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: Wrong Answer)

def solve(x, y):
  if x<y:
    x, y = y, x
  cd=[]
  for i in range(2, int(y**0.5)+1):
    if x%i==0 and y%i==0:
      flag=True
      for z in cd:
        if i%z==0:
          flag=False
          break
      if flag:
      	cd.append(i)
      tmp=y//i
      if x%tmp==0:
        flag=True
        for z in cd:
          if tmp%z==0:
            flag=False
            break
        if flag:
      	  cd.append(tmp)
  return len(cd)+1
  
A, B=map(int, input().split())
print(solve(A, B))