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);
    ArrayList<Integer> list1 = new ArrayList<Integer>();
    ArrayList<Integer> list2 = new ArrayList<Integer>();
    
    int max = sc.nextInt();
    
    for(int i = 1; i <= max; i++){
      list1.add(i);
    }
    
    int num1 = 0;
    int num2 = list1.size() - 1;
    for(int i = 0; i < list1.size() / 2; i++){
      list2.add(list1.get(num1) % list1.get(num2));
      num1++;
      num2--;
    }
    
    Collections.sort(list2, Collections.reverseOrder());
    System.out.println(list2.get(0));

  }
}