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.io.*;
import java.util.*;
import java.awt.Point;
public class Main {
	static Scanner sc;
	static PrintWriter out;
	static final int uncal = -1;
	static final int mod = (int) (1e9)+7;
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		sc = new Scanner(System.in); 
		out = new PrintWriter(System.out);
		int n = sc.nextInt();
		int[] s = sc.inArr(n);
		int cnt = 0;
		for (int i = 0; i < n; i++) {
			for (int j = i+1; j < n; j++) {
				if(s[i] == s[j]) continue;

				for (int j2 = j+1; j2 < n; j2++) {
						if(s[i] == s[j2] || s[j] == s[j2]) continue;
						if(checkTri(s[i], s[j], s[j2])) cnt++;
				}
			}
		}
		out.println(cnt);
		out.close();
	}
	static boolean checkTri(int a, int b,int c) {
		return a+b>c && a+c>b && b+c>a;
	}
	static void shuffle(int[] array) {
		Random rand = new Random();
		for (int i = 0; i < array.length; i++) {
			int randomIndexToSwap = rand.nextInt(array.length);
			int temp = array[randomIndexToSwap];
			array[randomIndexToSwap] = array[i];
			array[i] = temp;
		}
	}
	static boolean isPalindrome(String s) {
		int l = s.length();
		char[] sa = s.toCharArray();
		for(int i=0;i<l/2;i++) {
			if(sa[i] != sa[l-i-1])
				return false;
		}
		return true;
	}
	static class Point extends java.awt.Point implements Comparable<Point>{
		public Point(int x,int y) {
			// TODO Auto-generated constructor stub
			super(x,y);
		}
		public String toString() {
			return x+" "+y;
		}
		@Override
		public int compareTo(Point p) {
			// TODO Auto-generated method stub
			if(x == p.x)
				return y - p.y;
			return x - p.x;
		}
		
	}
	static class Scanner{
		private BufferedReader br;
		private StringTokenizer st;
		public Scanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		public Scanner(String filename) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(filename));
		}
		public String next() throws IOException{
			while(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
		public int nextInt() throws IOException{
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException{
			return Long.parseLong(next());
		}
		public double nextDouble() throws IOException{
			return Double.parseDouble(next());
		}
		public int[] inArr(int n) throws Exception{
			int a [] = new int[n];
			st = new StringTokenizer(br.readLine());
			for(int i=0;i<n;i++) {
				a[i] = Integer.parseInt(next());
			}
			return a;
		}
	}

}