Problem:
Score : 200 points

Problem Statement

We have sticks numbered 1, \cdots, N. The length of Stick i (1 \leq i \leq N) is L_i.

In how many ways can we choose three of the sticks with different lengths that can form a triangle?

That is, find the number of triples of integers (i, j, k) (1 \leq i < j < k \leq N) that satisfy both of the following conditions:

L_i, L_j, and L_k are all different.

There exists a triangle whose sides have lengths L_i, L_j, and L_k.

Constraints

1 \leq N \leq 100

1 \leq L_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 \cdots L_N

Output

Print the number of ways to choose three of the sticks with different lengths that can form a triangle.

Sample Input 1

5
4 4 9 7 5

Sample Output 1

5

The following five triples (i, j, k) satisfy the conditions: (1, 3, 4), (1, 4, 5), (2, 3, 4), (2, 4, 5), and (3, 4, 5).

Sample Input 2

6
4 5 4 3 3 5

Sample Output 2

8

We have two sticks for each of the lengths 3, 4, and 5. To satisfy the first condition, we have to choose one from each length.

There is a triangle whose sides have lengths 3, 4, and 5, so we have 2 ^ 3 = 8 triples (i, j, k) that satisfy the conditions.

Sample Input 3

10
9 4 6 1 9 6 10 6 6 8

Sample Output 3

39

Sample Input 4

2
1 1

Sample Output 4

0

No triple (i, j, k) satisfies 1 \leq i < j < k \leq N, so we should print 0.

Solution in Perl (5.26.1) (judge verdict: Accepted)

use strict;
use warnings;
use utf8;

use feature qw(say);
use Data::Dumper;

my $n = <STDIN>;
my $input = <STDIN>;
chomp $input;

my $array = [split / /, $input];
$array = [sort { $a <=> $b } @$array];

my $count = 0;

for (my $i = 0; $i < $n; $i++) {
    my $num = $array->[$i];
    for (my $second_index = $i+1; $second_index < $n; $second_index++) {
        my $second_num = $array->[$second_index];
        for (my $third_index = $second_index+1; $third_index < $n; $third_index++) {
            my $third_num = $array->[$third_index];

            if ($num + $second_num > $third_num && $num != $second_num && $second_num != $third_num) {
                $count++;
            }
        }
    }
}

say $count;