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 <iomanip>
#include <cstdio>
#include <queue>
#include <cstring>
#include <vector>
#include <map>
#include <algorithm>
#include <cctype>
#include <cmath>
#include <bitset>
#include <set>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define RREP(i,n) for(int i=n-1;i>=0;i--)
#define FOR(i,k,n) for(int i=(k);i<(int)(n);i++)
#define all(i,n) (i),(i+n)

int dx4[4]={1,0,-1,0};
int dy4[4]={0,-1,0,1};
int dx8[8]={1,0,-1,1,-1,1,0,-1};
int dy8[8]={1,1,1,0,0,-1,-1,-1};

typedef pair<int, int> P;
typedef pair<string, int> SP;
typedef long long ll;

const int INF = 1e9;
const ll LLINF = 1e18;
const int MAX_V = 1e6+1;
const ll mod = 1000000007;

// --------------------------------------
ll n;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> n;
  cout << (((n - 1) * (n - 1) + n) / 2) << endl;
}