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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
  "fmt"
)

func main(){
  var N, ans int
  fmt.Scan(&N)
  
  for i := 1; i<=N; i++ {
    for j := 1; j<=N; j++ {
      for k := 1; k<=N; k++ {
        ans += gcd(i,gcd(j,k))
      }
    }
  }
  fmt.Println(ans)    
}

func gcd(a,b int) int {
  if b==0 {
    return a
  }
  return gcd(b,a%b)
}