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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php

$n = (int)fgets(STDIN);
$l = preg_split('/ /', trim(fgets(STDIN)));
$count = 0;
$array = [];

for ($i = 1; $i < $n-1; $i++) {
    for ($j = $i + 1; $j < $n; $j++) {
        $array[] = [$i, $j];
    }
}

foreach ($array as $a) {
    $second = $a[0];
    $third = $a[1];
    for ($m = 0; $m < $second; $m++) {
        if ($m === $third)
            continue;
        $i = $l[$m];
        $j = $l[$second];
        $k = $l[$third];
        if (($i < $j + $k) && ($j < $i + $k) && ($k < $i + $j)) {
            $count++;
        }
    }
}

echo $count;