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
# スペース区切りの文字列の入力
fscanf(STDIN, "%d", $d);
$s = fgets(STDIN);

$lengths = array_map('intval', explode(' ', $s));

$size = count($lengths);
$count = 0;

// 総当たりで数える
// 同じ長さは使用不可
// 三角形の成立条件は a+b>c かつ b+c>a かつ c+a>b
for ($i = 0; $i < $size; $i++) {
	$l1 = $lengths[$i];
	$checks = [];

	for ($j = $i + 1; $j < $size; $j++) {
		$ln = $lengths[$j];
		if ($ln === $l1) {
			continue;
		}

		$checks[] = $ln;
	}

	$checkSize = count($checks);
	for ($j = 0; $j < $checkSize; $j++) {
		$l2 = $checks[$j];

		for ($k = $j + 1; $k < $checkSize; $k++) {
			$l3 = $checks[$k];
			if ($l2 !== $l3 && $l1 + $l2 > $l3 && $l2 + $l3 > $l1 && $l3 + $l1 > $l2) {
				++$count;
			}
		}
	}
}

# 出力
echo $count . "\n";