8),(5,9),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,5),(3,7),(4,9),(8,10)]=>[(1,3),(2,7),(4,8),(5,10),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,5),(3,6),(4,9),(8,10)]=>[(1,3),(2,7),(4,10),(5,8),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,5),(3,6),(4,9),(7,10)]=>[(1,4),(2,7),(3,10),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,5),(3,6),(4,8),(7,10)]=>[(1,4),(2,10),(3,7),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,5),(3,6),(4,8),(7,9)]=>[(1,10),(2,4),(3,7),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,6),(3,5),(4,8),(7,9)]=>[(1,10),(2,4),(3,7),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,6),(3,5),(4,8),(7,10)]=>[(1,4),(2,10),(3,7),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,6),(3,5),(4,9),(7,10)]=>[(1,4),(2,7),(3,10),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,6),(3,5),(4,9),(8,10)]=>[(1,3),(2,7),(4,10),(5,9),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,7),(3,5),(4,9),(8,10)]=>[(1,3),(2,7),(4,9),(5,10),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,7),(3,6),(4,9),(8,10)]=>[(1,3),(2,7),(4,9),(5,8),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,7),(3,6),(5,9),(8,10)]=>[(1,3),(2,6),(4,9),(5,8),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,7),(4,6),(5,9),(8,10)]=>[(1,3),(2,6),(4,9),(5,7),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,7),(4,6),(5,9),(8,10)]=>[(1,3),(2,6),(4,8),(5,7),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,8),(4,6),(5,9),(7,10)]=>[(1,4),(2,6),(3,8),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,8),(4,6),(5,9),(7,10)]=>[(1,4),(2,6),(3,9),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,8),(3,6),(5,9),(7,10)]=>[(1,4),(2,6),(3,9),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,8),(3,6),(4,9),(7,10)]=>[(1,4),(2,7),(3,9),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,8),(3,5),(4,9),(7,10)]=>[(1,4),(2,7),(3,9),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,8),(3,5),(4,9),(6,10)]=>[(1,5),(2,7),(3,9),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,7),(3,5),(4,9),(6,10)]=>[(1,5),(2,7),(3,10),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,7),(3,5),(4,8),(6,10)]=>[(1,5),(2,10),(3,7),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,7),(3,5),(4,8),(6,9)]=>[(1,10),(2,5),(3,7),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,8),(3,5),(4,7),(6,9)]=>[(1,10),(2,5),(3,9),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,8),(3,5),(4,7),(6,10)]=>[(1,5),(2,10),(3,9),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,9),(3,5),(4,7),(6,10)]=>[(1,5),(2,9),(3,10),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,9),(3,5),(4,8),(6,10)]=>[(1,5),(2,9),(3,7),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,9),(3,5),(4,8),(7,10)]=>[(1,4),(2,9),(3,7),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,9),(3,6),(4,8),(7,10)]=>[(1,4),(2,9),(3,7),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,9),(3,6),(5,8),(7,10)]=>[(1,4),(2,9),(3,6),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,9),(4,6),(5,8),(7,10)]=>[(1,4),(2,9),(3,6),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,9),(4,6),(5,8),(7,10)]=>[(1,4),(2,8),(3,6),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,10),(4,6),(5,8),(7,9)]=>[(1,8),(2,4),(3,6),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,10),(4,6),(5,8),(7,9)]=>[(1,9),(2,4),(3,6),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,10),(3,6),(5,8),(7,9)]=>[(1,9),(2,4),(3,6),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,10),(3,6),(4,8),(7,9)]=>[(1,9),(2,4),(3,7),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,10),(3,5),(4,8),(7,9)]=>[(1,9),(2,4),(3,7),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,10),(3,5),(4,8),(6,9)]=>[(1,9),(2,5),(3,7),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,10),(3,5),(4,7),(6,9)]=>[(1,9),(2,5),(3,10),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,10),(3,5),(4,7),(6,8)]=>[(1,9),(2,10),(3,5),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,9),(3,5),(4,7),(6,8)]=>[(1,10),(2,9),(3,5),(4,7),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,9),(3,4),(5,7),(6,8)]=>[(1,10),(2,9),(3,5),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,10),(3,4),(5,7),(6,8)]=>[(1,9),(2,10),(3,5),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,10),(3,4),(5,7),(6,9)]=>[(1,9),(2,5),(3,10),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,10),(3,4),(5,8),(6,9)]=>[(1,9),(2,5),(3,6),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,10),(3,4),(5,8),(7,9)]=>[(1,9),(2,4),(3,6),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,10),(3,4),(6,8),(7,9)]=>[(1,9),(2,4),(3,5),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,10),(3,5),(6,8),(7,9)]=>[(1,9),(2,4),(3,5),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,10),(4,5),(6,8),(7,9)]=>[(1,9),(2,4),(3,5),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,10),(4,5),(6,8),(7,9)]=>[(1,8),(2,4),(3,5),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,9),(4,5),(6,8),(7,10)]=>[(1,4),(2,8),(3,5),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,9),(4,5),(6,8),(7,10)]=>[(1,4),(2,9),(3,5),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,9),(3,5),(6,8),(7,10)]=>[(1,4),(2,9),(3,5),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,9),(3,4),(6,8),(7,10)]=>[(1,4),(2,9),(3,5),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,9),(3,4),(5,8),(7,10)]=>[(1,4),(2,9),(3,6),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,9),(3,4),(5,8),(6,10)]=>[(1,5),(2,9),(3,6),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,9),(3,4),(5,7),(6,10)]=>[(1,5),(2,9),(3,10),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,8),(3,4),(5,7),(6,10)]=>[(1,5),(2,10),(3,9),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,8),(3,4),(5,7),(6,9)]=>[(1,10),(2,5),(3,9),(4,6),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,7),(3,4),(5,8),(6,9)]=>[(1,10),(2,5),(3,6),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,7),(3,4),(5,8),(6,10)]=>[(1,5),(2,10),(3,6),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,7),(3,4),(5,9),(6,10)]=>[(1,5),(2,6),(3,10),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,8),(3,4),(5,9),(6,10)