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)

#![allow(unused_imports)]

use std::cmp::{max, min};
use std::collections::*;
use std::io::{stdin, stdout, BufWriter, Write};

#[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 solve() {
    let mut scan = Scanner::default();
    let n: usize = scan.next();
    let mut v = vec![0;n];
    for i in 0..n {
        v[i] = scan.next();
    }
    let v = v;
    let mut res = 0;
    for i in 0..n {
        for j in i+1..n {
            for k in j+1..n {
                if v[i] == v[j] || v[j] == v[k] || v[k] == v[i] {
                    continue
                }
                if v[i]+v[j]>v[k] && v[j]+v[k]>v[i] && v[i]+v[k]>v[j] {
                    res += 1;
                }
            }
        }
    }
    println! ("{}", res);
}

fn main() {
    let mut scan = Scanner::default();
    // let t = scan.next::<u64>();
    let t = 1;
    for _ in 0..t {
        solve();
    }
}