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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Collections;
import java.util.Arrays;

public class Main {
	public static void main(final String[] args){
    
    final Scanner sc = new Scanner(System.in);
    final List<Long> list = new ArrayList<>();
    //final List<Long> list2 = new ArrayList<>();

    long n = sc.nextLong();
    int count = 0;

    for(int i = 0; i < n ; i++){
        list.add(sc.nextLong());
    }

    for(int i = 0; i < n ; i++){
        for(int j = i + 1; j < n ; j++){
            for(int l = j + 1; l < n ; l++){
                if(list.get(i) != list.get(j) && list.get(j) != list.get(l) && list.get(l) != list.get(i)){
                    if(list.get(i) < list.get(l) && list.get(j) < list.get(l) && list.get(i) + list.get(j) > list.get(l)){
                        count++;
                        //System.out.println((i+1) + " " + (j+1) + " " + (l+1));
                    }else if(list.get(j) < list.get(i) && list.get(l) < list.get(i) && list.get(j) + list.get(l) > list.get(i)){
                        count++;
                        //System.out.println((i+1) + " " + (j+1) + " " + (l+1));
                    }else if(list.get(i) < list.get(j) && list.get(l) < list.get(j) && list.get(l) + list.get(i) > list.get(j)){
                        count++;
                        //System.out.println((i+1) + " " + (j+1) + " " + (l+1));
                    }
                }
            }
        }
    }

    System.out.println(count);



    


    

   
    





}
}