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

namespace c
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());

            var total = 0L;
            for(var i = 1L; i <= n; i++){
                for(var j = 1L; j <= n; j++){
                    for(var k = 1L; k <= n; k++){
                        var x = Gcd(i, j);
                        total += Gcd(x, k);
                    }
                }
            }

            Console.WriteLine(total);
        }

        static long Gcd(long m, long n)
        {
	        while (m % n != 0){
        		var temp = n;
		        n = m % n;
		        m = temp;
	        }
        	return n;
        }
    }
}