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: Runtime Error)

import java.util.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner stdIn = new Scanner(System.in);
		
		int n = stdIn.nextInt();
		
		int[] order = new int[n];
		
		for(int i = 0; i < n; i++) {
			order[i] = i+1;
		}
		
		int [] reverseOrder = new int[n];
		for(int i = 0; i < n; i++) {
			reverseOrder[i] = order[n-i-1];
		}
		
		int max = 0;
		
		for(int i = 0; i < n; i++) {
			max += order[i] % reverseOrder[i];
		}
		System.out.println(max);
	}

}