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.util.Arrays;
import java.util.Scanner;

fun main (args : Array<String>) {
  val input = Scanner(System.`in`)
  
  while (input.hasNext()) {
    val N = input.nextInt()
    val L = IntArray(N)
    
    for (i in L.indices) {
      L[i] = input.nextInt()
    }
    
    Arrays.sort(L)
    
    var count = 0
    for (i in 0..L.lastIndex) {
      for (j in (i + 1)..L.lastIndex) {
        for (k in (j + 1)..L.lastIndex) {
          if (L[i] != L[j] && L[j] != L[k]) {
            if (L[i] + L[j] > L[k] && L[j] - L[i] < L[k]) {
              ++count
            }
          }
        }
      }
    }
    
    println(count)
  }
}