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;
public class ABC143D {
    public static void Main() {
        int N, ans = 0;
        List<int> L = new List<int>();
        N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        for (int i = 0; i < str.Length; i++) {
            L.Add(int.Parse(str[i]));
        }

        L.Sort();
        L.Reverse();

        for (int i = 0; i < N - 2; i++) {
            int a = L[i];
            for (int j = i + 1; j < N - 1; j++) {
                int b = L[j];
                for (int k = j + 1; k < N; k++) {
                    int c = L[k];
                    if (a < b + c) ans++;
                    else break;
                }
            }
        }
        Console.WriteLine(ans);
    }
}