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.Scanner;

// 提出時にclass Main に書き換え
public class Main {
	public static void main(String[] args)  {
		// 標準入力を受け取る
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt(); // int Nを受け取る

		int[] L = new int[N]; // L[N]を格納する配列

		for (int i = 0; i < N; i++) {
			L[i] = sc.nextInt(); // int L[i]を受け取る
		}
		sc.close(); // 標準入力を終了

		int ans = 0; // 解答の数

		for (int i = 0; i < N - 2; i++) {
			for (int j = i + 1; j < N - 1; j++) {
				for (int k = j + 1; k < N; k++) {
					// L[i],L[j],L[k]が全て異なる値かどうか判定
					if(L[i] != L[j] && L[i] != L[k] && L[j] != L[k]) {
                       // 3辺の長さがL[i],L[j],L[k]の三角形があるかどうか判定
						if(Math.abs(L[i] - L[j]) < L[k] && L[k] < L[i] + L[j]) {ans += 1;}
					}
				}
			}
		}
		System.out.println(ans);
	}
}