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 static System.Console;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Xml;
using System.Diagnostics;

namespace ConsoleApplication1
{
    internal class Program
    {

        public static void Main(string[] args)
        {
            var nums = ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            long A = nums[0];
            long B = nums[1];
            WriteLine(factorize(gcd(A, B)).Count);
        }

        static long gcd(long x, long y)
        {
            return (y == 0) ? x : gcd(y, x % y);
        }

        static List<ValueTuple<long, int>> factorize(long n)
        {
            var list = new List<ValueTuple<long, int>>();
            list.Add(new ValueTuple<long, int>(1, 1));
            for (long i = 2; i * i < n; i++)
            {
                if (n%i != 0) continue;
                int divideCount = 0;
                while (n%i == 0)
                {
                    n /= i;
                    divideCount++;
                }
                list.Add(new ValueTuple<long, int>(i, divideCount));
            }
            if (n != 1) list.Add(new ValueTuple<long, int>(n, 1));
            return list;
        }
      
        public struct ValueTuple<T1, T2>{
          public T1 item1;
          public T2 item2;
          public ValueTuple(T1 a, T2 b){
            item1 = a;
            item2 = b;
          }
        }
    }
}