]=>[(1,5),(2,6),(3,9),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,8),(3,4),(5,9),(7,10)]=>[(1,4),(2,6),(3,9),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,8),(3,4),(6,9),(7,10)]=>[(1,4),(2,5),(3,9),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,8),(3,5),(6,9),(7,10)]=>[(1,4),(2,5),(3,9),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,8),(4,5),(6,9),(7,10)]=>[(1,4),(2,5),(3,9),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,8),(4,5),(6,9),(7,10)]=>[(1,4),(2,5),(3,8),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,7),(4,5),(6,9),(8,10)]=>[(1,3),(2,5),(4,8),(6,7),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,3),(2,7),(4,5),(6,9),(8,10)]=>[(1,3),(2,5),(4,9),(6,7),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,7),(3,5),(6,9),(8,10)]=>[(1,3),(2,5),(4,9),(6,8),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,5),(2,7),(3,4),(6,9),(8,10)]=>[(1,3),(2,5),(4,9),(6,10),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,7),(3,4),(5,9),(8,10)]=>[(1,3),(2,6),(4,9),(5,10),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,7),(2,6),(3,4),(5,9),(8,10)]=>[(1,3),(2,6),(4,10),(5,9),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,6),(3,4),(5,9),(7,10)]=>[(1,4),(2,6),(3,10),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,6),(3,4),(5,8),(7,10)]=>[(1,4),(2,10),(3,6),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,6),(3,4),(5,8),(7,9)]=>[(1,10),(2,4),(3,6),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,5),(3,4),(6,8),(7,9)]=>[(1,10),(2,4),(3,5),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,9),(2,5),(3,4),(6,8),(7,10)]=>[(1,4),(2,10),(3,5),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>[(1,4),(2,5),(3,10),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,7),(2,5),(3,4),(6,9),(8,10)]=>[(1,3),(2,5),(4,10),(6,9),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,5),(3,4),(7,9),(8,10)]=>[(1,3),(2,4),(5,10),(6,9),(7,8)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,5),(2,6),(3,4),(7,9),(8,10)]=>[(1,3),(2,4),(5,9),(6,10),(7,8)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,4),(2,6),(3,5),(7,9),(8,10)]=>[(1,3),(2,4),(5,9),(6,8),(7,10)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,3),(2,6),(4,5),(7,9),(8,10)]=>[(1,3),(2,4),(5,9),(6,7),(8,10)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,2),(3,6),(4,5),(7,9),(8,10)]=>[(1,3),(2,4),(5,8),(6,7),(9,10)]=>[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]
[(1,2),(3,5),(4,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,7),(6,8),(9,10)]=>[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]
[(1,3),(2,5),(4,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,7),(6,9),(8,10)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,8),(6,9),(7,10)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,5),(2,4),(3,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,8),(6,10),(7,9)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,6),(2,4),(3,5),(7,9),(8,10)]=>[(1,3),(2,4),(5,10),(6,8),(7,9)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,7),(2,4),(3,5),(6,9),(8,10)]=>[(1,3),(2,5),(4,10),(6,8),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,8),(2,4),(3,5),(6,9),(7,10)]=>[(1,4),(2,5),(3,10),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,9),(2,4),(3,5),(6,8),(7,10)]=>[(1,4),(2,10),(3,5),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,10),(2,4),(3,5),(6,8),(7,9)]=>[(1,10),(2,4),(3,5),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,10),(2,3),(4,5),(6,8),(7,9)]=>[(1,10),(2,4),(3,5),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,9),(2,3),(4,5),(6,8),(7,10)]=>[(1,4),(2,10),(3,5),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,8),(2,3),(4,5),(6,9),(7,10)]=>[(1,4),(2,5),(3,10),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,7),(2,3),(4,5),(6,9),(8,10)]=>[(1,3),(2,5),(4,10),(6,7),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,6),(2,3),(4,5),(7,9),(8,10)]=>[(1,3),(2,4),(5,10),(6,7),(8,9)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,5),(2,3),(4,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,7),(6,10),(8,9)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,4),(2,3),(5,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,6),(7,10),(8,9)]=>[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]
[(1,3),(2,4),(5,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,6),(7,9),(8,10)]=>[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]
[(1,2),(3,4),(5,6),(7,9),(8,10)]=>[(1,3),(2,4),(5,6),(7,8),(9,10)]=>[1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[],[]]
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[],[]]
[(1,3),(2,4),(5,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,6),(7,9),(8,10)]=>[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]
[(1,5),(2,3),(4,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,7),(6,10),(8,9)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,7),(2,3),(4,5),(6,10),(8,9)]=>[(1,5),(2,3),(4,10),(6,7),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,8),(2,3),(4,5),(6,10),(7,9)]=>[(1,5),(2,4),(3,10),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,9),(2,3),(4,5),(6,10),(7,8)]=>[(1,5),(2,10),(3,4),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,10),(2,4),(3,5),(6,9),(7,8)]=>[(1,10),(2,5),(3,4),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,9),(2,4),(3,5),(6,10),(7,8)]=>[(1,5),(2,10),(3,4),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,8),(2,4),(3,5),(6,10),(7,9)]=>[(1,5),(2,4),(3,10),(6,8),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,7),(2,4),(3,5),(6,10),(8,9)]=>[(1,5),(2,3),(4,10),(6,8),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,4),(3,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,10),(6,8),(7,9)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,5),(2,4),(3,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,8),(6,10),(7,9)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,4),(2,5),(3,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,8),(6,9),(7,10)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,3),(2,5),(4,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,7),(6,9),(8,10)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,2),(3,5),(4,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,7),(6,8),(9,10)]=>[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]
