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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
static const int INF (1<<30);

int main() {
  ll N; cin >> N;

  if (N == 1) {
    cout << 0 << endl;
    return 0;
  } else if (N == 2) {
    cout << 1 << endl;
    return 0;
  }

  ll ans;

  if ((N-2)%2 == 0) {
    ans = ((N-2)/2) * (N+1) + 1;
    //ans = ((N-2)/2) * (N+1);
  } else {
    ans = ((N+1)/2) * (N-2) + 1;
  }

  cout << ans << endl; 

  return 0;
}