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: Accepted)

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

namespace ConsoleApp10
{
    class Program
    {
        static void MainA(string[] args)
        {
            Console.WriteLine(Console.ReadLine().ToCharArray().Zip(Console.ReadLine().ToCharArray(), (x, y) => x == y).Count(x => x));
        }

        static void MainB()
        {
            var arr = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var ans = (arr[1] - 1 + arr[0] - 2) / (arr[0] - 1);
            Console.WriteLine(ans);
        }

        static void MainC()
        {
            Console.ReadLine();
            var arr = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            int cnt = 0;
            int cntmax = 0;
            for (int i = 0; i < arr.Length - cntmax - 1; i++)
            {
                cnt = 0;
                for (int j = i + 1; j < arr.Length; j++)
                {
                    if (arr[j - 1] >= arr[j])
                        cnt++;
                    else
                    {

                        break;
                    }
                }
                if (cnt > cntmax)
                    cntmax = cnt;
            }
            Console.WriteLine(cntmax);
        }

        static void Main()
        {
            long n = int.Parse(Console.ReadLine()) - 1;
            Console.WriteLine((n * n + n) / 2);
        }
    }

}