=>

[(1,2)]=>[(1,2)]=>[2,1]=>1 [(1,2),(3,4)]=>[(1,2),(3,4)]=>[2,1,4,3]=>101 [(1,3),(2,4)]=>[(1,3),(2,4)]=>[3,4,1,2]=>100 [(1,4),(2,3)]=>[(1,4),(2,3)]=>[4,3,2,1]=>111 [(1,2),(3,4),(5,6)]=>[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>10101 [(1,3),(2,4),(5,6)]=>[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>10100 [(1,4),(2,3),(5,6)]=>[(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>10111 [(1,5),(2,3),(4,6)]=>[(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>11010 [(1,6),(2,3),(4,5)]=>[(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>11110 [(1,6),(2,4),(3,5)]=>[(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>11010 [(1,5),(2,4),(3,6)]=>[(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>11001 [(1,4),(2,5),(3,6)]=>[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>10000 [(1,3),(2,5),(4,6)]=>[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>11000 [(1,2),(3,5),(4,6)]=>[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>10001 [(1,2),(3,6),(4,5)]=>[(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>11101 [(1,3),(2,6),(4,5)]=>[(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>11100 [(1,4),(2,6),(3,5)]=>[(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>11010 [(1,5),(2,6),(3,4)]=>[(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>10110 [(1,6),(2,5),(3,4)]=>[(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>11111 [(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>1010101 [(1,3),(2,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>1010100 [(1,4),(2,3),(5,6),(7,8)]=>[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>1010111 [(1,5),(2,3),(4,6),(7,8)]=>[(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>1011010 [(1,6),(2,3),(4,5),(7,8)]=>[(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>1011110 [(1,7),(2,3),(4,5),(6,8)]=>[(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>1101010 [(1,8),(2,3),(4,5),(6,7)]=>[(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>1111010 [(1,8),(2,4),(3,5),(6,7)]=>[(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>1111000 [(1,7),(2,4),(3,5),(6,8)]=>[(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>1101000 [(1,6),(2,4),(3,5),(7,8)]=>[(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>1011010 [(1,5),(2,4),(3,6),(7,8)]=>[(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>1011001 [(1,4),(2,5),(3,6),(7,8)]=>[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>1010000 [(1,3),(2,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>1011000 [(1,2),(3,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>1010001 [(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>1011101 [(1,3),(2,6),(4,5),(7,8)]=>[(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>1011100 [(1,4),(2,6),(3,5),(7,8)]=>[(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>1011010 [(1,5),(2,6),(3,4),(7,8)]=>[(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>1010110 [(1,6),(2,5),(3,4),(7,8)]=>[(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>1011111 [(1,7),(2,5),(3,4),(6,8)]=>[(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>1101110 [(1,8),(2,5),(3,4),(6,7)]=>[(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>1111110 [(1,8),(2,6),(3,4),(5,7)]=>[(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>1111100 [(1,7),(2,6),(3,4),(5,8)]=>[(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>1110101 [(1,6),(2,7),(3,4),(5,8)]=>[(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>1100100 [(1,5),(2,7),(3,4),(6,8)]=>[(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>1100110 [(1,4),(2,7),(3,5),(6,8)]=>[(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>1101000 [(1,3),(2,7),(4,5),(6,8)]=>[(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>1101000 [(1,2),(3,7),(4,5),(6,8)]=>[(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>1101001 [(1,2),(3,8),(4,5),(6,7)]=>[(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>1111001 [(1,3),(2,8),(4,5),(6,7)]=>[(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>1111000 [(1,4),(2,8),(3,5),(6,7)]=>[(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>1111000 [(1,5),(2,8),(3,4),(6,7)]=>[(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>1110110 [(1,6),(2,8),(3,4),(5,7)]=>[(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>1101100 [(1,7),(2,8),(3,4),(5,6)]=>[(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>1011100 [(1,8),(2,7),(3,4),(5,6)]=>[(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>1111101 [(1,8),(2,7),(3,5),(4,6)]=>[(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>1110101 [(1,7),(2,8),(3,5),(4,6)]=>[(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>1010100 [(1,6),(2,8),(3,5),(4,7)]=>[(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>1100110 [(1,5),(2,8),(3,6),(4,7)]=>[(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>1100100 [(1,4),(2,8),(3,6),(5,7)]=>[(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>1111000 [(1,3),(2,8),(4,6),(5,7)]=>[(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>1101000 [(1,2),(3,8),(4,6),(5,7)]=>[(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>1101001 [(1,2),(3,7),(4,6),(5,8)]=>[(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>1100101 [(1,3),(2,7),(4,6),(5,8)]=>[(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>1100100 [(1,4),(2,7),(3,6),(5,8)]=>[(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>1110010 [(1,5),(2,7),(3,6),(4,8)]=>[(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>1100010 [(1,6),(2,7),(3,5),(4,8)]=>[(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>1100010 [(1,7),(2,6),(3,5),(4,8)]=>[(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>1110011 [(1,8),(2,6),(3,5),(4,7)]=>[(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>1110110 [(1,8),(2,5),(3,6),(4,7)]=>[(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>1100100 [(1,7),(2,5),(3,6),(4,8)]=>[(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>1100010 [(1,6),(2,5),(3,7),(4,8)]=>[(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>1010001 [(1,5),(2,6),(3,7),(4,8)]=>[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>1000000 [(1,4),(2,6),(3,7),(5,8)]=>[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>1100000 [(1,3),(2,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>1010000 [(1,2),(3,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>1000001 [(1,2),(3,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>1100001 [(1,3),(2,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>1101000 [(1,4),(2,5),(3,7),(6,8)]=>[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>1100000 [(1,5),(2,4),(3,7),(6,8)]=>[(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>1101001 [(1,6),(2,4),(3,7),(5,8)]=>[(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>1110000 [(1,7),(2,4),(3,6),(5,8)]=>[(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>1110010 [(1,8),(2,4),(3,6),(5,7)]=>[(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>1111000 [(1,8),(2,3),(4,6),(5,7)]=>[(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>1101010 [(1,7),(2,3),(4,6),(5,8)]=>[(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>1100110 [(1,6),(2,3),(4,7),(5,8)]=>[(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>1010010 [(1,5),(2,3),(4,7),(6,8)]=>[(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>1101010 [(1,4),(2,3),(5,7),(6,8)]=>[(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>1000111 [(1,3),(2,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>1000100 [(1,2),(3,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>1000101 [(1,2),(3,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>1110101 [(1,3),(2,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>1110100 [(1,4),(2,3),(5,8),(6,7)]=>[(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>1110111 [(1,5),(2,3),(4,8),(6,7)]=>[(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>1111010 [(1,6),(2,3),(4,8),(5,7)]=>[(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>1111010 [(1,7),(2,3),(4,8),(5,6)]=>[(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>1111010 [(1,8),(2,3),(4,7),(5,6)]=>[(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>1111110 [(1,8),(2,4),(3,7),(5,6)]=>[(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>1111010 [(1,7),(2,4),(3,8),(5,6)]=>[(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>1111000 [(1,6),(2,4),(3,8),(5,7)]=>[(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>1111000 [(1,5),(2,4),(3,8),(6,7)]=>[(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>1111001 [(1,4),(2,5),(3,8),(6,7)]=>[(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>1110000 [(1,3),(2,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>1111000 [(1,2),(3,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>1110001 [(1,2),(3,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>1101001 [(1,3),(2,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>1111000 [(1,4),(2,6),(3,8),(5,7)]=>[(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>1101000 [(1,5),(2,6),(3,8),(4,7)]=>[(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>1100100 [(1,6),(2,5),(3,8),(4,7)]=>[(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>1110101 [(1,7),(2,5),(3,8),(4,6)]=>[(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>1110100 [(1,8),(2,5),(3,7),(4,6)]=>[(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>1110110 [(1,8),(2,6),(3,7),(4,5)]=>[(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>1101110 [(1,7),(2,6),(3,8),(4,5)]=>[(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>1101101 [(1,6),(2,7),(3,8),(4,5)]=>[(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>1001100 [(1,5),(2,7),(3,8),(4,6)]=>[(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>1010100 [(1,4),(2,7),(3,8),(5,6)]=>[(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>1011000 [(1,3),(2,7),(4,8),(5,6)]=>[(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>1111000 [(1,2),(3,7),(4,8),(5,6)]=>[(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>1011001 [(1,2),(3,8),(4,7),(5,6)]=>[(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>1111101 [(1,3),(2,8),(4,7),(5,6)]=>[(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>1111100 [(1,4),(2,8),(3,7),(5,6)]=>[(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>1111010 [(1,5),(2,8),(3,7),(4,6)]=>[(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>1110110 [(1,6),(2,8),(3,7),(4,5)]=>[(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>1101110 [(1,7),(2,8),(3,6),(4,5)]=>[(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>1011110 [(1,8),(2,7),(3,6),(4,5)]=>[(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>1111111 [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>101010101 [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101