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: Accepted)

import java.util.*;

class Main {
	public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int N = Integer.parseInt(sc.next());
      List<Integer> list = new ArrayList<>();
      
      for (int i = 0; i < N; ++i) {
        list.add(Integer.parseInt(sc.next()));
      }
      
      list.sort(Comparator.comparing(Integer::intValue));
      
      int result = 0;
      
      for (int i = 0; i < N - 2; ++i) {
        for (int j = i + 1; j < N - 1; ++j) {
          for (int k = j + 1; k < N; ++k) {
            if (list.get(k) < list.get(i) + list.get(j)) result++;
            else break;
          }
        }
      }
      
      
      System.out.println(result);
    }
}