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;

public class Solution
{
    static int BinSearchIndex(int v, int[] list)
    {
        int minRange = 0;
        int maxRange = list.Count();
        while (minRange != maxRange)
        {
            var center = (minRange + maxRange) / 2;
            if (list[center] < v)
            {
                minRange = center + 1;
            }
            else
            {
                maxRange = center;
            }
        }

        return minRange;
    }

    public static void Main()
    {
        var N = int.Parse(Console.ReadLine());
        var L = Console.ReadLine().Split(' ').Select(int.Parse).OrderBy(x => x).ToArray();

        long pattern = 0;
        for (int i = 0; i < L.Length; i++)
        {
            for (int j = i + 1; j < L.Length; j++)
            {
                var a = L[i];
                var b = L[j];
                var min = Math.Max(a - b, b - a);
                var max = a + b;

                var left = BinSearchIndex(min, L);
                while (left < N && L[left] <= min)
                {
                    left++;
                }
                left = Math.Max(left, j + 1);
                var right = BinSearchIndex(max, L);
                while (0 <= right && right < N && L[right] >= max)
                {
                    right--;
                }
                if (right == N)
                {
                    right--;
                }

                var count = Math.Max(right - left + 1, 0);
                pattern += count;
            }
        }

        Console.WriteLine(pattern);
    }
}