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)

import fractions
import math
from collections import deque
A,B = list(map(int,input().split()))
gcd = fractions.gcd(A,B)
def gcd_another(N):
    R = deque()
    for i in range(1,math.ceil(int(N**0.5))+1):
        if N % i == 0:
            R.append(i)
            if i != N // i:
                R.append(N//i)
    R = list(R)
    R.sort()
    return R
C = gcd_another(gcd)
C.pop(0)
total = 1
while C != []:
    i = C[0]
    C = [j for j in C if j % i != 0]
    total += 1
print(total)