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.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		ArrayList<Integer> list = new ArrayList<>();

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		for (int i = 0; i < n; i++) {
			int l = sc.nextInt();
			list.add(l);
		}
		sc.close();

		int count = 0;

		for (int i = 0; i < list.size(); i++) {
			for (int j = i + 1; j < list.size(); j++) {
				for (int k = j + 1; k < list.size(); k++) {
					int first = list.get(i);
					int second = list.get(j);
					int third = list.get(k);
					if (first == second || second == third || third == first) {
						continue;
					}
					if (isTriangle(list.get(i), list.get(j), list.get(k))) {
						count++;
					}
				}
			}
		}
		print(count);
	}

	public static boolean isTriangle(int i, int j, int k) {
		int max = Math.max(i, j);
		max = Math.max(max, k);
		if (i + j + k - max > max) {
			return true;
		}
		return false;
	}

	public static void print(Object obj) {
		System.out.println(obj);
	}

}