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.Numerics;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var N = int.Parse(ReadLine());
        var L = ReadLine().Split().Select(int.Parse).ToArray();
        Array.Sort(L);
        var ans = 0L;
        for (int i = 0; i < N; i++)
        {
            for (int j = i + 1; j < N; j++)
            {
                var d = L[i] + L[j];
                var ok = 0;
                var ng = N;
                while (ng - ok > 1)
                {
                    var m = (ok + ng) / 2;
                    if (L[m] < d)
                    {
                        ok = m;
                    }
                    else
                    {
                        ng = m;
                    }
                }
                ans += ok - j;
            }
        }
        WriteLine(ans);
    }
}