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 <cstdio>
#include <cstdlib>
#include <string>
#include <cstring>
#include <cstdint>
#include <vector>
#include <algorithm>
#include <cmath>
#include<iomanip>
#include <unordered_map>
#include <map>
using namespace std;
static const long long MOD = 1000000007LL;
typedef long long ll;
unordered_map <string,int> ump;
map <int,int> mp;
 
int main()
{
	ll n;
	cin>>n;
	if(n==1)
		cout<<0<<endl;
	else if(n==2)
		cout<<1<<endl;
	else
	{
		cout<<n*(n-1)/2<<endl;
	}
 	

	return 0;
}