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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn gcd(a: i64, b: i64) -> i64 {
  return if b == 0 { a } else { gcd(b, a % b) };
}

fn main() {
  input! {
    k: i64,
  }

  let mut res: i64 = 0;

  for a in 1..k+1 {
    for b in 1..k+1 {
      for c in 1..k+1 {
        res += gcd(a, gcd(b, c));
      }
    }
  }

  println!("{}", res);
}