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 (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
int gcd(int a,int b){
    int r,tmp;
    if(a<b){
        tmp = a;
        a = b;
        b = tmp;
    }
    r = a % b;
    while(r!=0){
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}
int main(void)
{
    int n,i,j,k,b,c,total=0;
    scanf("%d",&n);

    for(i=1;i<n+1;i++){
        for(j=1;j<n+1;j++){
            for(k=1;k<n+1;k++){
                b=gcd(i,j);
                c=gcd(k,b);
                total = total +c;
            }
        }
    }
    printf("%d\n",total);
    return 0;
}