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 OCaml (4.10.0) (judge verdict: Accepted)

open Batteries
let get_max a b c = max a @@ max b c
let get_others a b c =
  let max_ = get_max a b c in
    if a = max_ then (b, c) else
    if b = max_ then (a, c) else (a, b)


let n = read_int ()
let l = Array.init n @@ fun _ -> Scanf.scanf " %d" @@ fun a -> a

let is_triangle a b c =
  let cosa = (float_of_int @@ b * b + c * c - a * a) /. (float_of_int @@ 2 * b * c) in
  -1. < cosa && cosa < 1.


let rec i_loop i result_i =

  let rec j_loop j result_j =

    let rec k_loop k result_k =
      if k >= n then result_k else (
        if l.(i) = l.(j) || l.(j) = l.(k) || l.(i) = l.(k) then k_loop (k+1) result_k else
        if is_triangle l.(i) l.(j) l.(k) then k_loop (k+1) (result_k+1) else k_loop (k+1) result_k
      )
    in if j >= n then result_j else j_loop (j+1) (result_j + k_loop (j+1) 0)
  in if i >= n then result_i else i_loop (i+1) (result_i + j_loop (i+1) 0)

let _ = Printf.printf "%d\n" @@ i_loop 0 0