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)

import scala.io.StdIn._
object Main extends App{
  val k = readLine().toInt

  var sum = 0
  (1 to k).foreach(h =>{
    (1 to k).foreach(i => {
      (1 to k).foreach(j => {
        sum = sum + gcd(h, i ,j)
      })
    })
  })

  println(sum)

  def gcd(a: Int, b:Int, c: Int):Int = {
    val ab = gcd(a, b)
    if(ab > c) gcd(ab, c)
    else if(ab == c) c
    else gcd(c, ab)
  }

  def gcd(a: Int, b:Int):Int = {
    val remains = a % b
    if(remains == 0) b
    else gcd(b, remains)
  }
}