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 ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());
            long sum = 0;
            for (int i = 0; i < n; i++)
            {
                sum += i;
            }
            Console.WriteLine(sum);
        }

        static List<T[]> GeneratePermutation<T>(params T[] array) where T : IComparable
        {
            var a = new List<T>(array).ToArray();
            var res = new List<T[]>
            {
                new List<T>(a).ToArray()
            };
            var n = a.Length;
            var next = true;
            while (next)
            {
                next = false;

                int i;
                for (i = n - 2; i >= 0; i--)
                {
                    if (a[i].CompareTo(a[i + 1]) < 0)
                        break;
                }
                if (i < 0)
                    break;

                var j = n;
                do
                {
                    j--;
                } while (a[i].CompareTo(a[j]) > 0);

                if (a[i].CompareTo(a[j]) < 0)
                {
                    var tmp = a[i];
                    a[i] = a[j];
                    a[j] = tmp;
                    Array.Reverse(a, i + 1, n - i - 1);
                    res.Add(new List<T>(a).ToArray());
                    next = true;
                }
            }
            return res;
        }
    }
}