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 Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
  //最大公約数
  def gcd(x: Long, y: Long): Long = {
    if(y == 0) x
    else gcd(y, (x % y))
  }

  val k =  scala.io.StdIn.readInt()
  var result = 0L

  (1 to k).foreach { a =>
    (1 to k).foreach { b =>
      (1 to k).foreach { c =>
        val gcdResult = gcd(gcd(a.toLong, b.toLong), c.toLong)
        if(a == b && a == c && b ==c) {
          result += gcdResult
        } else {
          result += gcdResult
        }

      }
    }
  }
  println(result)
}