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 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import javax.swing.tree.TreeNode;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Deque;
import java.util.Vector;
import static java.lang.System.*;


public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	
		int n = sc.nextInt();
		int[] l = new int[n];
		for(int i = 0; i < n; i++) {
			l[i] = sc.nextInt();
		}
		int ans = 0;
		Arrays.sort(l);
		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] && l[i]+l[j] > l[k] && l[j]+l[k] > l[i] && l[k]+l[i] > l[j]) {
						++ans;
					}
				}
			}
		}
		
		System.out.println(ans);
	}
	
}