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 Ruby (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor *(?a..?z).to_a.map(&:to_sym)
  def initialize
    @n = gets.to_s.to_i
    @a = gets.split.map(&:to_i)
  end

  def solve
    ans = 0
    0.upto(n-3) do |i|
      (i+1).upto(n-2) do |j|
        (j+1).upto(n-1) do |k|
          ans += 1 if query(i,j,k)
        end
      end
    end
    ans
  end

  def query(i,j,k)
    a[i] < a[j] + a[k] &&
    a[j] < a[i] + a[k] &&
    a[k] < a[j] + a[i] &&
    a[i] != a[j] &&
    a[i] != a[k] &&
    a[k] != a[j]
  end

  def show(ans)
    puts ans
  end
end

Problem.new.instance_eval do
  show(solve)
end