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)

//package abc175;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		
		String[] ip = br.readLine().split(" ");
		
		int[]ary = new  int[N];
		
		for(int i = 0 ; i < N ;i ++) {
			ary[i] = Integer.parseInt(ip[i]);
		}
		
		Arrays.sort(ary);
		
		long ans = 0;
		
		for(int i = 0 ; i < N ; i++) {
			for(int j = i+1 ; j < N ; j++) {
				for(int k = j+1 ; k < N ; k++) {
					long a = ary[i];
					long b = ary[j];
					long c = ary[k];
					
					if(a!=b && b!=c && c != a) {
						if(a+b > c && b+c > a && a+c > b)
							ans++;
					}
				}
			}
		}
		
		System.out.println(ans);
	}
	
}