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 Python (3.8.2) (judge verdict: Wrong Answer)

import itertools
N = int(input())
L = list(map(int, input().strip().split()))
print(L);
t_count = 0;
three_numbers = list(itertools.combinations(L, 3))
print(three_numbers)

for i in range(len(three_numbers)):
    three_number = three_numbers[i];
    print(three_number)
    li = three_number[0]
    lj = three_number[1]
    lk = three_number[2]
    print(li);
    print(lj);
    print(lk);

    if li == lj:
        continue;
    elif li == lk:
        continue;
    elif lj == lk:
        continue;

    if li+lj <= lk:
        continue;
    elif li+lk <= lj:
        continue;
    elif lj+lk <= li:
        continue;
    t_count+=1;
            
print(t_count);