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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var seqL = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

        Array.Sort(seqL);

        var k = 0;
        for (int a = 0; a < seqL.Length; ++a)
        for (int b = a + 1; b < seqL.Length; ++b)
        {
            var ok = b + 1;
            var ng = seqL.Length;
            while (Math.Abs(ok - ng) > 1)
            {
                var m = (ok + ng) / 2;
                if (seqL[m] < seqL[a] + seqL[b])
                {
                    ok = m;
                }
                else
                {
                    ng = m;
                }
            }
            if (ok >= seqL.Length || seqL[ok] >= seqL[a] + seqL[b])
            {
                continue;
            }

            k += ok - b;
        }
        Console.WriteLine(k);
    }
}