Problem:
Score : 300 points

Problem Statement

Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.

Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Constraints

1 \leq K \leq 200

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the value of \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.

Sample Input 1

2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

200

Sample Output 2

10813692

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;

namespace C_Sum_of_gcd_of_Tuples__Easy_
{
    class Program
    {
        public static int Ggcd(int x,int y)
        {
            int t = x % y;
            if (t == 0)
            {
                return y;
            }

            return Ggcd(y, t);
        }

        public static int Gcd(int x, int y, int z)
        {
            int s = Ggcd(x, y);

            return Ggcd(s, z);
        }

        static void Main(string[] args)
        {
            int ans = 0;
            int k = int.Parse(Console.ReadLine());
            for(int a = 1; a <= k; a++)
            {
                for (int b = 1; b <= k; b++)
                {
                    for (int c = 1; c <= k; c++)
                    {
                        ans += Gcd(a, b,c);
                    }
                }
            }
            Console.WriteLine(ans);
        }

        
    }
}