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(arg: Array<String>) {
    val K = nextLong()
    var ans = 0L
    for (a in 1 .. K)
    for (b in 1 .. K)
    for (c in 1 .. K)
        ans += gcd(a, gcd(b, c))
    return println(ans)
}
fun gcd(a: Long, b: Long): Long = if (a % b == 0L) b else gcd(b, a % b)
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b

fun next() = readLine()!!
fun nextInt(offset: Int = 0) = Integer.parseInt(next()) + offset
fun nextLong() = next().toLong()