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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.math.BigInteger;
    import java.util.*;
    import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    TreeSet<Integer> l = new TreeSet<>();
    ArrayList<Integer> lList = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      int tmp = sc.nextInt();
      l.add(tmp);
      lList.add(tmp);
    }
    lList.sort(Comparator.naturalOrder());
    long result = 0;
    for (int i = 0; i < n; i++) {
      int a = lList.get(i);
      for (int j = i + 1; j < n; j++) {
        int sum = a + lList.get(j);
        result += Math.max(l.headSet(sum).size() - j - 1, 0);
      }
    }
    System.out.println(result);
  }
}