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 <iostream>
#include <vector>
#include <string>
#include <utility>
#include <queue>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <climits>
using namespace std;

#define MOD1097 1000000007

#define ll long long
#define pint pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define mpair make_pair
#define pm(first, second) pb(mpair(first, second))
#define SPACE " "
#define fpf first.first
#define fps first.second
#define spf second.first
#define sps second.second

#define all(X) (X).begin(), (X).end()
#define reall(X) (X).rbegin(), (X).rend()
#define divcel(a, b) (((a) + ((b) - 1)) / (b))

int main(){

    ll N;
    cin >> N;
    ll ans = N * (N + 1) / 2 - N;
    cout << ans << endl;

    return 0;
}