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.*;
import java.io.*;
class Main{
	public static void main(String[]args){
		Scanner sc=new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out, true);
		int n = sc.nextInt();
		int a[]=new int[n];
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
		}
		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++){
					Solve obj = new Solve(a[i], a[j], a[k]);
					if(obj.solve())
						count++;
				}
			}
		}
		out.println(count);
	}
}

class Solve{
	int a, b, c;

	public Solve(int x, int y, int z){
		this.a=x;
		this.b=y;
		this.c=z;
	}

	public boolean solve(){
		if(this.a > this.b){
			int temp = this.a;
			this.a = this.b;
			this.b = temp;
		}

		if(this.a > this.c){
			int temp = this.a;
			this.a = this.c;
			this.c = temp;
		}

		if(this.b > this.c){
			int temp = this.b;
			this.b = this.c;
			this.c = temp;
		}

		return this.a != this.b && this.b != this.c && this.a + this.b > this.c;
	}
}