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: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String...args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Long> lst = new ArrayList<>();
        for (Long i = 0L; i < n; i++){
            lst.add (i + 1L);
        }
        Long ans = 0L;
        Long max = 0L;
        for (int i  = 0; i < n; i++) {
            Long soezi = i + 1L;
            Iterator<Long> it = lst.iterator();
            while (it.hasNext()) {
                Long l = it.next();
                max = Math.max(max, l % soezi);
            }
            ans += max;
        }
        System.out.println(ans);
    }
}