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 PHP (7.4.4) (judge verdict: Accepted)

<?php
$n=trim(fgets(STDIN));
$i=1;
$ans=0;
while($i<=$n){
  $j=1;
  while($j<=$n){
    $k=1;
    while($k<=$n){
      $gcd=gcd($i,$j);
      ($gcd==1)?++$ans:$ans+=gcd($k,$gcd);
      ++$k;
    }
    ++$j;
  }
  ++$i;
}
echo $ans;
function gcd($x,$y){
  return($x%$y)?gcd($y,$x%$y):$y;
}