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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC143D
{
    class Program
    {
        static int ans = 0;
        static void Main(string[] args)
        {
            int N=int.Parse(Console.ReadLine());
            string[] Linput = Console.ReadLine().Split(' ');
            int[] L = new int[N];
            for(int i = 0; i < N; i++)
            {
                L[i] = int.Parse(Linput[i]);
            }
            Array.Sort(L);
            //Console.WriteLine(string.Join(" ",L));
            for (int i = 0; i < N - 2; i++)
            {
                for(int j = i + 1; j < N-1; j++)
                {
                    nibun(j + 1, N - 1, L, L[i] + L[j], j);
                    //Console.WriteLine(ans);
                }
                //Console.WriteLine(ans);
            }
            Console.WriteLine(ans);
        }
        static void nibun(int min, int max, int[] L, int ab, int j)
        {
            int center = (min + max) / 2;
            if (min == center)
            {
                if (L[min] == ab)
                {
                    while (L[min] == L[min - 1]&&min>j)
                    {
                        min -= 1;
                    }
                    ans += min - j - 1;
                    //Console.WriteLine("a");
                    //Console.WriteLine(ans);
                }
                else if(L[min]<ab)
                {
                    //

                    if (L[max] >= ab)
                    {
                        ans += min - j;
                        //Console.WriteLine("b");
                        //Console.WriteLine(ans);
                    }
                    else
                    {
                        ans += max - j;
                        //Console.WriteLine("c");
                        //Console.WriteLine(ans);
                    }
                }
                return;
            }
            else
            {
                if (L[center] <= ab)
                {
                    nibun(center, max, L, ab, j);
                }
                else
                {
                    nibun(min, center, L, ab, j);
                }
            }
        }
    }
}