[(1,3),(2,6),(4,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,9),(6,7),(8,10)]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[(1,4),(2,6),(3,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,9),(6,8),(7,10)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,5),(2,6),(3,4),(7,10),(8,9)]=>[(1,4),(2,3),(5,9),(6,10),(7,8)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[(1,7),(2,5),(3,4),(6,10),(8,9)]=>[(1,5),(2,3),(4,10),(6,9),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,8),(2,5),(3,4),(6,10),(7,9)]=>[(1,5),(2,4),(3,10),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,9),(2,5),(3,4),(6,10),(7,8)]=>[(1,5),(2,10),(3,4),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,10),(2,6),(3,4),(5,9),(7,8)]=>[(1,10),(2,6),(3,4),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,6),(3,4),(5,10),(7,8)]=>[(1,6),(2,10),(3,4),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,8),(2,6),(3,4),(5,10),(7,9)]=>[(1,6),(2,4),(3,10),(5,9),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,6),(3,4),(5,10),(8,9)]=>[(1,6),(2,3),(4,10),(5,9),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,6),(2,7),(3,4),(5,10),(8,9)]=>[(1,6),(2,3),(4,9),(5,10),(7,8)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,7),(3,4),(6,10),(8,9)]=>[(1,5),(2,3),(4,9),(6,10),(7,8)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,4),(2,7),(3,5),(6,10),(8,9)]=>[(1,5),(2,3),(4,9),(6,8),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,3),(2,7),(4,5),(6,10),(8,9)]=>[(1,5),(2,3),(4,9),(6,7),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,2),(3,7),(4,5),(6,10),(8,9)]=>[(1,5),(2,3),(4,8),(6,7),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,2),(3,8),(4,5),(6,10),(7,9)]=>[(1,5),(2,4),(3,8),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,8),(4,5),(6,10),(7,9)]=>[(1,5),(2,4),(3,9),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,8),(3,5),(6,10),(7,9)]=>[(1,5),(2,4),(3,9),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,8),(3,4),(6,10),(7,9)]=>[(1,5),(2,4),(3,9),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,8),(3,4),(5,10),(7,9)]=>[(1,6),(2,4),(3,9),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,8),(3,4),(5,10),(6,9)]=>[(1,6),(2,5),(3,9),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,7),(3,4),(5,10),(6,9)]=>[(1,6),(2,5),(3,10),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,7),(3,4),(5,10),(6,8)]=>[(1,6),(2,10),(3,5),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,7),(3,4),(5,9),(6,8)]=>[(1,10),(2,6),(3,5),(4,9),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,8),(3,4),(5,9),(6,7)]=>[(1,10),(2,6),(3,9),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,8),(3,4),(5,10),(6,7)]=>[(1,6),(2,10),(3,9),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,9),(3,4),(5,10),(6,7)]=>[(1,6),(2,9),(3,10),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,9),(3,4),(5,10),(6,8)]=>[(1,6),(2,9),(3,5),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,9),(3,4),(5,10),(7,8)]=>[(1,6),(2,9),(3,4),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,9),(3,4),(6,10),(7,8)]=>[(1,5),(2,9),(3,4),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,9),(3,5),(6,10),(7,8)]=>[(1,5),(2,9),(3,4),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,9),(4,5),(6,10),(7,8)]=>[(1,5),(2,9),(3,4),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,9),(4,5),(6,10),(7,8)]=>[(1,5),(2,8),(3,4),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,10),(4,5),(6,9),(7,8)]=>[(1,9),(2,5),(3,4),(6,7),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,10),(3,5),(6,9),(7,8)]=>[(1,9),(2,5),(3,4),(6,8),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,10),(3,4),(6,9),(7,8)]=>[(1,9),(2,5),(3,4),(6,10),(7,8)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,10),(3,4),(5,9),(7,8)]=>[(1,9),(2,6),(3,4),(5,10),(7,8)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,10),(3,4),(5,9),(6,8)]=>[(1,9),(2,6),(3,5),(4,10),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,10),(3,4),(5,9),(6,7)]=>[(1,9),(2,6),(3,10),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,10),(3,4),(5,8),(6,7)]=>[(1,9),(2,10),(3,6),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,9),(3,5),(4,8),(6,7)]=>[(1,10),(2,9),(3,7),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,10),(3,5),(4,8),(6,7)]=>[(1,9),(2,10),(3,7),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,10),(3,5),(4,9),(6,7)]=>[(1,9),(2,7),(3,10),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,10),(3,5),(4,9),(6,8)]=>[(1,9),(2,7),(3,5),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,10),(3,5),(4,9),(7,8)]=>[(1,9),(2,7),(3,4),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,10),(3,6),(4,9),(7,8)]=>[(1,9),(2,7),(3,4),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,10),(3,6),(5,9),(7,8)]=>[(1,9),(2,6),(3,4),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,10),(4,6),(5,9),(7,8)]=>[(1,9),(2,6),(3,4),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,10),(4,6),(5,9),(7,8)]=>[(1,8),(2,6),(3,4),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,9),(4,6),(5,10),(7,8)]=>[(1,6),(2,8),(3,4),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,9),(4,6),(5,10),(7,8)]=>[(1,6),(2,9),(3,4),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,9),(3,6),(5,10),(7,8)]=>[(1,6),(2,9),(3,4),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,9),(3,6),(4,10),(7,8)]=>[(1,7),(2,9),(3,4),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,9),(3,5),(4,10),(7,8)]=>[(1,7),(2,9),(3,4),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,9),(3,5),(4,10),(6,8)]=>[(1,7),(2,9),(3,5),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,9),(3,5),(4,10),(6,7)]=>[(1,7),(2,9),(3,10),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,8),(3,5),(4,10),(6,7)]=>[(1,7),(2,10),(3,9),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,8),(3,5),(4,9),(6,7)]=>[(1,10),(2,7),(3,9),(4,5),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,7),(3,5),(4,9),(6,8)]=>[(1,10),(2,7),(3,5),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>[(1,7),(2,10