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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// 2019/09/01
// AtCoder Beginner Contest 139 - D

#include <bits/stdc++.h>
using namespace std;

int main(){
    // Input
    long long n;
    cin >> n;
    long long ans;

    // Calc Sum
    if(n % 2 == 0){
        ans = (n + 1) * (n / 2) - n;
    } else {
        ans = (n + 1) * (floor(n / 2)) + floor(n / 2) - n;
        ans += 1;
    }

    // Output
    cout << ans << endl;
}