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: Accepted)

def GCD(a:int , b: int) -> int:
    return a if b == 0 else GCD(b, a % b)

from collections import defaultdict
def factorize(n: int) -> dict:
    f = defaultdict(int)
    tmp_n = n
    p = 2
    while tmp_n > 1 and p * p < n:
        while tmp_n % p == 0:
            f[p] += 1
            tmp_n = tmp_n // p
        p += 1 if p == 2 else 2

    if tmp_n != 1:
        f[tmp_n] += 1
    return f

a, b = map(int, input().split())
factors = factorize(GCD(a, b))

ans = len(factors) + 1

print(ans)