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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	// gcd(a, b, c) = gcd(gcd(a, b), c)
	var K int
	fmt.Scanf("%d", &K)

	sum := 0
	for i := 1; i <= K; i++ {
		for j := 1; j <= K; j++ {
			for k := 1; k <= K; k++ {
				sum += gcd(gcd(i, j), k)
			}
		}
	}
	fmt.Println(sum)
}

func gcd(a, b int) int {
	if a > b {
		b, a = a, b
	} else if a == b {
		return a
	}
	// b > a
	for a != 0 {
		a, b = b%a, a
	}
	return b
}