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;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = Io.Read<int>();

            var output = 0L;
            for (var i = 1; i < N; i++)
            {
                output += i;
            }

            Console.WriteLine(output);
        }
    }

    class Io
    {
        public static string Read()
        {
            return Console.ReadLine();
        }

        public static IEnumerable<string> ReadRepeat(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read());
        }

        public static T Read<T>()
        {
            return (T)Convert.ChangeType(Read(), typeof(T));
        }

        public static IEnumerable<T> ReadRepeat<T>(int count)
        {
            return Enumerable.Range(0, count).Select(_ => Read<T>());
        }

        public static string[] ReadSplit(char devide = ' ')
        {
            return Read().Split(devide);
        }

        public static T[] ReadSplit<T>(char devide = ' ')
        {
            return ReadSplit(devide)
                .Select(s => (T)Convert.ChangeType(s, typeof(T)))
                .ToArray();
        }

        public static IEnumerable<T[]> ReadSplitRepeat<T>(int count, char devide = ' ')
        {
            return Enumerable.Range(0, count).Select(_ => ReadSplit<T>(devide));
        }
    }
}