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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  	$num = fgets(STDIN);
 	$arr = explode(" ",fgets(STDIN));
	$ans = 0;

	arsort($arr);

    for($i=0; $i< $num; $i++){
      for($j=$i+1; $j<$num; $j++){
        if($arr[$j+1] <= $arr[$i] - $arr[$j]){
        	break; 
        }
        for($k=$j+1; $k<$num; $k++){
          if ($arr[$i] < $arr[$j] + $arr[$k])
          {
            if ($arr[$j] < $arr[$i] + $arr[$k]){
               if ($arr[$k] < $arr[$i] + $arr[$j]){
                 $ans++;
               }
            }
          }
      	}
      }
    }
	echo $ans;