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: Runtime Error)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;

public class Main{
    public static void main(String[] args){
        //入力
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        ArrayList<Integer> lengthList = new ArrayList<>();
        for(int i = 0; i < n; i++){
            lengthList.add(sc.nextInt());
        }

        lengthList = sort(lengthList);

        for(int i = 0; i<n-1; i++){
            while(lengthList.get(i) == lengthList.get(i+1)){
                lengthList.remove(i);
                n--;
            }
        }

        int count = 0;

        for(int i = 0; i < n; i++){
            for(int j = i + 1; j < n; j++){
                for(int k = j + 1; k < n; k++){
                    if(lengthList.get(i) + lengthList.get(j) > lengthList.get(k)){
                        count++;
                    }
                }
            }
        }

        System.out.println(count);
    }

    
    private static ArrayList<Integer> sort(ArrayList<Integer> list){
        int n = list.size();
        for(int i = 1; i<n; i++){
            for(int j = 0; j<n-i; j++){
                if(list.get(j) > list.get(j+1)){
                    int tmp = list.get(j+1);
                    list.set(j+1, list.get(j));
                    list.set(j, tmp);
                }
            }
        }
        return list;
    }
}