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;
typedef long long ll;
// #define int long long

typedef vector<int> vi;
typedef pair<int, int> pi;

const ll INF = 1LL << 60;
const ll MOD = 1e9 + 7;

#define pb push_back
#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define REP2(i, b, e) for (int i = (b); i <= (int)(e); i++)
#define DEBUG(x) cout << #x << ": " << (x) << endl
#define DEBUGA(a) cout << #a << ": "; for (const auto& v: (a)) cout << v << endl

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

    ll ans = 0;
    REP2(i, 1, N-1) {
        ans += i;
    }
    cout << ans << endl;
}