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.*;
    
public class Main {
    public static void main(String[] args) throws Exception {
    Scanner sc = new Scanner(System.in);
     
 	int n = Integer.parseInt(sc.next());
 	int[] l = new int[n];
	int cnt = 0;
	for(int i=0; i<n; i++){
	    l[i] = Integer.parseInt(sc.next());
	}
	
	for(int i=0; i<n; i++){
	    for(int j=i; j<n; j++){
	        if(i==j){
	            continue;
	        }
	        for(int k=j; k<n; k++){
	            if(j==k){
	                continue;
	            }
	            if(l[i]+l[j] > l[k] && l[j]+l[k] > l[i] && l[k]+l[i] > l[j]){
	                cnt++;
	            }
	        }
	    }
	}
	
	System.out.println(cnt);
		sc.close();
    }
}