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
    $sankaku = fgets(STDIN);
    $create = fgets(STDIN);
    $c_array = explode(' ', $create);

    $cnt = 0;
    for($i=0; $i<$sankaku-2; $i++){
        $a = (int)$c_array[$i];
        for($j=$i+1; $j<$sankaku; $j++){
            $b = (int)$c_array[$j];
            for($n=$j+1; $n<$sankaku; $n++){
                $c = (int)$c_array[$n];
                if($a < $b + $c &&
                   $b < $a + $c &&
                   $c < $a + $b
                )
                $cnt = $cnt + 1;
            }
        }        
    }
    echo $cnt;
?>