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: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

// https://atcoder.jp/contests/abc143/tasks/abc143_c
public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		List<Integer> list = new ArrayList<Integer>();
		for(int i=0;i<N;i++) {
			list.add(sc.nextInt());
		}

		sc.close();

		Collections.sort(list);
		int result = 0;
		for(int i=0;i<N;i++) {
//			int a = list.get(i);
			for(int j=i+1;j<N&&j!=N;j++) {
//				int b = list.get(j);
				for(int l=j+1;l<N&&l!=N;l++) {
//					int c = list.get(l);
					if((list.get(l)<list.get(i)+list.get(j))) {
						result++;
					}else {
						break;
					}
				}
			}
		}
		System.out.println(result);
	}
}