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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local read = io.read
local insert = table.insert

local N = read("n")
local L = {}
local L_have_same_num = {}
for i = 1, N do
	local num = read("n")
	if L_have_same_num[num] == nil then
		insert(L, num)
		L_have_same_num[num] = 1
	else
		L_have_same_num[num] = L_have_same_num[num] + 1
	end
end

table.sort(L)

local count = 0
for i = 1, #L - 2 do
	for j = i + 1, #L - 1 do
		for k = j + 1, #L do
			if L[k] >= L[j] + L[i] then
				break
			end
			count = count + L_have_same_num[L[i]] * L_have_same_num[L[j]] * L_have_same_num[L[k]]
		end
	end
end

print(count)