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.awt.*;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

public class Main {

    static String br = System.getProperty("line.separator");
    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        long N = nextLong();

        long n = N-1;
        long a = 1;
        long l = N-1;

        println(n*(a+l)/2L);
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }

    static Long nextLong() {
        return Long.parseLong(next());
    }

    static String next() {
        return sc.next();
    }

    static String nextLine(){
        return sc.nextLine();
    }

    static void println(Object o) {
        out.println(o);
        out.flush();
    }

    static void print(Object o) {
        PrintWriter out = new PrintWriter(System.out);
        out.print(o);
        out.flush();
    }
}