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 void main(String[] args) {
		// TODO Auto-generated method stub
		try (Scanner sc = new Scanner(System.in)) {
			int n = Integer.valueOf(sc.nextLine());
			int[] bars = new int[n];

			if (n < 3) {
				System.out.println("0");
				return;
			}

			for (int i = 0; i < n; i++) {
				bars[i] = sc.nextInt();
			}

			if (bars.length != n) {
				System.out.println("OUT");
			}
			int ans = 0;
			for (int frist = 0; frist < n; frist++) {
				int a = bars[frist];

				for (int second = frist + 1; second < n; second++) {
					int b = bars[second];

					for (int third = second + 1; third < n; third++) {
						int c = bars[third];
						if (a ==b || b == c || a == c) {
							continue;
						} else if (isATriangle(a, b, c) && isATriangle(b, c, a) && isATriangle(c, a, b)) {
							ans++;
						}
					}
				}
			}

			System.out.println(ans);


		} catch (Exception e) {
			// TODO: handle exception
		}
	}

	private static boolean isATriangle(int x, int y, int z) {
		return ((x + y ) > z);

	}
}