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)

def qual(a,b,c)
  if (a + b > c) && (a + c > b) && (b + c > a)
    return true
  else
    return false
  end
end
n = gets.to_i
arr = gets.chomp.split(' ').map(&:to_i)
i = 0
cand = []
while i < n - 2
  j = i + 1
  while j < n - 1
    k = j + 1
    while k < n
      cand.push([arr[i],arr[j],arr[k]])
      k += 1
    end
    j += 1
  end
  i += 1
end
count = 0
cand.each do |trio|
  unless trio.uniq.size != 3
    if qual(trio[0],trio[1],trio[2])
      count += 1
    end
  end
end
puts count