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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace csharp
{
    class Program
    {
        private const float V = 1.0f;
        private const string Separator = " ";

        static int subfunc(ref int a, int v)
        {
            int ret = 0;

            while (a % v == 0)
            {
                ret++;
                a /= v;
            }

            return ret;
        }

        static Dictionary<int, int> soinsu(int a)
        {
            Dictionary<int, int> ret = new Dictionary<int, int>();

            ret.Add(1, 1);
            for (int i = 2; i <= a; i++)
            {
                int v = subfunc(ref a, v: i);
                if (v > 0) ret.Add(i, v);
            }

            return ret;
        }

        static void Main(string[] args)
        {
            string lineStr;
            lineStr = Console.ReadLine();

            int a = int.Parse(lineStr.Split(' ')[0]);
            int b = int.Parse(lineStr.Split(' ')[1]);

            Dictionary<int, int> aa = soinsu(a);
            Dictionary<int, int> bb = soinsu(b);
            var cc = aa.Where((v) => bb.ContainsKey(v.Key)).Select(selector: v => v.Key);

            //Console.WriteLine(string.Join(" ", aa));
            //Console.WriteLine(string.Join(" ", bb));
            //Console.WriteLine(string.Join(" ", cc));
            Console.WriteLine(cc.Count());
            return;
        }
    }
}