),(3,5),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,7),(3,5),(4,10),(6,9)]=>[(1,7),(2,5),(3,10),(4,9),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,8),(3,5),(4,10),(6,9)]=>[(1,7),(2,5),(3,9),(4,10),(6,8)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,8),(3,5),(4,10),(7,9)]=>[(1,7),(2,4),(3,9),(5,10),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,8),(3,6),(4,10),(7,9)]=>[(1,7),(2,4),(3,9),(5,8),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,8),(3,6),(5,10),(7,9)]=>[(1,6),(2,4),(3,9),(5,8),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,8),(4,6),(5,10),(7,9)]=>[(1,6),(2,4),(3,9),(5,7),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,8),(4,6),(5,10),(7,9)]=>[(1,6),(2,4),(3,8),(5,7),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,7),(4,6),(5,10),(8,9)]=>[(1,6),(2,3),(4,8),(5,7),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,3),(2,7),(4,6),(5,10),(8,9)]=>[(1,6),(2,3),(4,9),(5,7),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,4),(2,7),(3,6),(5,10),(8,9)]=>[(1,6),(2,3),(4,9),(5,8),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,5),(2,7),(3,6),(4,10),(8,9)]=>[(1,7),(2,3),(4,9),(5,8),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,7),(3,5),(4,10),(8,9)]=>[(1,7),(2,3),(4,9),(5,10),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,7),(2,6),(3,5),(4,10),(8,9)]=>[(1,7),(2,3),(4,10),(5,9),(6,8)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,8),(2,6),(3,5),(4,10),(7,9)]=>[(1,7),(2,4),(3,10),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,6),(3,5),(4,10),(7,8)]=>[(1,7),(2,10),(3,4),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,6),(3,5),(4,9),(7,8)]=>[(1,10),(2,7),(3,4),(5,9),(6,8)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,10),(2,5),(3,6),(4,9),(7,8)]=>[(1,10),(2,7),(3,4),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,9),(2,5),(3,6),(4,10),(7,8)]=>[(1,7),(2,10),(3,4),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,8),(2,5),(3,6),(4,10),(7,9)]=>[(1,7),(2,4),(3,10),(5,8),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,5),(3,6),(4,10),(8,9)]=>[(1,7),(2,3),(4,10),(5,8),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,6),(2,5),(3,7),(4,10),(8,9)]=>[(1,7),(2,3),(4,8),(5,10),(6,9)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,5),(2,6),(3,7),(4,10),(8,9)]=>[(1,7),(2,3),(4,8),(5,9),(6,10)]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[(1,4),(2,6),(3,7),(5,10),(8,9)]=>[(1,6),(2,3),(4,8),(5,9),(7,10)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,3),(2,6),(4,7),(5,10),(8,9)]=>[(1,6),(2,3),(4,7),(5,9),(8,10)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,2),(3,6),(4,7),(5,10),(8,9)]=>[(1,6),(2,3),(4,7),(5,8),(9,10)]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[(1,2),(3,5),(4,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,7),(6,8),(9,10)]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[(1,3),(2,5),(4,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,7),(6,9),(8,10)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,5),(3,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,8),(6,9),(7,10)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,5),(2,4),(3,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,8),(6,10),(7,9)]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[(1,6),(2,4),(3,7),(5,10),(8,9)]=>[(1,6),(2,3),(4,8),(5,10),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,7),(2,4),(3,6),(5,10),(8,9)]=>[(1,6),(2,3),(4,10),(5,8),(7,9)]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[(1,8),(2,4),(3,6),(5,10),(7,9)]=>[(1,6),(2,4),(3,10),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,9),(2,4),(3,6),(5,10),(7,8)]=>[(1,6),(2,10),(3,4),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,4),(3,6),(5,9),(7,8)]=>[(1,10),(2,6),(3,4),(5,8),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,10),(2,3),(4,6),(5,9),(7,8)]=>[(1,10),(2,6),(3,4),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,9),(2,3),(4,6),(5,10),(7,8)]=>[(1,6),(2,10),(3,4),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,8),(2,3),(4,6),(5,10),(7,9)]=>[(1,6),(2,4),(3,10),(5,7),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,7),(2,3),(4,6),(5,10),(8,9)]=>[(1,6),(2,3),(4,10),(5,7),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,6),(2,3),(4,7),(5,10),(8,9)]=>[(1,6),(2,3),(4,7),(5,10),(8,9)]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[(1,5),(2,3),(4,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,7),(6,10),(8,9)]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[(1,4),(2,3),(5,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,6),(7,10),(8,9)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,3),(2,4),(5,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,6),(7,9),(8,10)]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[(1,2),(3,4),(5,7),(6,10),(8,9)]=>[(1,5),(2,3),(4,6),(7,8),(9,10)]=>[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]
[(1,2),(3,4),(5,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,6),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,3),(2,4),(5,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,6),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,4),(2,3),(5,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,6),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,5),(2,3),(4,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,7),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,6),(2,3),(4,8),(5,10),(7,9)]=>[(1,6),(2,4),(3,7),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,7),(2,3),(4,8),(5,10),(6,9)]=>[(1,6),(2,5),(3,7),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,7),(5,10),(6,9)]=>[(1,6),(2,5),(3,10),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,7),(5,10),(6,8)]=>[(1,6),(2,10),(3,5),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,3),(4,7),(5,9),(6,8)]=>[(1,10),(2,6),(3,5),(4,7),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,4),(3,7),(5,9),(6,8)]=>[(1,10),(2,6),(3,5),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,7),(5,10),(6,8)]=>[(1,6),(2,10),(3,5),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,7),(5,10),(6,9)]=>[(1,6),(2,5),(3,10),(4,8),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