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: Wrong Answer)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
	    // input N
        // 整数 N に対して 1,2,...,N を入れ替えた P1,P2,...PN なる数列を選ぶ
        // P1 % 1 + P2 % 2 + ... PN % N の最大値を出力せよ
        // N = 13 の場合、 ANS = 78
        // 13 1 2 3 4 5 6 7 8 9 10 11 12
        Scanner sc = new Scanner(System.in);
        int numN = sc.nextInt();
        int retNum = 0;
        if(numN > 1){
            double subN = numN - 1;
            retNum = (int)((subN + 1) * subN / 2.0);
        }
        System.out.println(retNum);
    }
}