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 text_io::*;
use std::collections::HashMap;
use std::process::exit;

fn main() {
    let n:usize = read!();
    let mut sum:usize = 0;
    for i in 1..n+1 {
        for j in 1..n+1 {
            for k in 1..n+1 {
                sum += gcd(k,gcd(i,j));
            }
        }
    }
    println!("{}",sum);
}

fn gcd(a: usize, b: usize) -> usize {
    match b {
        0 => a,
        _ => gcd(b, a % b)
    }
}