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 kotlin.math.*

fun main() {
    println(solve())
}

val solve: () -> Any = {
    val N = readInt()
    val L = readIntList().sorted()
    var res = 0
    for (i in 0 until N) {
        val a = L[i]

        for (j in i until N) {
            val b = L[j]
            if (a == b) continue

            for (k in j until N) {
                val c = L[k]
                if (b == c) continue
                if (a+b > c)
                    res++
            }
        }
    }
    res
}

val mod: Int = 1_000_000_007


fun readString() = readLine()!!
fun readStringList() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)

fun <T> T.alsoPrintln() = also { println(this) }

fun Boolean.toYesOrNo(yes: String = "Yes", no: String = "No") = if (this) yes else no

fun <E> List<E>.toPair() = this[0] to this[1]

fun <T> readPair(t: (String) -> T) = readPair(t, t)
fun <S, T> readPair(s: (String) -> S, t: (String) -> T) =
    readLine()!!.split(" ").let { Pair(s(it[0]), t(it[1])) }

fun Int.pow(n: Int) = this.toDouble().pow(n).toInt()

fun minAndMax(a: Int, b: Int) = if (a < b) a to b else b to a

fun <T> T.ifOrThis(bool: (T) -> Boolean, trans: (T) -> T) = if (bool(this)) trans(this) else this
fun <T> T.ifOrThis(bool: Boolean, trans: (T) -> T) = if (bool) trans(this) else this