,4),(3,8),(5,10),(6,9)]=>[(1,6),(2,5),(3,8),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,4),(3,8),(5,10),(7,9)]=>[(1,6),(2,4),(3,8),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,4),(3,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,8),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,5),(3,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,8),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,5),(4,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,7),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,5),(4,8),(6,10),(7,9)]=>[(1,5),(2,4),(3,7),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,6),(4,8),(5,10),(7,9)]=>[(1,6),(2,4),(3,7),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,6),(4,8),(5,10),(7,9)]=>[(1,6),(2,4),(3,7),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,6),(3,8),(5,10),(7,9)]=>[(1,6),(2,4),(3,8),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,6),(3,8),(4,10),(7,9)]=>[(1,7),(2,4),(3,8),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,5),(3,8),(4,10),(7,9)]=>[(1,7),(2,4),(3,8),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,5),(3,8),(4,10),(6,9)]=>[(1,7),(2,5),(3,8),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,7),(4,10),(6,9)]=>[(1,7),(2,5),(3,10),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,7),(4,10),(6,8)]=>[(1,7),(2,10),(3,5),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,5),(3,7),(4,9),(6,8)]=>[(1,10),(2,7),(3,5),(4,8),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,6),(3,7),(4,9),(5,8)]=>[(1,10),(2,7),(3,6),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,7),(4,10),(5,8)]=>[(1,7),(2,10),(3,6),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,7),(4,10),(5,9)]=>[(1,7),(2,6),(3,10),(4,8),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,8),(4,10),(5,9)]=>[(1,7),(2,6),(3,8),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,7),(3,8),(4,10),(5,9)]=>[(1,7),(2,6),(3,8),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,7),(3,8),(4,10),(6,9)]=>[(1,7),(2,5),(3,8),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,7),(3,8),(5,10),(6,9)]=>[(1,6),(2,5),(3,8),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,7),(4,8),(5,10),(6,9)]=>[(1,6),(2,5),(3,7),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,7),(4,8),(5,10),(6,9)]=>[(1,6),(2,5),(3,7),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,8),(4,7),(5,10),(6,9)]=>[(1,6),(2,5),(3,8),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,8),(4,7),(5,10),(6,9)]=>[(1,6),(2,5),(3,9),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,8),(3,7),(5,10),(6,9)]=>[(1,6),(2,5),(3,9),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,8),(3,7),(4,10),(6,9)]=>[(1,7),(2,5),(3,9),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,8),(3,7),(4,10),(5,9)]=>[(1,7),(2,6),(3,9),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,6),(4,10),(5,9)]=>[(1,7),(2,6),(3,9),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,6),(4,10),(5,9)]=>[(1,7),(2,6),(3,10),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,6),(4,10),(5,8)]=>[(1,7),(2,10),(3,6),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,6),(4,9),(5,8)]=>[(1,10),(2,7),(3,6),(4,9),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,6),(4,9),(5,7)]=>[(1,10),(2,7),(3,9),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,6),(4,10),(5,7)]=>[(1,7),(2,10),(3,9),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,6),(4,10),(5,7)]=>[(1,7),(2,9),(3,10),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,6),(4,10),(5,8)]=>[(1,7),(2,9),(3,6),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,9),(3,7),(4,10),(5,8)]=>[(1,7),(2,9),(3,6),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,9),(3,7),(4,10),(6,8)]=>[(1,7),(2,9),(3,5),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,9),(3,7),(5,10),(6,8)]=>[(1,6),(2,9),(3,5),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,9),(4,7),(5,10),(6,8)]=>[(1,6),(2,9),(3,5),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,9),(4,7),(5,10),(6,8)]=>[(1,6),(2,8),(3,5),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,10),(4,7),(5,9),(6,8)]=>[(1,8),(2,6),(3,5),(4,7),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,10),(4,7),(5,9),(6,8)]=>[(1,9),(2,6),(3,5),(4,7),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,10),(3,7),(5,9),(6,8)]=>[(1,9),(2,6),(3,5),(4,8),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,10),(3,7),(4,9),(6,8)]=>[(1,9),(2,7),(3,5),(4,8),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,10),(3,7),(4,9),(5,8)]=>[(1,9),(2,7),(3,6),(4,8),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,6),(4,9),(5,8)]=>[(1,9),(2,7),(3,6),(4,10),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,6),(4,9),(5,7)]=>[(1,9),(2,7),(3,10),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,6),(4,8),(5,7)]=>[(1,9),(2,10),(3,7),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,9),(3,6),(4,8),(5,7)]=>[(1,10),(2,9),(3,7),(4,6),(5,8)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,9),(3,7),(4,8),(5,6)]=>[(1,10),(2,9),(3,7),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,7),(4,8),(5,6)]=>[(1,9),(2,10),(3,7),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,7),(4,9),(5,6)]=>[(1,9),(2,7),(3,10),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,8),(4,9),(5,6)]=>[(1,9),(2,7),(3,8),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,10),(3,8),(4,9),(5,7)]=>[(1,9),(2,7),(3,8),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,10),(3,8),(4,9),(6,7)]=>[(1,9),(2,7),(3,8),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,10),(3,8),(5,9),(6,7)]=>[(1,9),(2,6),(3,8),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,10),(4,8),(5,9),(6,7)]=>[(1,9),(2,6),(3,7),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,10),(4,8),(5,9),(6,7)]=>[(1,8),(2,6),(3,7),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,9),(4,8),(5,10),(6,7)]=>[(1,6),(2,8),(3,7),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,9),(4,8),(5,10),(6,7)]=>[(1,6),(2,9),(3,7),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,9),(3,8),(5,10),(6,7)]=>[(1,6),(2,9),(3,8),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,9),(3,8),(4,10),(6,7)]=>[(1,7),(2,