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
  list($n) = explode(" ", trim(fgets(STDIN)));
  $l = explode(" ", trim(fgets(STDIN)));

  //$l = range(1, 2000);

  $ans = 0;

  //echo count($l);
  rsort($l);

  for ($i=0; $i<$n-2; $i++) {
    for ($j=$i+1; $j<$n-1; $j++) {
      $p = $l[$i] - $l[$j];
      // 全件NG
      if($l[$j+1] <= $p){
        //echo "NG".PHP_EOL;
        continue;
      }
      // 全件OK
      if($l[$n-1] > $p){
    //    echo "OK".($n-$j-1)." ".$p.PHP_EOL;
        $ans += $n-$j-1;
        continue;
      }
      // 探索
      $a = $j+1;
      $b = $n-1;
      while(($b-$a) > 1){
        $x = intdiv($b-$a, 2)+$a;
  //      echo $i." ".$j." ".$x." ".$a." ".$b." ".$p." ".$l[$x].PHP_EOL;
        if($l[$x] <= $p){
          $b = $x;
        }else{
          $a = $x;
        }
      }
      $ans += $a-$j;
    }
  }
echo $ans;