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 Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl

sub main() {
  chomp(my $N = <>);
  my $ans = prob($N);
  print $ans;
}

sub prob() {
  my ($N) = @_;
  if($N%2==0){
    return $N/2*($N+1);
  }
  else {
    return(($N-1)/2*$N);
  }
}

&main();