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 C (GCC 5.4.1) (judge verdict: Accepted)

/*
 * main.c
 *
 *  Created on: 2019/07/21
 *      Author: family
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

typedef unsigned long long int uint64_t;

int main()
{
	uint64_t N = 0, ans = 0;
	scanf("%llu", &N);
	if (N%2 == 1) {
		ans = N * ((N-1)/2);
	} else {
		ans = (N+1) * N/2;
		ans -= N;
	}
	printf("%llu\n", ans);
    return 0;
}