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);
$rod = explode(" ", trim(fgets(STDIN)));

sort($rod);
$th = 0;
$maxno = 0;
$thmap = [];
$start = -1;
$goal = 0;
for($i=0;$i<=1000;$i++){
    if($rod[$th] == $i){
        $start = $th;
        while($rod[$th] == $i){
            $th++;
            if($th == $n){
                $thmap = $thmap +array_fill($i, 1002-$i, [$start, $n-1]);
                break 2;
            }
        }
        $goal = $th-1;
    }
    $thmap[$i] = [$start,$goal];
}
//$thmap[1001] = $n;

$ans = 0;

for($i=0;$i<$n-2;$i++){
    for($j=$i+1;$j<$n-1;$j++){
        $min = max(0, $rod[$j] - $rod[$i] + 1);
        $max = min($rod[$j] + $rod[$i] - 1, 1000);
        $start = max($thmap[$min][0], $j+1);
        $goal = $thmap[$max][1];
        $ans += max(0,($goal - $start) + 1 );
    }
}

echo $ans;