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.