9),(3,8),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,9),(3,8),(4,10),(5,7)]=>[(1,7),(2,9),(3,8),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,8),(4,10),(5,6)]=>[(1,7),(2,9),(3,8),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,7),(4,10),(5,6)]=>[(1,7),(2,9),(3,10),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,7),(4,10),(5,6)]=>[(1,7),(2,10),(3,9),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,7),(4,9),(5,6)]=>[(1,10),(2,7),(3,9),(4,8),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,8),(4,9),(5,6)]=>[(1,10),(2,7),(3,8),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,8),(4,10),(5,6)]=>[(1,7),(2,10),(3,8),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,9),(4,10),(5,6)]=>[(1,7),(2,8),(3,10),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,9),(4,10),(5,6)]=>[(1,7),(2,8),(3,9),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,8),(3,9),(4,10),(5,7)]=>[(1,7),(2,8),(3,9),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,8),(3,9),(4,10),(6,7)]=>[(1,7),(2,8),(3,9),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,8),(3,9),(5,10),(6,7)]=>[(1,6),(2,8),(3,9),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,8),(4,9),(5,10),(6,7)]=>[(1,6),(2,7),(3,9),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,8),(4,9),(5,10),(6,7)]=>[(1,6),(2,7),(3,8),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,7),(4,9),(5,10),(6,8)]=>[(1,6),(2,7),(3,5),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,7),(4,9),(5,10),(6,8)]=>[(1,6),(2,7),(3,5),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,7),(3,9),(5,10),(6,8)]=>[(1,6),(2,8),(3,5),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,7),(3,9),(4,10),(6,8)]=>[(1,7),(2,8),(3,5),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,7),(3,9),(4,10),(5,8)]=>[(1,7),(2,8),(3,6),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,9),(4,10),(5,8)]=>[(1,7),(2,8),(3,6),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,9),(4,10),(5,7)]=>[(1,7),(2,8),(3,10),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,8),(4,10),(5,7)]=>[(1,7),(2,10),(3,8),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,6),(3,8),(4,9),(5,7)]=>[(1,10),(2,7),(3,8),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,5),(3,8),(4,9),(6,7)]=>[(1,10),(2,7),(3,8),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,8),(4,10),(6,7)]=>[(1,7),(2,10),(3,8),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,9),(4,10),(6,7)]=>[(1,7),(2,8),(3,10),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,7),(2,5),(3,9),(4,10),(6,8)]=>[(1,7),(2,8),(3,5),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,5),(3,9),(4,10),(7,8)]=>[(1,7),(2,8),(3,4),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,5),(2,6),(3,9),(4,10),(7,8)]=>[(1,7),(2,8),(3,4),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,4),(2,6),(3,9),(5,10),(7,8)]=>[(1,6),(2,8),(3,4),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,3),(2,6),(4,9),(5,10),(7,8)]=>[(1,6),(2,7),(3,4),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,2),(3,6),(4,9),(5,10),(7,8)]=>[(1,6),(2,7),(3,4),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,2),(3,5),(4,9),(6,10),(7,8)]=>[(1,5),(2,7),(3,4),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,3),(2,5),(4,9),(6,10),(7,8)]=>[(1,5),(2,7),(3,4),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,5),(3,9),(6,10),(7,8)]=>[(1,5),(2,8),(3,4),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,5),(2,4),(3,9),(6,10),(7,8)]=>[(1,5),(2,8),(3,4),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,6),(2,4),(3,9),(5,10),(7,8)]=>[(1,6),(2,8),(3,4),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,7),(2,4),(3,9),(5,10),(6,8)]=>[(1,6),(2,8),(3,5),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,9),(5,10),(6,7)]=>[(1,6),(2,8),(3,10),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,8),(5,10),(6,7)]=>[(1,6),(2,10),(3,8),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,4),(3,8),(5,9),(6,7)]=>[(1,10),(2,6),(3,8),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,10),(2,3),(4,8),(5,9),(6,7)]=>[(1,10),(2,6),(3,7),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,8),(5,10),(6,7)]=>[(1,6),(2,10),(3,7),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,9),(5,10),(6,7)]=>[(1,6),(2,7),(3,10),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,7),(2,3),(4,9),(5,10),(6,8)]=>[(1,6),(2,7),(3,5),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,6),(2,3),(4,9),(5,10),(7,8)]=>[(1,6),(2,7),(3,4),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,5),(2,3),(4,9),(6,10),(7,8)]=>[(1,5),(2,7),(3,4),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,4),(2,3),(5,9),(6,10),(7,8)]=>[(1,5),(2,6),(3,4),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,3),(2,4),(5,9),(6,10),(7,8)]=>[(1,5),(2,6),(3,4),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,2),(3,4),(5,9),(6,10),(7,8)]=>[(1,5),(2,6),(3,4),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[(1,3),(2,4),(5,10),(6,9),(7,8)]=>[(1,6),(2,5),(3,4),(7,9),(8,10)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[(1,5),(2,3),(4,10),(6,9),(7,8)]=>[(1,7),(2,5),(3,4),(6,10),(8,9)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,6),(2,3),(4,10),(5,9),(7,8)]=>[(1,7),(2,6),(3,4),(5,10),(8,9)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,7),(2,3),(4,10),(5,9),(6,8)]=>[(1,7),(2,6),(3,5),(4,10),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,8),(2,3),(4,10),(5,9),(6,7)]=>[(1,7),(2,6),(3,10),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,9),(2,3),(4,10),(5,8),(6,7)]=>[(1,7),(2,10),(3,6),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,10),(2,4),(3,9),(5,8),(6,7)]=>[(1,10),(2,8),(3,6),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,9),(2,4),(3,10),(5,8),(6,7)]=>[(1,8),(2,10),(3,6),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,8),(2,4),(3,10),(5,9),(6,7)]=>[(1,8),(2,6),(3,10),(4,5),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,7),(2,4),(3,10),(5,9),(6,8)]=>[(1,8),(2,6),(3,5),(4,10),(7,9)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,6),(2,4),(3,10),(5,9),(7,8)]=>[(1,8),(2,6),(3,4),(5,10),(7,9)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,4),(3,10),(6,9),(7,8)]=>[(1,8