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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

let input = process.argv[2];
var result = 0;
for (var a = 1; a <= input; a++) {
  for (var b = 1; b <= input; b++) {
    for (var c = 1; c <= input; c++) {
      // console.log(a + " " + b + " " + c);
      result += gcd(gcd(a, b), c);
    }
  }
}
console.log(result);

function gcd(a, b) {  
  if (b == 0) {
    return a;
  }
  return gcd(b, a%b);
}