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 i,int j,int k)
{
  int min;
  
  if(i<j)
    min=i;
  else
    min=j;
  if(k<min)
    min=k;
  for(int cnt=min;cnt>0;cnt--)
  {
    if (i%cnt==0 && j%cnt==0 && k%cnt==0)
      return (cnt);
  }
  return(0);
}

int main()
{
  int num;
  long ans=0;
  
  scanf("%d",&num);
  for(int i=1;i<=num;i++)
  {
    for(int j=1;j<=num;j++)
    {
      for(int k=1;k<=num;k++)
      {
        ans+=gcd(i,j,k);
      }
    }
  }
  printf("%lu",ans);
}