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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

namespace ABC139
{
    class D
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());

            long res = 0;
            if (N % 2 == 1) res++;
            for (long i = 2; i < N; i++)
            {
                res += i;
            }
            if (N == 1) Console.WriteLine(0);
            else if (N == 2) Console.WriteLine(1);
            else Console.WriteLine(res);
        }
    }
}