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.PrintWriter;
import java.util.*;

public class Main {
    static Scanner scanner;
    static PrintWriter out;
    public static void main(String[] args) {
        scanner = new Scanner(System.in);
        out = new PrintWriter(System.out);

        int count = nextInt();

        List<Long> sticks = new ArrayList<>();

        for (int i = 0; i < count; i++) {
            sticks.add(nextLong());
        }

        int ret = 0;

        for (int i = 0; i < count-2; i++) {
            long one = sticks.get(i);
            for (int j = i+1; j < count-1; j++) {
                if (i == j) continue;
                long two = sticks.get(j);
                if (one == two) continue;
                for (int k = j+1; k < count; k++) {
                    if (i == k || j == k) continue;
                    long three = sticks.get(k);
                    if (two == three || one == three) continue;
                    if (one + two > three && Math.abs(one- two )< three) {
                        ret++;
                    }
                }
            }
        }
        out.println(ret);
        out.flush();
    }

    public static void println(Object o) {
        out.println(o);
    }

    public static void print(Object o) {
        out.print(o);
    }

    public static void printf(String format, Object... o) {
        out.printf(format, o);
    }

    public static String next() {
        return scanner.next();
    }

    public static int nextInt() {
        return Integer.parseInt(scanner.next());
    }

    public static long nextLong() {
        return Long.parseLong(scanner.next());
    }

    public static double nextDouble() {
        return Double.parseDouble(scanner.next());
    }

    public static short nextShort() {
        return Short.parseShort(scanner.next());
    }

    public static float nextFloat() {
        return Float.parseFloat(scanner.next());
    }

    public static void printYes() {
        System.out.println("Yes");
    }

    public static void printYES() {
        System.out.println("YES");
    }

    public static void printNo() {
        System.out.println("No");
    }

    public static void printNO() {
        System.out.println("NO");
    }

    public static String nextLine() {
        return scanner.nextLine();
    }

    public static double distance(double x, double y, double x2, double y2) {
        return Math.sqrt((x2 - x) * (x2 - x) + (y2 - y) * (y2 - y));
    }

    public static int MOD = 1_000_000_007;
    public static int MAX = 100000;
    public static long[] fac = new long[MAX];
    public static long[] finv = new long[MAX];
    public static long[] inv = new long[MAX];

    public static void combinit() {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i < MAX; i++) {
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }

    public static long combination(int n, int k) {
        if (n < k || n < 0 || k < 0) return 0;
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }

    public static long factorial(long n) {
        return n <= 0 ? 1 : n * factorial(n - 1);
    }
}