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;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    partial class Program
    {
        static long bmod = 1000000007;
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Console.Out.Flush();
            Console.ReadKey();
        }

        //ここから
        static void Solve()
        {
            int N = GetInt();
            var ans = N * (N - 1) / 2;
            Console.WriteLine(ans);
        }

    }


    //拡張メソッド
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }
    }

    partial class Program
    {
        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public char GetChar() { return Console.ReadLine().Trim()[0]; }
        static public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        static public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        static public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        static public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        static public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        static public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        static public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        static public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        static public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        static public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }


        static public void WriteObjects<T>(IReadOnlyCollection<T> values) { var array = values.ToArray(); var num = array.Length; if (num == 0) return; Console.Write(array[0]); for (int i = 1; i < num; i++) { Console.Write(" " + array[i]); } Console.WriteLine(); }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        static void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
        }
    }
}