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.lang.management.MemoryUsage

fun main(){
    val n = readLine()!!.split(" ")[0].toInt()
    val l = readLine()!!.split(" ").map { it.toInt() }.sorted()
    val ll = mutableListOf<Int>()
    val kaisuu = mutableListOf<Int>()
    ll.add(l[0])
    kaisuu.add(1)
    for (i in 1 until n){
        if (l[i] == l[i-1]){
            val size = ll.size - 1
            kaisuu[size]++
        } else {
            ll.add(l[i])
            kaisuu.add(1)
        }
    }
    val m = ll.size
    var ans = 0
    for (i in 0 until m){
        for (j in i+1 until m){
            val total = ll[i] + ll[j]
            for (k in j+1 until m){
                if (total > ll[k]) {
                    ans += kaisuu[i] * kaisuu[j] * kaisuu[k]
                }
            }
        }
    }
    println(ans)
}