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 $y = \alpha x$.

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.

Constraints

• All values in input are integers.
• $1 \leq A, B \leq 10^{12}$

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.

见题面 Input 部分

见题面 Output 部分