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 <bits/stdc++.h>
typedef long long lint;
using namespace std;

lint gcd(lint x, lint y) {
  if(x == 0) { return y; }
  else { return gcd(y%x,x); }
}

lint lcm(lint x, lint y) { return x/gcd(x,y)*y; }

lint C(lint n, lint k) {
  if(n == k) { return 1; }
  else if(n < k) { return 0; }
  else if(k == 0) { return 1; }
  else if(k == 1) { return n; }
  else return C(n-1,k-1) + C(n-1,k);
}

lint P(lint n, lint k) {
  if(k == 1) { return n; }
  return (n*(P(n-1,k-1)%1000000007)%1000000007);
}


int main() {
  lint n; cin >> n;
  cout  << (n-1)*n/2 << endl;
  return 0;
}