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: Time Limit Exceeded)

import itertools

a,b = map(int,input().split())

def cf(x1,x2):
    cf=[]
    for i in range(1,min(x1,x2)+1):
        if x1 % i == 0 and x2 % i == 0:
            cf.append(i)
    return cf
  
def hogehoge(yakusu):
    is_ok = True
    m = len(yakusu)
    for i in range(m):
        c = yakusu[i]
        for j in range(i+1,m):
            d = yakusu[j]
            if len(cf(c,d)) > 1:
                is_ok = False            
    return is_ok

def hogehoge2(stuff):
    max_num = 1
    tmp_num = 1
    for L in range(2, len(stuff)+1):
        for subset in itertools.combinations(stuff, L):
            if len(subset) > tmp_num+1:
                return max_num

            #print(hogehoge(subset))
            if hogehoge(subset):
                max_num = len(subset)
                tmp_num = len(subset)
    return max_num
            

yakusu = cf(a,b)
max_num = hogehoge2(yakusu)
print(max_num)