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.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int array[] = new int[n];

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

        int ans = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    if (i == j || j == k || i == k) {
                    } else {
                        int a = 0;
                        int b = 0;
                        int c = 0;
                        a = array[i];
                        b = array[j];
                        c = array[k];
                        if (a == b || b == c || a == c) {
                        } else {
                            if (a >= b && a >= c) {
                                if (Math.abs(b - c) < a && a < b + c) {
                                    ans++;
                                }
                            } else if (b >= a && b >= c){
                                if (Math.abs(a - c) < b && b < a + c) {
                                    ans++;
                                }
                            } else if (c >= a && c >= b){
                                if (Math.abs(b - a) < c && c < a + b) {
                                    ans++;
                                }
                            }
                        }
                    }
                }
            }
        }

        System.out.println(ans / 6);

        sc.close();

        }

    }