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 <stdio.h>
#include <vector>
#include <algorithm>
#include <string>
#include <iostream>
#include <math.h>

#define rep(i,n) for(int i = 0; i <(n); i++)
using namespace std;
typedef long long ll;
const ll INF = 1LL << 60;

template<class T> inline bool chmin(T& a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}



int main(void) {
	ll i, j, k, ans = 0, cnt = 0, N, tmp, at, M = 0;
	
	scanf("%lld", &N);
	for (i = 1; i <= N -1; i++) {
			M += i;
	}
	printf("%lld", M);



	return 0;
}