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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
    public class Main {
    	public static void main(String[] args){
    		Scanner sc = new Scanner(System.in);
    		// 整数の入力
    		int n = sc.nextInt();
          	int[] a = new int[n];
          
          	for (int i = 0; i<a.length; i++){
              a[i] = sc.nextInt();
            }
          
            int result = 0;
          	for (int i = 0; i<a.length; i++){
              for (int j = i + 1; j<a.length; j++){
                for (int k = j + 1; k<a.length; k++){
                	if(a[i] + a[j] > a[k] && a[j] + a[k] > a[i] && a[i] + a[k] > a[j]){
                  	    result++;
                    }  
                }                  
              }
            }
          	
          	
              
          
    		// 出力
    		System.out.println(result);
    	}
    }