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

namespace ConsoleApplication41
{
    class Program
    {
        static void Main(string[] args)
        {
            int res = 0;
            //var n = 7 - 1;
            //var st = "218 786 704 233 645 728 389";
            var n = int.Parse(Console.ReadLine()) - 1;
            var st = Console.ReadLine();

            var array = st.Split(' ').Select(d => int.Parse(d)).OrderBy(d => d).ToArray();

            for (int i = n; i >= 2; i--)
            {
                var n1 = array[i];
                for (int j = 1; j < i; j++)
                {
                    var n2 = array[i - j];
                    var max = i - j - 1;
                    res += CountSearch(array, max, n1, n2);
                }
            }

            Console.WriteLine(res);
            //Console.Read();
        }

        static int CountSearch(int[] array, int maxIdx, int f, int s)
        {
            var min = 0;
            var max = maxIdx;

            while (min <= max)
            {
                if (min == max)
                {
                    return f >= s + array[min] ? 0 : maxIdx - max + 1;
                }

                var mid = Convert.ToInt32(Math.Floor((min + (max - min)) / 2m));
                var n3 = array[mid];

                if (f >= s + n3)
                {
                    min = mid + 1;
                    continue;
                }

                max = mid - 1;
            }

            return maxIdx - min + 1;
        }
    }
}