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.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        Main m = new Main(sc);
        m.show(m.solve());
        sc.close();
    }
    
	//フィールド
    Scanner sc;
    int N;
    int[] L;
    
    //入力
    Main(Scanner sc) {
        this.sc = sc;
        this.N = sc.nextInt();
        L = new int[N];
        for (int i=0; i<N; i++) {
        	L[i] = sc.nextInt();
        }
    }
    
    //解答処理
    private int solve() {
        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++) {
        			if (L[i]!=L[j] && L[j]!=L[k] && L[i]!=L[k] && isTriangle(L[i],L[j],L[k])) {
        				answer++;
        			}
        		}
        	}
        }
        
        return answer;
    }
    
    //三辺の長さがL[i],L[j],L[k]の三角形が存在するか判定するメソッド
    private boolean isTriangle(int i, int j, int k) {
    	boolean judge = false;
    	if (i+j>k && j+k>i && k+i>j) {
    		judge = true;
    	}
    	
    	return judge;
    }
    
    //出力
    public void show(int answer) {
        System.out.println(answer);
    }

}