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);
$L = explode(' ', trim(fgets(STDIN)));
/* $n = 4; */
/* $L = [3, 4, 2, 1,]; */

sort($L);

$cnt = 0;
for ($i = 0; $i < $n - 2; ++$i) {
    for ($j = $i + 1; $j < $n - 1; ++$j) {
        $target = $L[$i] + $L[$j];

        $l = $j + 1;
        $r = $n;

        while ($r - $l >= 1) {
            $mid = floor(($r + $l) / 2);
            $x = $L[$mid];

            if ($x == $target) {
                $r = $mid;
                break;
            } else if ($x > $target) {
                $r = $mid;
            } else {
                $l = $mid + 1;
            }
        }

        $cnt += max(0, $r - ($j + 1));
        /* echo "i: $i, j: $j, l: $l, r: $r", PHP_EOL; */
    }
}

echo $cnt;