Problem:
Score : 400 points

Problem Statement

For an integer N, we will choose a permutation \{P_1, P_2, ..., P_N\} of \{1, 2, ..., N\}.

Then, for each i=1,2,...,N, let M_i be the remainder when i is divided by P_i.

Find the maximum possible value of M_1 + M_2 + \cdots + M_N.

Constraints

N is an integer satisfying 1 \leq N \leq 10^9.

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum possible value of M_1 + M_2 + \cdots + M_N.

Sample Input 1

2

Sample Output 1

1

When the permutation \{P_1, P_2\} = \{2, 1\} is chosen, M_1 + M_2 = 1 + 0 = 1.

Sample Input 2

13

Sample Output 2

78

Sample Input 3

1

Sample Output 3

0

Solution in PHP7 (7.0.15) (judge verdict: Runtime Error)

<?php
    $a = (int)fgets(STDIN);
    $b[];
	for($i=1; $i<=$a; $i++){
      array_push($b,$i);
    }
$c = $b;
$ans = 0;

for($j=1; $j<=$a; $j++){
  $maxDif = 0;
   for($k=1; $k<=$a; $k++){
       $dif = $b[$j] % $c[$k];
       if($dif > $maxDif){
         $maxDif = $dif;
         $jout = $j;
         $kout = $k;
       }
   }
   $ans += $maxDif;
   unset($b[$jout]);
   unset($c[$kout]);
}

echo $ans;