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.*; 


public class Main{
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
                
                int N = scan.nextInt();
                
                long[] L = new long[N];
                
                for(int i=0; i<N; i++){
                    L[i] = scan.nextLong();
                }
                
                int ans = 0;
                
                if(N<=2){
                    System.out.println(0);
                }else{
                    for(int i=0; i<N-2; i++){
                        for(int j=i; j<N-1; j++){
                            for(int k=j; k<N; k++){
                                if(L[i]!=L[j] && L[k]!=L[j] && L[k]!=L[i]){
                                    long a = L[i]+L[j];
                                    long b = L[j]+L[k];
                                    long c = L[k]+L[i];
                                    if(a>L[k] && b>L[i] && c>L[j]){
                                        ans++;
                                    }
                                }
                            }
                        }
                    }
                    
                    System.out.println(ans);
                }
                
                
   
        }
}