p02900 AtCoder Beginner Contest 142 - Disjoint Set of Common Divisors
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.

Examples

Input

12 18


Output

3


Input

420 660


Output

4


Input

1 2019


Output

1
```python
import fractions

a,b=map(int,input().split())
g=fractions.gcd(a,b)
#print(g)
ans=1
i=2
while i*i<=g:
    if(g%i==0):
        ans+=1
        while g%i==0:
            g/=i
    i=i+1
if(g!=1):ans+=1
print(ans)
```