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# (Mono-csc 3.5.0) (judge verdict: Accepted)

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

public class Hello{
    public static void Main(){
        var n = Int32.Parse(Console.ReadLine());
        var ret = 0;
        for(var i = 1; i <= n; ++i){
            for(var j = 1; j <= n; ++j){
                for(var k = 1; k <= n; ++k){
                    ret += gcd(i, j, k);
                }
            }
        }

        Console.WriteLine(ret);
    }
    
    public static int gcd(int i, int j, int k){
        return gcd(gcd(i, j), k);
    }

    public static int gcd(int i, int j){
        if (j == 0) return i;

        return gcd(j, i % j);
    }
}