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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace abc139_Virtual
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Convert.ToInt32(Console.ReadLine());
            int[] Ni = new int[N];
            for(int i = 0; i < N; i++)
            {
                Ni[i] = i+1;
            }
            int sum = Ni[N - 1] % Ni[0];
            for (int i = 0; i < N-1; i++)
            {
                sum = sum + Ni[i] % Ni[i+1];
            } 
            Console.WriteLine(sum);
            Console.ReadLine();
        }
    }
}