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: Accepted)

import java.util.*;
import java.lang.*;
import java.io.*;

public class Main{

    static final FastReader in = new FastReader();
    static final FastWriter out = new FastWriter();

    public static void main(String[] args) throws IOException{
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = in.nextInt();
        int ans = 0;
        for (int i = 0; i < n-2; i++){
            for (int j = i+1; j < n-1; j++){
                for (int k = j+1; k < n; k++){
                    if (a[i]!=a[j]&&a[i]!=a[k]&&a[j]!=a[k]&&(a[i]+a[j]>a[k]&&a[j]+a[k]>a[i]&&a[i]+a[k]>a[j])&&(i!=j&&j!=k&&i!=k)){
                        //out.pl(i + " " + j + " " + k);
                        ans++;
                    }
                }
            }
        }
        out.pl(ans);
        out.close();
    }
}
class FastReader{
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in)); 
    } 
    String next(){ 
        while (st == null || !st.hasMoreElements()) { 
            try{ 
                st = new StringTokenizer(br.readLine()); 
            }catch (IOException  e){ 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
    int nextInt(){ 
        return Integer.parseInt(next()); 
    } 
    long nextLong(){ 
        return Long.parseLong(next()); 
    } 
    double nextDouble(){ 
      return Double.parseDouble(next()); 
    } 
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        } 
        catch (IOException e){ 
            e.printStackTrace(); 
        } 
        return str; 
    }
}
class FastWriter{
    PrintWriter out;
    FastWriter(){
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	out.flush();
    }
    void pl(Object o){
        out.write(o.toString());
	    out.write("\n");
        out.flush();
    }
    void pl(){
        out.write("\n");
    }
    void p(Object o){
        out.write(o.toString());
    }
    void close(){
        out.flush();
        out.close();
    }  
}