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)

import java.util.*

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

fun findGCD(arr: IntArray, n: Int): Int {
    var result = arr[0]
    for (i in 1 until n)
        result = gcd(arr[i], result)
    return result
}
fun main(args: Array<String>)
{
    val scan = Scanner(System.`in`)
    var kotlin=scan.nextLine().toInt()
    var ans: Long=0
    for(i in 1..kotlin)
    {
        for(j in 1..kotlin)
        {
            for(k in 1..kotlin)
            {
                val x = arrayOf(i,j,k)
                    ans+=findGCD(x.toIntArray(),3)
            }
        }
    }
    println(ans)
}