Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var array = Console.ReadLine().Split().Select(int.Parse).OrderBy(_ => _).ToArray();

            //var ggg = array.GroupBy(n => n)
            //    .OrderBy(n => n)
            //    .Select(g => new { g.Key, Count = g.Count() });


            //var str = string.Join(" ", Enumerable.Range(1, 2000));
            //var N = 2000;
            //var array = str.Split().Select(int.Parse).OrderBy(_ => _).ToArray();

            //var aaa = new SortedList<short, short>();
            //foreach (var item in array)
            //{
            //    aaa.Add(item, item);
            //}

            var count = 0;

            for (int i = 0; i < N - 2; i++)
            {
                var a = array[i];

                for (int j = i + 1; j < N - 1; j++)
                {
                    var b = array[j];
                    var ab = a + b;

                    //array.BinarySearch(a + b - 1);
                    var idx = array.LowerBound(ab);

                    for (int k = idx-1; k > j; k--)
                    {
                        var c = array[k];

                        if (c >= ab) break;
                        if (b >= c + a) continue;
                        if (a >= b + c) continue;

                        count++;
                    }
                }
            }

            Console.WriteLine(count);
        }
    }
    public static class EnumerableExtension
    {
        /// <summary>
        /// 指定した値以上の先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="source">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(this IList<T> source, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(source[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        public static int LowerBound<T>(this IList<T> source, T value)
            where T : IComparable
        {
            return LowerBound(source, 0, source.Count, value, Comparer<T>.Default);
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        public static int UpperBound<T>(T[] arr, T value)
        {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
    }
}