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() {
	var K, sum int
	fmt.Scan(&K)
	w := make([][]int, K+1)
	for i := 0; i < len(w); i++ {
		w[i] = make([]int, K+1)
		for j := 0; j < len(w[i]); j++ {
			w[i][j] = gcd(i, j)
		}
	}
	for a := 1; a <= K; a++ {
		for b := 1; b <= K; b++ {
			for c := 1; c <= K; c++ {
				sum += gcd(w[a][b], c)
			}
		}
	}
	fmt.Println(sum)
}
func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}