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 PHP (7.4.4) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d", $N);

$inputs = trim(fgets(STDIN));
$inputs = array_map("intval", explode(" ", $inputs));
sort($inputs);
// var_dump($inputs);

$ans = 0;
if ($N < 3) {
    echo 0 . "\n";
    exit;
}
for ($i = 0; $i < $N-2; $i++) {
    for ($j = $i+1; $j < $N-1; $j++) {
        for($k = $j+1; $k < $N; $k++) {
            if ($inputs[$i] == $inputs[$j] ||  $inputs[$i] == $inputs[$k] || $inputs[$j] == $inputs[$k]) continue;
            if ($inputs[$i] + $inputs[$j]  > $inputs[$k] &&  $inputs[$i] + $inputs[$k] > $inputs[$j] && $inputs[$j] + $inputs[$k] > $inputs[$i]) {
                // echo $inputs[$i] . $inputs[$j] . $inputs[$k] . "\n";
                $ans++;
            }
        }
    }
}
echo $ans . "\n";