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
$ans = 0;
define('MAX', 2000);

fscanf(STDIN, "%d", $N);
$L = array_map('intval', explode(" ", trim(fgets(STDIN))));
$max = max($L);
$sum = array_pad(array(), MAX + 1, 0);
foreach ($L as $v) {
    $sum[$v]++;
}
for ($i = 1; $i <= MAX; $i++) {
    $sum[$i] = $sum[$i - 1] + $sum[$i];
}
sort($L);
// var_dump($L);
// var_dump($sum);
// a<b+c
// b<c+a
// c<a+b
// var_dump($sum);
for ($i = 0; $i < $N - 2; $i++) {
    for ($j = $i + 1; $j < $N - 1; $j++) {
        $x = $L[$i] + $L[$j] - 1;
        $ans += $sum[$x] - $j - 1;
        // printf("i:%d j:%d L[i]:%d L[j]:%d x:%d ans:%d\n", $i, $j, $L[$i], $L[$j], $L[$i] + $L[$j] - 1, $ans);
    }
}
echo $ans;