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)

import math
A, B = [int(i) for i in input().split()]
# 公約数リストを作る
C = [1]
for i in range(2, int(math.sqrt(max(A, B)))+1):
    if A%i == 0 and B%i == 0:
        C.append(i)
        if A == B and i != A//i:
            C.append(A//i)
        else:
            if i != A//i and B%(A//i) == 0:
                C.append(A//i)
            if i != B//i and A%(B//i) == 0:
                C.append(B//i)
C.sort()
for i in range(len(C)-1, 0, -1):
    for j in range(1, i):
        if C[i]%C[j] == 0:
            del C[i]
            break
print(len(C))