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: Accepted)

use std::collections::BTreeSet;

fn main() {
    let stick_cnt = read::<usize>()[0];
    let stick_lengthes = read::<u64>();
    let mut result = 0;
    'root: for i in 0..stick_cnt {
        if i == stick_cnt {
            break;
        }
        for j in (i+1)..stick_cnt {
            if j == stick_cnt {
                continue'root;
            }
            for k in (j+1)..stick_cnt {
                let i_len = stick_lengthes[i];
                let j_len = stick_lengthes[j];
                let k_len = stick_lengthes[k];
                if i_len == j_len || j_len == k_len || i_len == k_len {
                    continue
                }
                if i_len + j_len > k_len && j_len + k_len > i_len && i_len + k_len > j_len {
                    result += 1;
                }
                // if i_len + j_len > k_len {
                //     result += 1;
                // }
            }
        }
    }
    println!("{}", result);
}

use std::io::{self, BufRead, Read};
use std::vec::Vec;
fn read<T: std::str::FromStr>() -> Vec<T> {
    let stdin = io::stdin();
    let mut buf = String::new();
    stdin.lock().read_line(&mut buf).unwrap();
    parse_line(&buf)
}

fn read_lines<T: std::str::FromStr>(count: usize) -> Vec<Vec<T>> {
    let stdin = io::stdin();
    let mut stdin = stdin.lock();
    let mut result = Vec::<Vec<T>>::with_capacity(count);
    for _ in 0..count {
        let mut buf = String::new();
        stdin.read_line(&mut buf).unwrap();
        result.push(parse_line(&buf));
    }
    result
}

fn parse_line<T: std::str::FromStr>(string: &str) -> Vec<T> {
    string.trim().split(' ').map(|s| T::from_str(s).ok().unwrap()).collect()
}