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)

/*
    Author: Anthony Ngene
    Created: 15/08/2020 - 12:58
*/

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

public class Main {
// Life has no limitations, except the ones you make. - Les Brown
    public static void main(String[] args) throws IOException {
        in = new FastScanner();

        int n = in.intNext();
        long[] arr = in.nextLongArray(n);
        int count = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (arr[i] != arr[j]) {
                    for (int k = j + 1; k < n; k++) {
                        if (arr[k] != arr[i] && arr[k] != arr[j] && check(arr[i], arr[j], arr[k])) count++;
                    }
                }
            }
        }
        out.println(count);

        out.close();
    }

    static boolean check(long a, long b, long c) {
        return a + b > c && a + c > b && b + c > a;
    }

// Generated Code Below:
private static final FastWriter out = new FastWriter();
private static FastScanner in;
static ArrayList<Integer>[] adj;
private static long e97 = (long)1e9 + 7;
static class FastWriter {
    private static final int IO_BUFFERS = 128 * 1024;
    private final StringBuilder out;
    public FastWriter() { out = new StringBuilder(IO_BUFFERS); }
    public FastWriter p(Object object) { out.append(object); return this; }
    public FastWriter p(String format, Object... args) { out.append(String.format(format, args)); return this; }
    public FastWriter pp(Object... args) { for (Object ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public void println(long[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public void println(int[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public void println(char[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public void println(double[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public void println(boolean[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public <T>void println(T[] arr) { out.append(Arrays.toString(arr)).append("\n"); }
    public void println(long[][] arr) {  for (long[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(int[][] arr) {  for (int[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(char[][] arr) {  for (char[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(double[][] arr) {  for (double[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public <T>void println(T[][] arr) {  for (T[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public FastWriter println(Object object) { out.append(object).append("\n"); return this; }
    public void toFile(String fileName) throws IOException {
        BufferedWriter writer = new BufferedWriter(new FileWriter(fileName));
        writer.write(out.toString());
        writer.close();
    }
    public void close() throws IOException { System.out.print(out); }
}
static class FastScanner {
    private InputStream sin = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(){}
    public FastScanner(String filename) throws FileNotFoundException {
        File file = new File(filename);
        sin = new FileInputStream(file);
    }
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = sin.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long longNext() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int intNext() {
        long nl = longNext();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double doubleNext() { return Double.parseDouble(next());}
    public long[] nextLongArray(final int n){
        final long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = longNext();
        return a;
    }
    public int[] nextIntArray(final int n){
        final int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = intNext();
        return a;
    }
    public double[] nextDoubleArray(final int n){
        final double[] a = new double[n];
        for (int i = 0; i < n; i++)
            a[i] = doubleNext();
        return a;
    }
    public ArrayList<Integer>[] getAdj(int n) {
        ArrayList<Integer>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
        return adj;
    }
    public ArrayList<Integer>[] adjacencyList(int n, int m) throws IOException {
        adj = getAdj(n);
        for (int i = 0; i < m; i++) {
            int a = intNext(), b = intNext();
            adj[a].add(b);
            adj[b].add(a);
        }
        return adj;
    }
}
}