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 <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
using namespace std;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))
#define rep(i,a,b) for(int (i)=int(a);(i)<int(b);(i)++)
#define rrep(i,a,b) for(int (i)=int(a);(i)>=int(b);(i)--)

#define put(a) cout << (a) << endl

#define INF 1000000001
#define MOD 1000000007
#define INF64 1000000000000000001
#define llint long long int

#define F first
#define S second

#define Pii  pair<int,int>
#define Pll  pair<long long,long long>
#define Piii pair<int,pair<int,int>>
#define Plll pair<long long,pair<long long,long long>>

#define Vll(a,b,c)    vector<vector<long long>> (a)((b),vector<long long>((c))
#define Vlll(a,b,c,d) vector<vector<vector<long long>>> (a)((b),vector<vector<long long>>((c),vector<long long>((d)))

#define MAX_N 1000000

int main (void)
{
	//INPUT
	llint N;
	cin >> N;

	//SOLVE
  llint ans=0;
  // ans += 1;
  // rep(i,2,N){
  //   ans += (i % (i+1));
  // }
  ans = N * (N-1) / 2;

	//OUTPUT

	cout << ans << endl;


  return 0;
}