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: Runtime Error)

A, B = [int(s) for s in input().split(' ')]
limit = min(A, B)
p = [1] * (limit + 1)
p[0] = 0
p[1] = 0
primes = []
for i in range(2, limit + 1):
    if p[i] == 1:
        # prime
        primes.append(i)
        j = i + i
        while limit >= j:
            p[j] = 0
            j += i
    else:
        continue
d = dict() 
for pp in primes:
    count = 0
    while A % pp == 0 and B % pp == 0:
        count += 1
        A //= pp
        B //= pp
    if count > 0:
        d[pp] = count
print(1 + len(d.keys()))