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 PyPy3 (2.4.0) (judge verdict: Accepted)

#!/usr/bin/env python
# -*- coding: utf-8 -*-


# 最大公約数
def gcd(a, b):
  while b != 0:
    a, b = b, a % b

  return a


# 素因数分解
def primes(v):
  ps = []

  for i in range(2, int(v ** 0.5) + 1):
    if i ** 2 > v:
      break

    if v % i == 0:
      ps.append([i, 1])
      v //= i

      while v % i == 0:
        ps[-1][1] += 1
        v //= i

  if v > 1:
    ps.append([v, 1])

  return ps


def main():
  a, b = map(int, input().split())
  g = gcd(a, b)
  print(len(primes(g)) + 1)


if __name__ == '__main__':
  main()