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.*;
public class Main {
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] len = new long[n];
		for(int i = 0 ; i<n; i++){
			len[i] = sc.nextInt();
		}
		Arrays.sort(len);
		long res = 0;
		for(int i = 0 ; i<len.length-1; i++){
			for(int j = i+1 ; j<len.length-1; j++){
				for(int k = j+1 ; k<len.length; k++){
					if(! (len[i]+len[j] > len[k]))break;
					res++;
				}
			}
		}
		System.out.println(res);
	}
}