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 Perl (v5.18.2) (judge verdict: Accepted)

#!/usr/bin/perl
my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @l = map { $_ - 0 } split(/\s+/,<STDIN>);

my @d = ();
$#d = 2000;

for(my $i=0;$i<$n-1;$i++){
  for(my $j=$i+1;$j<$n;$j++){
    my $v = $l[$i] + $l[$j];
    $d[$v] ++;
  }
}

my @dsum = ();
$#d = 2000;
my $sm = 0;
for(my $i=$#d;$i>=0;$i--){
  $sm += $d[$i];
  $dsum[$i] = $sm;
}

my $r = 0;
my @sl = sort { $b <=> $a } @l;
my $a = 0;
for(my $i=0;$i<$n;$i++){
  my $h1 = $sl[$i];
  $a += ($n - 1 - $i) if ($n - 1 - $i)>=0;
  $r += ( $dsum[$h1+1] - $a );
}
print "$r\n";

exit(0);