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)

n = gets.chomp.to_i
l = gets.chomp.split(" ").map(&:to_i)

a = 0
b = 1
c = 2
count = 0
# if n < 3
#     puts "0"
# elsif n >= 3
#     until a == n-3
#         until b == n-2
#             until c == n-1
#                 r = [l[a],l[b],l[c]].sort
#                 if r[0] + r[1] >= r[2]
#                     count += 1
#                 end
#                 c =+ 1
#             end
#         b += 1
#         c = b + 1
#         end
#         a += 1
#         b = a + 1
#     end
# end
 count = 0
[*0..n-1].permutation (3) do |i|
    if i[0] < i[1] && i[1] < i[2]
        arr = []
        r = l[i[0]]
        rr = l[i[1]]
        rrr = l[i[2]]
         arr << r
         arr << rr
         arr<< rrr
         arr = arr.sort
         mae = arr[0] + arr[1]
         usiro = arr[2]
         if mae > usiro 
          
            if arr.uniq.size == 3

                count += 1
            end
        elsif mae == usiro
            if arr[0] ** 2 + arr[1] ** 2 == arr[2] ** 2
                count += 1
            
            end
        end
    end
end
puts count