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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Buffer([]byte{}, 1000000000)
	sc.Scan()
	line := sc.Text()
	sped := strings.Split(line, " ")
	a := mustAtoi(sped[0])
	b := mustAtoi(sped[1])

	faca := factorize(math.Sqrt(float64(a)), a, 2)
	facb := factorize(math.Sqrt(float64(b)), b, 2)
	res := []int{}
	for i := range faca {
		_, ok := facb[i]
		if ok {
			res = append(res, i)
		}
	}
	fmt.Printf("%v", len(res))
}

func factorize(maxDivide float64, num int, divide int) map[int]struct{} {
	var nums = map[int]struct{}{1: struct{}{}}
	for float64(divide) < maxDivide {
		mod := num % divide
		if mod == 0 {
			nums[divide] = struct{}{}
			num = num / divide
			continue
		}
		divide++
	}
	if num > 1 {
		nums[num] = struct{}{}
	}
	return nums
}

func mustAtoi(s string) int {
	i, err := strconv.Atoi(s)
	if err != nil {
		panic(err)
	}
	return i
}