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;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using pii = pair<int, int>;

#define INF 1e9
#define MOD 1000000007
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define each(x, v) for (auto& x: (v))
#define all(x) (x).begin(), (x).end()
#define print(x) cout << (x) << endl

void solve();
void in(){} template<class T, class... U> void in(T &t, U &...u){ cin >> t; in(u...); }
int main() { cin.tie(0); ios::sync_with_stdio(0); solve(); }

void solve() {
  ll N;
  in(N);
  print(N * (N - 1) / 2);
}