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.Collections.Generic;

namespace abc139_d
{
  class Program
  {
    static void Main(string[] args)
    {
      var n = CIn.ReadInt();

      Console.WriteLine(n * (n - 1) / 2);
    }
  }

  class CIn
  {
    private static readonly Queue<string> fieldBuffer = new Queue<string>();

    public static string Read()
    {
      if (fieldBuffer.Count == 0)
      {
        foreach (var field in Console.ReadLine().Split())
        {
          fieldBuffer.Enqueue(field);
        }
      }

      return fieldBuffer.Dequeue();
    }

    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());

    public static string[] ReadStringArray(long n)
    {
      var array = new string[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = Read();
      }

      return array;
    }

    public static int[] ReadIntArray(long n)
    {
      var array = new int[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadInt();
      }

      return array;
    }

    public static long[] ReadLongArray(long n)
    {
      var array = new long[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadLong();
      }

      return array;
    }
    public static double[] ReadDoubleArray(long n)
    {
      var array = new double[n];

      for (var i = 0; i < n; i++)
      {
        array[i] = ReadDouble();
      }

      return array;
    }
  }
}