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: Accepted)

const gcd = (m, n) => {
  while (n > 0) {
    const r = m % n
    m = n
    n = r
  }
  return m
}

const Main = (input) => {
  const tmp = parseInt(input.trim())

  let result = 0

  for (let i = 1; i <= tmp; ++i) {
    for (let j = 1; j <= tmp; ++j) {
      for (let k = 1; k <= tmp; ++k) {
        result += gcd(gcd(i, j), k)
      }
    }
  }

  console.log(result)
  return result
}

Main(require('fs').readFileSync('/dev/stdin', 'utf8'))