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)

# start 21:14
a, b = [int(item) for item in input().split()]

# 素因数リスト
import math
def factor(num):
    divisor_list = [1]
    divisor = 2
    max_prime = int(math.sqrt(num))
    while max_prime >= divisor:
        if num % divisor == 0:
            divisor_list.append(divisor)
            num //= divisor

        else:
            divisor += 1
    divisor_list.append(num)
    return divisor_list

def gcd(a, b):
    if b == 0: return a
    return gcd(b, a % b)

cd_list = set(factor(gcd(a, b)))

print(len(cd_list))