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.Scanner;
public class Main {
	public static int[] L;

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = Integer.parseInt(scan.next());
		L = new int[N];
		for (int n = 0;n < N ;n++ ) {
			L[n] = Integer.parseInt(scan.next());
		}
		scan.close();
		System.out.println(MakingTriangle(N));
	}

	public static long MakingTriangle(int N) {
		long ans = 0;
		if (N < 3) return ans;
		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 ((L[i] == L[j]) || (L[j] == L[k]) || (L[k] == L[i])) continue;
					if ((L[i] + L[j] <= L[k]) || (L[j] + L[k] <= L[i]) || (L[k] + L[i] <= L[j])) continue;
					ans++;
				}
			}
		}
		return ans;
	}
}