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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;

class Program
{

    static int gcd(int x, int y)
    {
        if(x>y){ int b=x; x=y; y=b; }
        while(x>0) { int b=x; x=y%x; y=b; }
        return y;
    }
    
    static void Main()
    {
        int K = int.Parse(Console.ReadLine())+1;

        int ans = 0;
        for(int i=1; i<K; ++i)
            for(int j=1; j<K; ++j) {
                int x = gcd(i, j);
                for(int k=1; k<K; ++k) ans+=gcd(k, x);
            }

        
        Console.WriteLine(ans);    

    }

    

}