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: Accepted)

fun main() {
    val numK = readLine()!!.toInt()
    val gcdList = mutableListOf<Int>()

    for(i in 1 .. numK ){
        for(j in 1 .. numK){
            for(k in 1 .. numK){
                gcdList.add(gcd(i, gcd(j, k)))
            }
        }
    }


    println(gcdList.sum())
}

fun gcd(a :Int, b :Int): Int{
    if(a < b) return gcd(b , a)
    if(b == 0) return a
    return gcd(b, a % b)
}