Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

def main():
  A, B = map(int,input().split())

  # ABが互いにそなら答えは１

  ans = 0
  import fractions as math

  if math.gcd(A,B) == 1:
    ans = 1
  else:
    # 公約数を求める
    cdlist =[]

    for i in range(1, min(A,B) + 1):
      if A % i == 0 and B % i == 0:
        cdlist.append(i)

    # print(cdlist)

    for i,cd1 in enumerate(cdlist):
      for cd2 in cdlist[i+1:]:
        # print(cd1,cd2)
        if math.gcd(cd1,cd2) == 1:
          ans += 1

  print(ans)

main()