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.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
public static class P {
  public static void Main() {
    var n = int.Parse(Console.ReadLine());
    var l = Console.ReadLine().Split().Select(int.Parse).OrderBy(x=>x).ToArray();
    var res = 0;
    foreach (int i in Enumerable.Range(1, l.Length - 1)) {
      foreach (int j in Enumerable.Range(0, i).Reverse()) {
        if (l[j] * 2 <= l[i]) continue;
        var ok = j;
        var ng = -1;
        while (ok - ng > 1) {
          var mid = (ok + ng) / 2;
          if (l[i] < l[mid] + l[j]) ok = mid;
          else ng = mid;
        }
        res += j - ok;
      }
    }
    Console.WriteLine(res);
  }
}