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
fscanf(STDIN, '%d', $n);//本数
$list = explode(' ', trim(fgets(STDIN)));//長さリスト

$count = 0;

for($s = 0; $s < $n-2; $s++) {
    $a = $list[$s];
    for($r = $s+1; $r < $n-1; $r++) {
        $b = $list[$r];
        for($q = $r+1; $q < $n; $q++) {
            $c = $list[$q];
            if(($a < $b + $c) && ($b < $c + $a) && ($c < $a + $b)) {
                $count++;
            }
        }
    }
}

echo $count.PHP_EOL;