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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static readonly long Mod = 1000000000 + 7;
        public class lower_bound<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1;
        }
        public class upper_bound<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 < x.CompareTo(y) ? 1 : -1;
        }
        static void Main(string[] args)
        {
            var N = Sarray()[0];
            var L = Slist();
            L.Sort();
            
            var lb = new lower_bound<long>();
            var ub = new upper_bound<long>();

            var ans = 0L;
            for (var i = 0; i < N - 2; ++i)
            {
                var a = L[i];
                for (var j = i + 1; j < N - 1; ++j) 
                {
                    var b = L[j];
                    var cl = Max(a - b, b - a);
                    var cu = a + b - 1;
                    var num = ~L.BinarySearch(cl, lb);
                    if (N <= num) continue;
                    num = Max(j + 1, num);
                    var num2 = (~L.BinarySearch(cu, ub)) - 1;
                    if (num2 <= j) continue;
                    ans += num2 - num + 1;
                }
            }
            WriteLine(ans);
        }
    }
}