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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main(){
  var a, b, c int
  fmt.Scan(&a, &b)
  var l []int
  for i := 1; a >= i * i || b >= i*i; i++ {
    if a % i == 0 && b % i == 0 {
      l = append(l, i)
    }
  }
  for i := 0; i < len(l); i++ {
    if sosu(l[i]) {
      c++
    }
  }
  fmt.Println(c)
}

func sosu(n int) bool {
  if n == 1 {
    return true
  }
  for i := 2; n >= i*i; i++{
    if n % i == 0 {
      //fmt.Println(n, i)
      return false
    }
  }
  return true
}