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

    val n = readLine()!!.toInt()
    var result = 0
    for (i in 1..n) {
        for (j in 1..n) {
            for (k in 1..n) {
                result += gcd(i, gcd(j, k))
            }
        }
    }

    println(result)
}