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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());

		Integer a[] = new Integer[n];
		String str[] = br.readLine().split(" ");

		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(str[i]);
		}

		Arrays.sort(a);

		int ans = 0;
		for (int i = 0; i < n; i++) {
			for (int j = i + 1; j < n; j++) {
				int k = ~Arrays.binarySearch(a, a[i] + a[j], (x, y) -> x.compareTo(y) >= 0 ? 1 : -1);

				ans += Math.max(k - (j + 1), 0);
			}
		}

		System.out.println(ans);

	}

}