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)

import math

def pf(n):
    ans=[1]
    i=2
    if(n%i==0):
        while(n%2==0):
            n = n/i
        ans.append(i)
    i+=1
    while(i<math.sqrt(n) and n!=1):
        if (n%i==0):
            while(n%i==0):
                n=n/i
            ans.append(i)
        i+=2
    if(n!=1):
        ans.append(n)
    return set(ans)

a,b = map(int,input().split())
pfa=pf(a)
pfb=pf(b)
a=0
for i in pfa:
    if(i in pfb):
        a+=1
print(a)