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 scala.io.StdIn

object Main extends App {
  StdIn.readLine()
  val sticks = StdIn.readLine().split(' ').map(_.toInt)

  val stickIdCombinations=scala.collection.mutable.Set.empty[Set[Int]]
  for(s1 <- 0 until sticks.length){
    for(s2 <- 0 until sticks.length){
      for(s3 <- 0 until sticks.length){
        val stickLens = List(s1,s2,s3).map(sticks(_)).toSet
        if(stickLens.size == 3){
          stickIdCombinations += Set(s1,s2,s3)
        }
      }
    }
  }

  val ans = (for (stickIds <- stickIdCombinations.toList) yield {
    val List(s1, s2, s3) = stickIds.toList.map(sticks(_))
    if (s1 + s2 > s3 && s2 + s3 > s1 && s3 + s1 > s2)
      1
    else
      0
  }).sum

  println(ans)



}