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: Time Limit Exceeded)

sub main {
    my $i=0;
    chomp(my $N = <STDIN>);
    chomp(my $tmp = <STDIN>);
    my @L = split(/ /, $tmp);
    print solver($N,\@L);
}
main() unless caller;

sub solver {
    my ($N,$L) = @_;
    my @s = sort{$b <=> $a}@$L;
    my $ans = 0;
    my $j, $k;
    for my $i(0 .. $N-3) {
        if(!$j){
            $j = $i+1;
        }
        if(!$k){
            $k = $i+2;
        }
        if($k==$N){
            $j++;
            $k=$j+1;
            if($k>=$N){
                $j=0;
                $k=0;
                next;
            }
        }
        if( $s[$i] < $s[$j] + $s[$k] &&
            $s[$j] < $s[$i] + $s[$k] &&
            $s[$k] < $s[$j] + $s[$i] ){
            $ans++;
            $k++;
            redo;
        }
        $j=0;
        $k=0;
    }
    return $ans;
}