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;

public class Program
{
    public static long loop;

    static long n;

    static long[] l;

    static long lMax = 1;
    static long lMin = 1000;

    static string output;

    public static void Main(string[] args)
    {
        loop = 0;

        Input();
        Proc();
        Output();
    }

    static void Input()
    {
        string[] input = null;

        // スペース区切りの整数の入力(横、個別)
        input = Console.ReadLine().Split(' ');

        n = long.Parse(input[0]);

        // スペース区切りの整数の入力(横、配列)
        input = Console.ReadLine().Split(' ');

        l = new long[n];
        for (long idx = 0; idx < n; idx++)
        {
            l[idx] = long.Parse(input[idx]);
        }
    }

    static void Proc()
    {

        Array.Sort(l);

        long result = 0;

        for (long idxA = 0; idxA < n - 2; idxA++)
        {
            long a = l[idxA];

            for (long idxB = idxA + 1; idxB < n - 1; idxB++)
            {
                long b = l[idxB];

                long idxResult = BinarySearch(ref l, idxB, n, a + b);
                result += idxResult - idxB;
            }
        }

        output = result.ToString();
    }

    static long BinarySearch(ref long[] searchArray, long idxLeft, long idxRight, long targetValue)
    {
        if (idxLeft >= idxRight - 1)
        {
            return idxLeft;
        }

        long idxNow = (idxLeft + idxRight) / 2;
        long arrayValue = searchArray[idxNow];

        if (arrayValue < targetValue)
        {
            idxLeft = idxNow;
        }
        else
        {
            idxRight = idxNow;
        }

        long result = BinarySearch(ref searchArray, idxLeft, idxRight, targetValue);

        return result;
    }

    static void Output()
    {
        // 出力
        Console.WriteLine(output);
        output = string.Empty;
    }
}