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>

#define INF INT_MAX
#define MOD 1000000007
#define REP(i,n) for(int i=0;i<n;i++)
#define all(x) (x).begin(),(x).end()

typedef long long ll;
typedef std::pair<int,int> pii;

using namespace std;

int main() {

    int n;
    cin >> n;
    ll ans = 0;
    for(ll i = 1;i < n;i++){
        ans += i;
    }
    cout << ans << endl;
    return 0;
}