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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main(args: Array<String>){
    val k = readLine()
    val num = k!!.toInt()


    var sumGcd = 0
    for(a in 1..num){
        for(b in 1..num){
            for(c in 1..num){
                sumGcd = gcd(gcd(a, b), c)
            }
        }
    }
    println(sumGcd)
}

fun gcd(p: Int, q: Int) : Int{
    if(p % q == 0){
        return q
    }
    return gcd(q, p % q)
}