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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long N = in.nextLong();
		ArrayList<Long> n = new ArrayList<>();
		ArrayList<Long> p = new ArrayList<>();
		for (long i = 0; i < N; i++) {
			n.add(i + 1);
			if (i != 0) {
				p.add(i + 1);
			}
		}
		p.add(n.get(0));
		long ans = 0;
		for (int i = 0; i < N - 1; i++) {
			ans += n.get(i);
		}
		System.out.println(ans);
		in.close();
	}
}