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 (7.3.0) (judge verdict: Accepted)

A, B = map(int, input().split())
a = set([])
b = set([])
n = 1
while n**2 <= max(A, B):
  if A%n == 0 and n**2 <= A:
    a.add(n)
    a.add(A//n)
  if B%n == 0 and n**2 <= B:
    b.add(n)
    b.add(B//n)
  n += 1
ab = a & b
ab.discard(1)
ab = list(ab)
answer = 0
for i, n in enumerate(ab):
  prime = True
  for j, m in enumerate(ab):
    if i != j and n%m == 0:
      prime = False
      break
  if prime:
    answer += 1
print(answer+1)