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: Wrong Answer)


public class Main {
	public static void main(String args[]) {
		java.util.Scanner sc = new java.util.Scanner(System.in);
		int N = sc.nextInt();

		int result = 0;

		if (N == 1) {
			result = 0;
		}

		if (N % 2 == 0) {
			result = (N - 1 + 1) * ((N-1) / 2) + ((N-1) / 2 + 1);
		} else {
			result = (N - 1 + 1) * (N / 2);
		}

		System.out.println(result);

	}
}