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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.util.Scanner;
import java.util.Comparator;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Triangles solver = new Triangles();
        solver.solve(1, in, out);
        out.close();
    }

    static class Triangles {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            List<Integer> list = new ArrayList<>();

            for (int i = 0; i < n; i++) {
                list.add(in.nextInt());
            }

            list.sort(Comparator.naturalOrder());

            long result = 0;
            for (int i = 0; i < list.size(); i++) {
                int a = list.get(i);
                for (int j = i + 1; j < list.size(); j++) {
                    int b = list.get(j);
                    int k = i;
                    while (k < list.size() && list.get(k) < a + b) {
                        k++;
                    }
                    result += k - (j + 1);
                }
            }
            out.println(result);
        }

    }
}