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 
  function kumiawase($n){
    $ans=0;
    if(count($n)<3) return 0;
    for($i=0;$i<count($n)-2;$i++){
      for($j=$i+1;$j<count($n)-1;$j++){
        for($k=$j+1;$k<count($n);$k++){
          if($n[$i]==$n[$j] || $n[$j]==$n[$k]) continue;
          if($n[$i]+$n[$j]>$n[$k] && $n[$i]+$n[$k]>$n[$j] && $n[$j]+$n[$k]>$n[$i]){
            $ans++;
          }
        }
      }
    }
    return $ans;
  }
function main(){
  $n = trim(fgets(STDIN));
  $l = explode(" ",trim(fgets(STDIN)));
  sort($l);
  $ans = kumiawase($l);
  echo $ans."\n";
}
main();