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

inputFormat

input are integers.

• 1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

outputFormat

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

样例

1 2019

1