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.BufferedReader
import java.util.*

fun main() = abc175b()

@OptIn(ExperimentalStdlibApi::class)
fun abc175b() = SimpleFastIOWithToken_abc175b().exec {
    val n = readInt()
    val lList = LongArray(n) { readLong() }.sortedArray()

    var answer = 0L

    for (i in 0 until n) for (j in i + 1 until n) for (k in j + 1 until n) {
        val a = lList[i]
        val b = lList[j]
        val c = lList[k]
        if (a + b > c && a < b && b < c) answer++
    }

    println(answer)
}

// region kokokara template dayo (^o^)
@Suppress("unused", "HasPlatformType", "MemberVisibilityCanBePrivate", "ClassName")
private class SimpleFastIOWithToken_abc175b(private val separator: String = System.lineSeparator()) {
    private val br: BufferedReader = System.`in`.bufferedReader()
    private var st: StringTokenizer = StringTokenizer("")
    private val sb: StringBuilder = StringBuilder()
    private fun prepareNext() = run { if (!st.hasMoreTokens()) st = StringTokenizer(br.readLine()) }

    fun readString(): String = run { prepareNext() }.run { st.nextToken() }
    fun readInt(): Int = Integer.valueOf(readString())
    fun readLong(): Long = java.lang.Long.valueOf(readString())

    fun println(): Unit = run { sb.append(separator) }
    fun print(any: Any): Unit = run { sb.append(any) }
    fun println(any: Any): Unit = run { sb.append(any.toString() + separator) }

    fun exec(action: SimpleFastIOWithToken_abc175b.() -> Unit) {
        var t: Throwable? = null
        Thread(null, { action() }, "solve", 128 * 1024 * 1024)
            .apply { setUncaughtExceptionHandler { _, t1 -> t = t1 } }
            .apply { start() }.join()
        t?.let { throw it }
        kotlin.io.print(sb)
    }

    fun readLine(): Nothing = error("readLine is disabled.")
}
// endregion kokomade template dayo (^o^)