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 Scala (2.13.1) (judge verdict: Accepted)

import io.StdIn.{readInt, readLine}
object Main extends App {
  val n = readInt
  val ls = readLine.split(" ").map(_.toInt)

  def different(i1: Int, i2: Int, i3: Int): Boolean = i1 != i2 && i2 != i3 && i3 != i1
  def makeable(i1: Int, i2: Int, i3: Int): Boolean = {
    val sorted = Seq(i1, i2, i3).sorted
    sorted(2) < sorted(0) + sorted(1)
  }

  val count = for (i <- 0 until n-2; j <- i until n-1; k <- j until n) yield {
    val li = ls(i)
    val lj = ls(j)
    val lk = ls(k)
    if (different(li, lj, lk) && makeable(li, lj, lk)) 1
    else 0
  }

  val result = count.sum
  println(result)
}