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)

#include <bits/stdc++.h>

#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
typedef long long ll;

using namespace std;


int inputValue(){
    int a;
    cin >> a;
    return a;
};

void inputArray(int * p, int a){
    rep(i, a){
        cin >> p[i];
    }
};

void inputVector(vector<int> * p, int a){
    rep(i, a){
        int input;
        cin >> input;
        p -> push_back(input);
    }
}

template <typename T>
void output(T a, int precision) {
    if(precision > 0){
        cout << setprecision(precision)  << a << "\n";
    }
    else{
        cout << a << "\n";
    }
}

int main(int argc, const char * argv[]) {
    
    // source code
  int n;
  cin >> n;
  cout << (n*(n - 1))/2;
}