from collections import defaultdict

def gcd(a, b):
   if a == 0:
       return b
   return gcd(b % a, a)

def number_of_ways(numerators, denominators):
   if len(numerators) != len(denominators):
       # return 0 for uneven/invalid pairs of numerators and denominators
       return 0

   m = defaultdict(set)

   for i in xrange(0, len(numerators)):
       new_n = numerators[i]
       new_d = denominators[i]
       if denominators[i] >= numerators[i]:
           common = gcd(numerators[i], denominators[i])
           new_n = numerators[i] / common
           new_d = denominators[i] / common
       m[(new_n, new_d)].add(i)

   t = 0
   s = 0
   for (n, d) in m.keys():
       if n == d - n:
           t += len(m[n, d])*(len(m[n, d])-1) / 2
       elif (d-n, d) in m:
           s += len(m[n, d]) * len(m[d - n, d])

   return t + s / 2

if __name__ == "__main__":
   X = [1, 1, 2]
   Y = [3, 2, 3]
   print number_of_ways(X, Y) == 1

   X = [1, 1, 1]
   Y = [2, 2, 2]
   print number_of_ways(X, Y) == 3

   X = [1, 2, 3, 1, 2, 12, 8, 4]
   Y = [5, 10, 15, 2, 4, 15, 10, 5]
   print number_of_ways(X, Y) == 10