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: Time Limit Exceeded)

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

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

$comb_arr = [];
for ($i = 0; $i < $N; $i++) {
    $a = $inputs[$i];
    for ($j = 0; $j < $N; $j++) {
        $b = $inputs[$j];
        if ($a === $b) {
            continue;
        }
        for($k = 0; $k < $N; $k++) {
            $c = $inputs[$k];
            if ($b !== $c && $c !== $a) {
                if ($a+$b > $c && $b+$c > $a && $c+$a > $b) {
                    $arr = [];
                    $arr[] = $i;
                    $arr[] = $j;
                    $arr[] = $k;
                    sort($arr);
                    if (!in_array($arr, $comb_arr)) {
                        $comb_arr[] = $arr;
                    }
                }
            }
        }
    }
}

echo count($comb_arr) . "\n";