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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use std::io::stdin;

#[derive(Default)]
struct Scanner {
	buffer: Vec<String>
}

impl Scanner {
	fn next<T: std::str::FromStr> (&mut self) -> T {
		loop {
			if let Some(token) = self.buffer.pop() {
				return token.parse().ok().expect("Failed parse");
			}
			let mut input = String::new();
			stdin().read_line(&mut input).expect("Failed read");
			self.buffer = input.split_whitespace().rev().map(String::from).collect();
		}
	}
}

fn main() {
	let mut scan = Scanner::default();

	let n: usize = scan.next();
	let mut a: Vec<usize> = vec![0;n];
	for i in 0..n {
		a[i] = scan.next();
	}
	a.sort();
	//println!("{:?}", a);
	let mut ans: usize = 0;
	for i in 0..n-2 {
		for j in i+1..n-1 {
			if a[i] == a[j] { continue; }
			let mut add: usize = 0;
			for k in j+1..n {
				if a[k] == a[j] {continue;}
				else if a[k] < a[i] + a[j] {add += 1;}
				else {break;}
			}
			ans += add;
		}
	}
	println!("{}", ans);
}