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 scan = new Scanner(System.in);
    int N = scan.nextInt();
    int[] P = new int[N+1]; 
    int[] M = new int[N+1]; 

    P[N]=1;
    M[N]=N%P[N];
    int sum=M[N];
    for (int i=1;i<N;i++){
      P[i]= i+1;
       M[i]=i%P[i];
      sum+=M[i];
    }

    System.out.println(sum);
  
  }
 
}