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 static System.Console;
using System.Linq;

namespace AC
{
   public class shiokara
   {
      static void Main(string[] args)
      {
         int k = int.Parse(ReadLine());
         int ans = 0;
         for(int n = 1; n <= k; n++){
             for(int m = 1; m <= k; m++){
                 for(int l = 1; l <= k; l++){
                     ans += Gcd(n,m,l);
                 }
             }
         }
         WriteLine(ans);
      }

      public static int Gcd(int a, int b) 
      {
         if (a < b)
             // 引数を入替えて自分を呼び出す
             return Gcd(b, a);
         while (b != 0) {
             var remainder = a % b;
             a = b;
             b = remainder;
         }
         return a;
     }

     public static int Gcd(int a, int b, int c){
         return Gcd(Gcd(a, b), c);
     }
   }
}