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: Time Limit Exceeded)

#include <stdio.h>

int main(void)
{
  int n,i,j,k,wari;
  int kys = 0;
  int goukei = 0;
  
  scanf("%d",&n);
  
  for(i=1; i<=n; i++){
    for(j=1; j<=n; j++){
      for(k=1; k<=n; k++){
        for(wari=1; wari<=n; wari++){
          if(i%wari==0 && j%wari==0 && k%wari==0)
            kys = wari;
        }
        goukei += kys;
      }
    }
  }
  printf("%d",goukei);
  return 0;
}