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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        Map<Integer, Integer> henMap = new HashMap<>();
        for(int i=0;i<N;i++){
            int len = sc.nextInt();
            henMap.putIfAbsent(len, 0);
            henMap.put(len, henMap.get(len)+1);
        }
        List<Integer> henLst = new ArrayList<>();
        henLst.addAll(henMap.keySet());
        int cnt = 0;
        for(int i=0;i<henLst.size();i++){
            for(int j=i+1;j<henLst.size();j++){
                for(int k=j+1;k<henLst.size();k++){
                    if(henLst.get(i) + henLst.get(j) > henLst.get(k))
                        cnt += henMap.get(henLst.get(i))*henMap.get(henLst.get(j)) * henMap.get(henLst.get(k));

                }
            }
        }
        System.out.println(cnt);
    }

}