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>
using namespace std;
 
#define whole(f,x,...) ([&](decltype((x)) whole) { return (f)(begin(whole), end(whole), ## __VA_ARGS__); })(x)
#define REP(i, n) for(int i = 0;i < n;++i)
#define REPR(i, n) for(int i = n;i >= 0;--i)
#define FOR(i, a, b) for(int i = a;i < b;++i)
#define ALL(x) (x).begin(),(x).end()
#define INF 999999999
 
#define lint long long
 
 
int main()
{
  lint n; cin>>n;
  lint sum = 0;
  if(n ==1) sum = 0;
  else sum = n*(n-1)*0.5;
  cout << sum<< "\n";
  return 0;
}