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: Time Limit Exceeded)

//
//  main.cpp
//  temp
//
//  Created by tolemy on 2019/08/04.
//  Copyright © 2019 tolemy. All rights reserved.
//

#include <iostream>

using namespace std;

int main(int argc, const char * argv[]) {
    
    int n;
    cin >> n;
    
    unsigned long long sum = 0;
    for(int i=n-1;i>0;i--)
    {
        sum += i%(i+1);
    }
    
    cout << sum << endl;
    
    return 0;
}