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.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Main {
    static final Scanner sc = new Scanner(System.in);
    static boolean check(long a, long b, long c){
        return a < b+c && b < a+c && c < a+b;
    }
    public static void main(String[] args) {
        int n = Integer.parseInt(sc.nextLine());
        String[] s = sc.nextLine().split("\\s");
        long[] arr = Arrays.stream(s).mapToLong(Long::parseLong).toArray();
        Map<Long, Integer> count = new HashMap<>(); 
        for (long a: arr){
            count.put(a, count.getOrDefault(a, 0) + 1);
        }
        Long[] keys = count.keySet().stream().sorted().toArray(Long[]::new);
        long a, b, c, ans = 0;
        for (int i=0; i<keys.length; i++){
            a = keys[i];
            for (int ii=i+1; ii<keys.length; ii++){
                b = keys[ii];
                for (int iii=ii+1; iii<keys.length; iii++){
                    c = keys[iii]; 
                    if (check(a, b, c)){
                        ans += count.get(a)*count.get(b)*count.get(c);
                    }
                }
            }
        }
        System.out.println(ans);
    }
}