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(){
    // Your code here!
    var k int64
    fmt.Scan(&k)
    

    var x,y,z,sum int64
    sum = 0
    for x = 1; x <= k; x++{
        for y = 1; y <= k; y++{
            for z = 1; z <= k; z++{
                sum = sum + gcd(gcd(z,y),x)
            }
        }
    }
    fmt.Println(sum)
}

func gcd(a int64, b int64) int64{
    var t int64
    if a < b{
        t = b
        b = a
        a = t
    }
    for ;;{
        if a % b == 0{
            return b
        }else{
            t = a
            a = b
            b = t % b
        }
    }
}