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: Wrong Answer)

//----------------------------------------------------------------------
#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)   FOR(i,0,n)
//----------------------------------------------------------------------

using namespace std;
using ll = long long;
using P = pair<int,int>;
using Graph = vector<vector<int>>;

int main(void) {
    int n; cin >> n;
    vector<int> p;
    vector<int> a;
    ll ans = 0;

    for(int i = n-1; i >=2; --i) {
        ans += i;
    }

    ll add = max(1, n % 2);

    ans += add;

    cout << ans << endl;
    return 0;
}