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: Accepted)

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

using static Input;
using static Util;
class Program
{
    static int N;
    static int[] L;
    static void INPUT()
    {
        N = NextInt();
        L = LineInt();
    }

    static void OUT()
    {
        //var s = L.OrderByDescending(__ => __).ToArray();
        Array.Sort(L);
        var count = 0L;
        for (var a = 0; a < N; a++)
            for (var b = a + 1; b < N; b++)
            {
                count += LowerBound<int>(L, L[a] + L[b]) - 1 - b;
            }

        Console.WriteLine(count);
    }
    static void Main(string[] args)
    {
#if DEBUG  
        //TESTINPUT();
        INPUT();

#else
        INPUT();
#endif
        OUT();
    }

    static void TESTINPUT()
    {
    }

}

public class Input
{
    public const long MOD = 1000000007;
    public const int INF = 1000000007;
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}

class Util
{
    /// <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="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>指定した値以上の先頭のインデクス</returns>
    public static int LowerBound<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;

    }

    //引数省略のオーバーロード
    public static int LowerBound<T>(T[] arr, T value) where T : IComparable
    {
        return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
    }
}