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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

func readString() string {
	sc.Scan()
	return sc.Text()
}

func readInt64() int64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return int64(i)
}

func readfloat64() float64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return float64(i)
}

func abs(a int) int {
	if a < 0 {
		return a * -1
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func main() {
	sc.Split(bufio.ScanWords)
	a, b := readInt(), readInt()

	if a < b {
		a, b = b, a
	}
	gcd := gcd(a, b)

	count := 0
	for i := 1; i*i <= gcd; i++ {
		if a%i == 0 && b%i == 0 && isPrime(i) {
			count++
		}
	}
	fmt.Println(count)
}

func gcd(x, y int) int {
	if y == 0 {
		return x
	}
	return gcd(y, x%y)
}

func isPrime(x int) bool {
	for i := 2; i*i <= x; i++ {
		if x%i == 0 {
			return false
		}
	}
	return true
}