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: Accepted)

#include<iostream>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<queue>
#include<set>
#include<stack>
#include<map>
#include<math.h>
#define EPS1 1e-6
#define EPS2 1e-9
#define EPS3 1e-15
#define fi first
#define se second
#define ff first.first
#define ss second.second
#define sf second.first
#define fs first.second
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ul;
typedef pair<ld,ld> ldd;
typedef pair<double,double> dd;
typedef pair<int,int> ii;
typedef pair<int, ii> iii;
typedef vector<int> vi;
typedef pair<ld,ii> dii;

int main(){
	ul a;
	cin>>a;
	ul ans = (a*(a-1))/2;
	cout<<ans<<"\n";
	return 0;
}