from math import factorial
F = factorial
 
# a: (-1, -1)
# b: (-1, 0)
# c: (-1, 1)
# d: (0, 0)
# e: (0, 1)
# f: (1, 1)
 
N = 1
 
total_probability = 0
 
for a in range(N+1):
    for b in range(N-a+1):
        for c in range(N-a-b+1):
            for d in range(N-a-b-c+1):
                for e in range(N-a-b-c-d+1):
                    f = N-a-b-c-d-e
 
                    prob = (1/36)**a * (1/18)**b * (1/12)**c * (1/9)**d * (1/6)**e * (1/4)**f
                    combs = F(N)/(F(a)*F(b)*F(c)*F(d)*F(e)*F(f)) * 2**(b+c+e)
 
                    if a-c+f == 0:
                        total_probability += prob * combs
 
print(total_probability)
 

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