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=1;
  while(r!=0){
    r=a%b;
    a=b;
    b=r;
  }
  return a;
}
int main()
{
  int k;
  scanf("%d",&k);
  int gcdsum=0;
  for(int i=1;i<=k;i++){
    for(int j=1;j<=k;j++){
      for(int m=1;m<=k;m++){
            gcdsum+=GCD(GCD(i,j),m);
      }
    }
  }
  printf("%d",gcdsum);
  return 0;
}