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{
    /**
     * メインメソッド
     */
    public static void main(final String[] args) {
        final Scanner sc = new Scanner(System.in);
        final int N = sc.nextInt();
        final ArrayList<Long> Lengths = new ArrayList<Long>();
        // while(sc.hasNext()){
        //     Lengths.add(sc.nextLong());
        // }
            for (int i = 0; i < N; i++){
                Lengths.add(sc.nextLong());
            }
        sc.close();
        final int answer = Logics(N, Lengths);
        System.out.println(answer);
    }

    /**
     * ロジック
     */
    public static int Logics(int N, List<Long> list) {
        int answer = 0;
        for (int i = 0; i < N; i++){
            for (int j = i + 1; j < N; j++){
                for (int k = j + 1; k < N; k++){
                    boolean judge1 = (list.get(i) == list.get(j) || list.get(i) == list.get(k) || list.get(j) == list.get(k));
                    boolean judge2 = (list.get(i) + list.get(j) > list.get(k) && list.get(j) + list.get(k) > list.get(i) && list.get(i) + list.get(k) > list.get(j));
                    if (judge1){
                        continue;
                    } else {
                        if(judge2) {
                            answer ++;
                        }
                    }
                }
            }
        }
        return answer;
    }
}