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


public class D
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		int MAX_LEN = 2000;

		int N = GetInt();
		int[] L = GetInts(N);

		long[] csum = new long[MAX_LEN + 1];
		for(int i = 0; i < N; i++)
			csum[L[i]]++;

		for(int i = 0; i < MAX_LEN; i++)
			csum[i + 1] += csum[i];

		long ans = 0;
		for(int i = 0; i < N; i++)
		{
			for(int j = 0; j < N; j++)
			{
				if(i == j)
					continue;

				int low = Math.Abs(L[i] - L[j]);
				int high = L[i] + L[j];

				long cnt = csum[high - 1] - csum[low];
				if(low < L[i] && L[i] < high)
					cnt--;

				if(low < L[j] && L[j] < high)
					cnt--;

				if(cnt > 0)
					ans += cnt;
			}
		}
		ans /= 6;

		Console.WriteLine(ans);
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}