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

class Program
{
    static void Main(string[] args) {
#if DEBUG
        //MyDebugger.MakeTestCase("../TextFile2.txt");
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        int n = int.Parse(input.ReadLine());
        int[] ll = ToIntArray(input.ReadLine(), n);

        int count = 0;

        for(int i=0; i<n; i++) {
            for(int j=i+1; j<n; j++) {
                for(int k=j+1; k<n; k++) {
                    if(isok(ll[i], ll[j], ll[k])) {
                        count++;
                    }
                }
            }
        }

        return count;
    }

    static bool isok(int a, int b, int c) {
        return (a < b + c)
            && (b < a + c)
            && (c < a + b);
    }

    
    static int[] ToIntArray(string strs, int n) {
        int[] ret = new int[n];
        var spl =strs.Split(' ');
        for (int i = 0; i < n; i++) ret[i] = int.Parse(spl[i]);
        return ret;
    }
}