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: Accepted)

import java.io.*;
import java.util.*;

class Main {

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		System.out.println(solve(1, N));
	}

	private static long solve(long a, long b) {
		if (a >= b) return 0;
		if (b == 2) return 1;

		long p = 1;
		for (long i = 2; i * i <= b + 1; i++) {
			if ((b + 1) % i == 0) {
				p = (b + 1) / i;
				break;
			}
		}

		long v = b * (b - 1) / 2 - (p - 1) * (p - 2) / 2;
		return solve(a, p - 1) + v;
	}
}