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;

#define LL long long
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define ALL(x) (x).begin(),(x).end()
const int IINF = 1e9;
const LL LINF = 1e18;
const LL mod = 1e9+7;

int main() {
    LL N;
    cin >> N;
    LL res = N*(N - 1)/2;
    cout << res << endl;
    return 0;
}