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: Runtime Error)

import java.lang.reflect.Array;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        List<Integer> L = new ArrayList<>();
        int count = 0;

        for (int i = 0; i < N; i++)
            L.add(sc.nextInt());

        L.sort(Comparator.naturalOrder());

        for (int i = 0; i < L.size() - 2; i++) {
            for (int j = i + 1; j < L.size() - 1; j++) {
                int idxAB = Collections.binarySearch(L, L.get(i) + L.get(j), Comparator.naturalOrder());
                count += (idxAB < 0 ? -idxAB - 2 : idxAB - 1) - j;
                int k = 1;
                while (idxAB >= 0 && L.get(idxAB) == L.get(idxAB + k)) {
                    count++;
                    k++;
                }
            }
        }
        System.out.println(count);
    }
}