In [1]:
# I learned this command from https://math.stackexchange.com/questions/527182/is-there-a-database-of-cubic-graphs-on-the-web
L = [G for G in graphs.nauty_geng("12 -d3 -D3")]
len(L)
Out[1]:
94
In [2]:
L = [G for G in L if G.is_connected()]
len(L)
Out[2]:
85
In [3]:
L = [G for G in L if G.edge_connectivity() >= 3]
len(L)
Out[3]:
57
In [4]:
for G in L:
    print(G.adjacency_matrix().rows())

[(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0), (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1), (1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0), (0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0), (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1), (1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0), (0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1), (0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0), (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1), (0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1), (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1), (1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0), (0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0), (1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0), (0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0), (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1), (1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0), (0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0), (0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0)]
[(0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0), (0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1), (0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1), (1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0), (0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1), (0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0), (0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0), (1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0), (0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0)]