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;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public static void Main(string[] args)
        {
            // 整数の入力
            int n = int.Parse(Console.ReadLine());

            var lArray = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToList();

            //配列をユニークにする
            Dictionary<long, long> dic = new Dictionary<long, long>();
            foreach (var l in lArray)
            {
                if (dic.ContainsKey(l))
                {
                    dic[l]++;
                }
                else
                {
                    dic.Add(l, 1);
                }
            }

            var keyArray = dic.Keys.ToList();
            keyArray.Sort();

            long result = 0;

            for(int i = 0; i < keyArray.Count; i++)
            {
                long aLength = keyArray[i];
                long aCount = dic[aLength];

                //その長さの棒だけで三角形を作れるか
                if (aCount > 2)
                {
                    result += (aCount * (aCount - 1) * (aCount - 2) / 6);
                }

                for(int j = i + 1; j < keyArray.Count; j++)
                {
                    long bLength = keyArray[j];
                    long bCount = dic[bLength];

                    //aとbだけで三角形を作れるか
                    if(aCount > 2 && bLength < (2 * aLength))
                    {
                        result += bCount * (aCount * (aCount - 1) / 2);
                    }
                    if(bCount > 2 && aLength < (2 * bLength))
                    {
                        result += aCount * (bCount * (bCount - 1) / 2);
                    }

                    for(int k = j + 1; k < keyArray.Count; k++)
                    {
                        long cLength = keyArray[k];
                        long cCount = dic[cLength];

                        //aとbとcで三角形を作れるか
                        if(cLength < aLength + bLength)
                        {
                            result += aCount * bCount * cCount;
                        }
                    }
                }
            }

            Console.WriteLine(result);

        }
    }
}