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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Numerics;

class Myon
{
    //chokudaiさんのコードをコピペ
    static Scanner cin;
    public Myon() { }
    public static int Main()
    {
        //Console.SetOut(new Printer(Console.OpenStandardOutput()));
        cin = new Scanner();
        new Myon().calc();
        Console.Read();

        return 0;
    }

    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
    public void calc()
    {
        long a = cin.nextLong();
        long b = cin.nextLong();

        long gcd2 = Gcd(a, b);
        int count = 0; //公約数のもつ素因数の数　ただし重複は数えない　12 なら 2(2^2 3 )だが3でない
        int temp = 1;
        long max = (long)Math.Sqrt(gcd2);
        
        while (gcd2 != 1)
        {
            temp++;
            if (gcd2 % temp == 0)
            {
                count++;
                while (gcd2 % temp == 0) gcd2 /= temp;
            }
            else if (temp > max) { count++; break; }
        }
        

        showL(count + 1);
    }


    

    public void backetSort(ref int[] a)
    {
        //max a << a.len に対して有効なソート
        //よってa = int[] とする
        long n = a.Length;
        var count = new int[n];
        var loc = new long[n];//loc[i] は i が終わる 位置 max index where c[index] = loc[i]
        for (long i = 0; i < n; i++) count[a[i]]++;
        loc[0] = count[0] - 1;
        for (long i = 0; i < n-1; i++) loc[i+1] = loc[i] + count[i+1]; 
        long index = 0;

        for(int i = 0; i < n; i++)
        {
            while (index <= loc[i]) a[index++] = i; //incex <= loc[i] == index < loc[i] + 1
        }
    }

    public static void showL(long n) { Console.WriteLine(n); }
    public static void showL(string s) { Console.WriteLine(s); }
}

class Printer : StreamWriter
{
    public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
    public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { }
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        while (i >= s.Length)
        {
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
        }
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }

}