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<bits/stdc++.h>
using namespace std;
int gcd1(int m,int n){
	if(m%n==0) return n;
	return gcd1(n,m%n);
}
int gcd(int a,int b,int c){
	return gcd1(gcd1(a,b),c);
}
int main(){
	int k,sum=0;
	scanf("%d",&k);
	for(int i=1;i<=k;i++){
		for(int j=1;j<=k;j++){
			for(int x=1;x<=k;x++){
				sum+=gcd(i,j,x);
			}
		}
	}
	printf("%d",sum);
	return 0;
}