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: Accepted)

<?php
fscanf(STDIN, '%d', $n);
$l = array_map('intval', explode(' ', trim(fgets(STDIN))));
sort($l);

$ans = 0;
for ($i = 0; $i < $n-2; $i++) {
    for ($j = $i+1; $j < $n-1; $j++) {
        if ($l[$j+1] >= $l[$i]+$l[$j]) {
            continue;
        }

        if ($l[$j+1] > abs($l[$i]-$l[$j])) {
            $start = $j + 1;
        } else {
            $left = $j+1;
            $right = $n-1;

            while ($right - $left > 1) {
                $mid = floor(($left + $right) / 2);
                if ($l[$mid] > abs($l[$i]-$l[$j])) $right = $mid;
                else $left = $mid;
            }
            $start = $right;
        }

        if ($l[$n-1] < $l[$i]+$l[$j]) {
            $end = $n -1;
        } else {
            $left = $j+1;
            $right = $n-1;

            while ($right - $left > 1) {
                $mid = floor(($left + $right) / 2);
                if ($l[$mid] < $l[$i]+$l[$j]) $left = $mid;
                else $right = $mid;
            }
            $end = $left;
        }

        $ans += $end - $start + 1;
    }
}
echo $ans.PHP_EOL;