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.Scanner;
import java.util.ArrayList;
import java.util.Collections;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
      	//長さの情報
		ArrayList<Long> length = new ArrayList<Long>();
        // 本数
        int n = sc.nextInt();
      	if(n<=2){//二本以下では成立しないので
          System.out.println(0);
        }else{
          
          //結果
          int result=0;



          for(int i=0;i<n;i++){//入力
            long input=sc.nextLong();
            length.add(input);
          }


          Collections.sort(length);//短い順に

          /*確認用
          for(int i=0;i<length.size();i++){
            System.out.print(length.get(i));
          }
          */



        for(int i=0;i<n-2;i++){
          for(int j=i+1;j<n-1;j++){
            for(int k=j+1;k<n;k++){
              if(length.get(i)!=length.get(j)&&length.get(j)!=length.get(k)){
                if(length.get(i)+length.get(j)>length.get(k)){
                  result+=1;
                  //System.out.println(length.get(i)+"　"+length.get(j)+"　"+length.get(k));
                }
              }
            }
          }
        }





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