),(2,5),(3,4),(6,10),(7,9)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,4),(2,5),(3,10),(6,9),(7,8)]=>[(1,8),(2,5),(3,4),(6,9),(7,10)]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[(1,3),(2,5),(4,10),(6,9),(7,8)]=>[(1,7),(2,5),(3,4),(6,9),(8,10)]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[(1,2),(3,5),(4,10),(6,9),(7,8)]=>[(1,7),(2,5),(3,4),(6,8),(9,10)]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[(1,2),(3,6),(4,10),(5,9),(7,8)]=>[(1,7),(2,6),(3,4),(5,8),(9,10)]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[(1,3),(2,6),(4,10),(5,9),(7,8)]=>[(1,7),(2,6),(3,4),(5,9),(8,10)]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[(1,4),(2,6),(3,10),(5,9),(7,8)]=>[(1,8),(2,6),(3,4),(5,9),(7,10)]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[(1,5),(2,6),(3,10),(4,9),(7,8)]=>[(1,8),(2,7),(3,4),(5,9),(6,10)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,6),(2,5),(3,10),(4,9),(7,8)]=>[(1,8),(2,7),(3,4),(5,10),(6,9)]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[(1,7),(2,5),(3,10),(4,9),(6,8)]=>[(1,8),(2,7),(3,5),(4,10),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,8),(2,5),(3,10),(4,9),(6,7)]=>[(1,8),(2,7),(3,10),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,9),(2,5),(3,10),(4,8),(6,7)]=>[(1,8),(2,10),(3,7),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,5),(3,9),(4,8),(6,7)]=>[(1,10),(2,8),(3,7),(4,5),(6,9)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,10),(2,6),(3,9),(4,8),(5,7)]=>[(1,10),(2,8),(3,7),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,6),(3,10),(4,8),(5,7)]=>[(1,8),(2,10),(3,7),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,6),(3,10),(4,9),(5,7)]=>[(1,8),(2,7),(3,10),(4,6),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,6),(3,10),(4,9),(5,8)]=>[(1,8),(2,7),(3,6),(4,10),(5,9)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,7),(3,10),(4,9),(5,8)]=>[(1,8),(2,7),(3,6),(4,9),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,7),(3,10),(4,9),(6,8)]=>[(1,8),(2,7),(3,5),(4,9),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,7),(3,10),(5,9),(6,8)]=>[(1,8),(2,6),(3,5),(4,9),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,7),(4,10),(5,9),(6,8)]=>[(1,7),(2,6),(3,5),(4,9),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,7),(4,10),(5,9),(6,8)]=>[(1,7),(2,6),(3,5),(4,8),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,8),(4,10),(5,9),(6,7)]=>[(1,7),(2,6),(3,8),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,8),(4,10),(5,9),(6,7)]=>[(1,7),(2,6),(3,9),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,8),(3,10),(5,9),(6,7)]=>[(1,8),(2,6),(3,9),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,8),(3,10),(4,9),(6,7)]=>[(1,8),(2,7),(3,9),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,8),(3,10),(4,9),(5,7)]=>[(1,8),(2,7),(3,9),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,8),(3,10),(4,9),(5,6)]=>[(1,8),(2,7),(3,9),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,7),(3,10),(4,9),(5,6)]=>[(1,8),(2,7),(3,10),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,7),(3,10),(4,8),(5,6)]=>[(1,8),(2,10),(3,7),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,7),(3,9),(4,8),(5,6)]=>[(1,10),(2,8),(3,7),(4,9),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>[(1,10),(2,8),(3,9),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,8),(3,10),(4,7),(5,6)]=>[(1,8),(2,10),(3,9),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,9),(3,10),(4,7),(5,6)]=>[(1,8),(2,9),(3,10),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,9),(3,10),(4,8),(5,6)]=>[(1,8),(2,9),(3,7),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,6),(2,9),(3,10),(4,8),(5,7)]=>[(1,8),(2,9),(3,7),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,5),(2,9),(3,10),(4,8),(6,7)]=>[(1,8),(2,9),(3,7),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,4),(2,9),(3,10),(5,8),(6,7)]=>[(1,8),(2,9),(3,6),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,3),(2,9),(4,10),(5,8),(6,7)]=>[(1,7),(2,9),(3,6),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,2),(3,9),(4,10),(5,8),(6,7)]=>[(1,7),(2,8),(3,6),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[(1,3),(2,10),(4,9),(5,8),(6,7)]=>[(1,9),(2,7),(3,6),(4,5),(8,10)]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[(1,4),(2,10),(3,9),(5,8),(6,7)]=>[(1,9),(2,8),(3,6),(4,5),(7,10)]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[(1,5),(2,10),(3,9),(4,8),(6,7)]=>[(1,9),(2,8),(3,7),(4,5),(6,10)]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[(1,6),(2,10),(3,9),(4,8),(5,7)]=>[(1,9),(2,8),(3,7),(4,6),(5,10)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,7),(2,10),(3,9),(4,8),(5,6)]=>[(1,9),(2,8),(3,7),(4,10),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,8),(2,10),(3,9),(4,7),(5,6)]=>[(1,9),(2,8),(3,10),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,9),(2,10),(3,8),(4,7),(5,6)]=>[(1,9),(2,10),(3,8),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]]]]]]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[]]],[]]]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[[[]]]],[]]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[[[]]],[]]]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[]]]]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[[],[[]]],[]]]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[[]]]],[]]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]]]
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[[[]],[]]]]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[],[]]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[[[]],[]]]]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]]]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[]]]]]
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[]]]
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[]]
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[]]]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[]],[]]]]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]]],[]]]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[],[]]]],[]]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[],[]],[[]]]
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[[]]]]
