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.FileNotFoundException;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		long startTime = System.currentTimeMillis();
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] L = new int[N];
		int[] cnt = new int[2001];
		int[] cnt2 = new int[2001];
		for (int i = 0; i < N; ++i) {
			L[i] = sc.nextInt();
			cnt[L[i]]++;
		}
		for (int i = 1; i < cnt.length; ++i) {
			cnt[i] += cnt[i - 1];
		}
		long ans = 0;
		Arrays.sort(L);
		for (int i = 0; i < N; ++i) {
			cnt2[L[i]]++;
			for (int j = 0; j < i; ++j) {
				int add = cnt[L[i] + L[j] - 1] - cnt[L[i] - 1] - cnt2[L[i]];
				ans += add;
			}
		}
		System.out.println(ans);
	}

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}