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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
    
		// 整数の入力
		int n = sc.nextInt();
        long ans = 0;
        int kari = n % (n - n % 2) / 2 + 1;
        int kouho = n % kari - 3;
        for(int i = 1; i <= n; i++) {
          if (i == 1) {
            continue;
          } else if (i == 2) {
            ans += 1;
            continue;
          }
          if (i != n - 1) {
            ans += i;
          } else if (kouho < n % 3) {
            ans += n % 3;
          } else {
            ans += kouho;
          }
        }
    
		// 出力
		System.out.println(ans);
	}
}