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[]],[],[]]
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[[]]]]
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[]],[[]]]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[[],[]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[]]]
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[]],[]]
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[[],[],[]]]
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[[[],[]]]]]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[],[]],[]]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[[[],[]]]]]
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[],[],[]]]
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[]]]]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[]],[],[]]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[[],[[]]]]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]]]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[],[[]]]]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[],[]]]]]]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]],[]]]
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[]]
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]],[]]]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[]]]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[]],[]]]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[]]],[]]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[[]]]
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[[],[],[]]]]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[]]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[[],[],[]]]]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[[]]]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[]]]]]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[],[]]]
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[]],[]]
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[],[]]]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]]],[]]]]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]]],[]]]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[]]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[[]]],[[]]]
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]]]]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]]],[],[]]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]]]]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]]],[[]]]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[]]]]]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]],[],[]]]
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[],[]],[]],[]]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[[],[]]]
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[],[[]]]]]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[],[[]],[]]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[[],[[]]]]]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[],[[],[]]]
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]]]]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[],[]]],[],[]]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[[[]]]]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[]]]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[],[[[]]]]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]]]]]]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[]]]
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[[]]],[]]
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[]]]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[],[]]]]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]]]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[]]],[]]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[],[[]]]
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[[],[]]]]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[]],[],[],[]]
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[],[[],[]]]]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[]],[],[[]]]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[[],[[[]]]]]]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[]]]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]]],[]]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[[[]],[]]]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[[[[]]]]]]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[]]],[]]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[[[[]]]]]]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]]]
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[],[]]]]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]]],[],[],[]]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[[[],[]]]]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]]],[],[[]]]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[[],[]]]]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]]]]]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]]],[],[]]]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[]]],[]],[]]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[],[]]]
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[[[]]]]]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[]]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[],[[[]]]]]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[]]]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[]]]]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[],[]]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[[]]]]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[]]]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[[]]]]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[[]]]]]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[]]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[[[[]]]]]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]]],[[],[]]]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[]]]]
Map
reverse
Description
The reverse of a perfect matching of $\{1,2,...,n\}$.
This is the perfect matching obtained by replacing $i$ by $n+1-i$.
This is the perfect matching obtained by replacing $i$ by $n+1-i$.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
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