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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.StringTokenizer

fun main() {

    fun PrintWriter.solve() {
        val n = nextInt()
        val L = List(n){nextInt()}

        var ans = 0
        for (i in L.indices){
            for (j in i+1..n-1){
                for (k in j+1..n-1){
                    if (L[i] == L[j] || L[j] == L[k] || L[i] == L[k]) continue
                    val list = listOf(L[i],L[j], L[k]).sorted()
                    if (list[0] + list[1] > list[2])ans++
                }
            }
        }

        println(ans)

    }

    writer.solve()
    writer.flush()


}


private val reader = System.`in`.bufferedReader()
private val writer = PrintWriter(System.out, false)

private var tokenizer: StringTokenizer = StringTokenizer("")

private fun next(): String {
    while (tokenizer.hasMoreTokens().not()) tokenizer = StringTokenizer(reader.readLine())
    return tokenizer.nextToken()
}

private fun nextInt() = next().toInt()
private fun nextLong() = next().toLong()
private fun nextDouble() = next().toDouble()
private fun nextLine() = reader.readLine()