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;

namespace ABC142
{
    class D
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split();
            long A = long.Parse(input[0]);
            long B = long.Parse(input[1]);

            long N = CalcGCD(A, B);
            double sqrt = Math.Sqrt(N);

            long count = 1;
            long n = 2;

            bool isFirst = true;
            while (n <= sqrt)
            {
                if (N % n == 0)
                {
                    N /= n;
                    if (isFirst) { count++; isFirst = false; }
                }
                else
                {
                    isFirst = true; n++;
                }
            }
            if (N != 1) count++;
            Console.WriteLine(count);
        }

        static long CalcGCD(long a, long b)
        {
            if (b == 0) { return a; }
            return CalcGCD(b, a % b);
        }
    }
}