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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
namespace Contest
{
    class Program
    {

        static void Main()
        {
            int n = int.Parse(Console.ReadLine());
            List<int> input = new List<int>();
            List<int> removeList = new List<int>();
            for (int i = 0; i < n; i++)
            {
                input.Add(i);
            }
            int result = 0;
            for (int i = 1; i <= n; i++)
            {
                int res = 0;
                int currentIdx = 0;
                
                for (int k = 0; k < input.Count; k++)
                {
                    if (input[k] % i > res)
                    {
                        res = input[k] % i;
                        currentIdx = k;
                    }
                }
                input.RemoveAt(currentIdx);
                result += res;
            }
            Console.WriteLine(result);
        }
    }
}