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

namespace AtCoder
{
    class Program
    {
        static List<int> GetDivisor(int a, int b)
        {
            int minValue = Math.Min(a, b);
            List<int> divisors = new List<int>();
            for (int i = 1; i <= minValue; i++)
            {
                if (a % i == 0 && b % i == 0)
                {
                    divisors.Add(i);
                }
            }

            return divisors;
        }

        static void Add(ref List<Disjoint> res, ref List<int> res2, int div0, int div1)
        {
            List<int> getDivisor = GetDivisor(div0, div1);
            if (getDivisor.Count == 1 && getDivisor[0] == 1)
            {
                foreach (Disjoint disjoint in res)
                {
                    if (disjoint.IsExist(div0, div1))
                    {
                        res2.Add(div0);
                        res2.Add(div1);
                        return;
                    }
                }

                Disjoint newJoint = new Disjoint(div0, div1);
                res.Add(newJoint);
            }
        }

        public class Disjoint
        {
            public int div0;
            public int div1;

            public Disjoint(int add0, int add1)
            {
                div0 = Math.Min(add0, add1);
                div1 = Math.Max(add0, add1);
            }

            public bool IsExist(int add0, int add1)
            {
                if(div0 == Math.Min(add0, add1) && div1 == Math.Max(add0, add1))
                {
                    return true;
                }

                return false;
            }
        }

        static void Main(string[] args)
        {
            int[] numbers = Console.ReadLine().Split().Select(int.Parse).ToArray();

            List<int> divisors = GetDivisor(numbers[0], numbers[1]);
            List<int> getDivisor = new List<int>();
            List<Disjoint> result = new List<Disjoint>();
            List<int> result2 = new List<int>();

            int div0 = 0;
            int div1 = 0;

            for (int i = 0;i < divisors.Count;i++)
            {
                div0 = divisors[i];
                for(int j = 0;j < divisors.Count;j++)
                {
                    div1 = divisors[j];

                    if(div0 != div1)
                    {
                        getDivisor = GetDivisor(div0, div1);
                        if (getDivisor.Count == 1 && getDivisor[0] == 1)
                        {
                            Add(ref result, ref result2, div0, div1);
                        }
                    }
                }
            }

            Console.WriteLine(result2.Distinct().ToList().Count);
        }
    }
}