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.Generic;
using System.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        // Arrayの中で指定された要素「以上」の値が現れる最初のインデックスを返す
        public static int LowerBound<T>(T[] a, T v) where T : IComparable<T>
        {
            int l = 0;
            int r = a.Length - 1;

            while (l <= r)
            {
                int mid = l + (r - l) / 2;
                if (a[mid].CompareTo(v) < 0)
                {
                    l = mid + 1;
                }
                else
                {
                    r = mid - 1;
                }
            }

            return l;
        }

        // Arrayの中で指定された要素「より大きい」値が現れる最初のインデックスを返す
        public static int UpperBound<T>(T[] a, T v) where T : IComparable<T>
        {
            int l = 0;
            int r = a.Length - 1;

            while (l <= r)
            {
                int mid = l + (r - l) / 2;

                if (a[mid].CompareTo(v) <= 0)
                {
                    l = mid + 1;
                }
                else
                {
                    r = mid - 1;
                }
            }

            return l;
        }




        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] s = Console.ReadLine().Split(' ');

            int[] v = new int[N];

            for (int i = 0; i < N; i++)
            {
                v[i] = int.Parse(s[i]);
            }
            Array.Sort(v);

            int ans = 0;
            for (int a = 0; a < N - 2; a++)
            {
                int va = v[a];

                for (int c = a + 2; c < N; c++)
                {
                    int vc = v[c];

                    int vb = vc - va;
                    int b = UpperBound(v,vb);

                    if (b <= a)
                    {
                        b = a + 1;
                    }

                    if (b < c)
                    {
                        ans += c - b;
                    }
                }
            }

            Console.WriteLine(ans);
        }
    }
}