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 Raku (Rakudo 2020.02.1) (judge verdict: Accepted)

my $in1 = get;
my $n = chomp($in1);

my $in2 = get;
my $s = chomp($in2);
my @d = split(" ",$s);
my @data;

for @d -> $s {
	@data.push($s.Int);
}
#@data .= sort: { $^b leg $^a };
#say @data;
my $ans = 0;

loop (my $i = 0; $i < @data.elems  ;$i++) {
	loop (my $j = $i+1; $j < @data.elems ; $j++) {
		loop (my $k = $j+1; $k < @data.elems;$k++) {
			#say "$i ~ ',' ~ $j ~ ',' ~ $k";
			if check(@data[$i],@data[$j], @data[$k]) == True {
				$ans +=1;
			}
		}
	}
}

say $ans;


sub check (Int $i, Int $j, Int $k ) {
	if  $i + $j > $k && $j + $k > $i && $k + $i > $j  {
		if $i != $j && $i != $k && $j != $k {
			return True;
		} 
	}
}