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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_143
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] ls = ReadInts();
            Dictionary<int, long> sames = new Dictionary<int, long>();
            long[] cnts = new long[2000 + 1];
            for (int i = 0; i < n; i++)
            {
                cnts[ls[i]]++;
                if (!sames.ContainsKey(ls[i]))
                {
                    sames.Add(ls[i], 0);
                }
                sames[ls[i]]++;
            }
            for(int i = 1; i <= 2000; i++)
            {
                cnts[i] += cnts[i - 1];
            }
            Array.Sort(ls);
            long res = 0;
            for (int i = 0; i < n; i++)
            {
                for(int j = i + 1; j < n; j++)
                {
                    res += cnts[ls[i] + ls[j] - 1] - cnts[ls[j]];

                }
            }
            foreach (int key in sames.Keys)
            {
                if (sames[key] >= 2)
                {
                    res += sames[key] * (sames[key] - 1) / 2;
                }
                if (sames[key] >= 3)
                {
                    res += sames[key] * (sames[key] - 1) * (sames[key] - 2) / 6;
                }
            }
            WriteLine(res);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}