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 1.8.0) (judge verdict: Accepted)

 import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        IO io = new IO();
        int n = io.nextInt();
        long[] a = io.nLongA(n);

        Arrays.sort(a);

        Set<String> set = new HashSet<>();
        for (int i = 0; i < a.length; i++) {
            for (int j = i + 1; j < a.length; j++) {
                for (int k = j + 1; k < a.length; k++) {

                    if (a[i] + a[j] > a[k] && a[i] + a[k] > a[j] && a[j] + a[k] > a[i]
                        && a[i] != a[j] && a[j] != a[k] && a[k] != a[i]) {
                        //System.out.println(a[i] + " " + a[j] + " " + a[k]);
                        String v = String.valueOf(i) + String.valueOf(j) + String.valueOf(k);
                        set.add(v);
                    }
                }

            }
        }

        io.write(set.size());
    }
    
    static class IO {
        BufferedWriter bw;
        BufferedReader br;
        StringTokenizer st;

        public IO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }

        public void write(String s) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(s);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }  
        }

        public void write(long value) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(value);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(int value) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(value);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(boolean b, String truev, String falsv) {
            try {
                StringBuilder sb = new StringBuilder();
                sb.append(b ? truev : falsv);
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(int[] a, char sep) {
            try {
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i < a.length; i++) {
                   sb.append(a[i]);
                   sb.append(sep);
                }
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }

        public void write(long[] a, char sep) {
            try {
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i < a.length; i++) {
                   sb.append(a[i]);
                   sb.append(sep);
                }
                sb.append("\n");
                bw.write(sb.toString());
                bw.flush();
            } catch(Exception e) {
                e.printStackTrace();
            }
        }
 
        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] nIntA(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public long[] nLongA(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        public double[] nDoubleA(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextDouble();
            }
            return a;
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}