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.IO;
using System.Net;
using System.Net.Sockets;
using System.Linq;
using System.Diagnostics;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    static int[] l;
    static int[] res;
    public static void Main()
    {
        int n = Reader.NextInt;
        l = new int[n];
        res = new int[n];
        for (int i = 0; i < l.Length; i++)
            l[i] = Reader.NextInt;
        Array.Sort(l);

        Parallel.For(0, l.Length - 2, i =>
        {
            for (int j = i + 1; j < l.Length - 1; j++)
                for (int k = j + 1; k < l.Length; k++)
                {
                    Op(i, j, k);
                }
        });

        Console.WriteLine(res.Sum());
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void Op(int i, int j, int k)
    {
        if (l[i] + l[j] <= l[k]) return;
        res[i]++;
    }
}

static class Reader
{
    const int BUF_SIZE = 1 << 12;
    static Stream Stream = Console.OpenStandardInput();
    static byte[] Buffer = new byte[BUF_SIZE];
    static int ptr = 0;
    static void Move() { if (++ptr >= Buffer.Length) { Stream.Read(Buffer, 0, BUF_SIZE); ptr = 0; } }

    public static int NextInt
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        get
        {
            int res = 0; while (Buffer[ptr] < 48) Move();
            do { res = res * 10 + (Buffer[ptr] ^ 48); Move(); } while (48 <= Buffer[ptr]);
            return res;
        }
    }
}