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)

// -*- coding:utf-8-unix -*-

#[macro_use]
extern crate lazy_static;

// use proconio::derive_readable;
use proconio::fastout;
use proconio::input;
// use std::convert::TryInto;
use libm::*;
use std::cmp::*;
use std::collections::{BinaryHeap, HashSet};
use std::io::*;
use std::str::FromStr;
use superslice::*;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

//abc175-B
// #[fastout]
fn main() {
    input![n: usize, l: [u64; n]];
    // let set: HashSet<u64> = v.into_iter().collect();
    // let l: Vec<u64> = set.into_iter().collect();
    let size = l.len();

    let mut ans = 0;
    // eprintln!("{:?}", l);

    // let mut set = HashSet::new();

    for i in 0..size {
        let li = l[i];
        for j in (i + 1)..size {
            if i == j {
                continue;
            }
            let lj = l[j];

            for k in (j + 1)..size {
                if k == j || k == i {
                    continue;
                }
                let lk = l[k];

                // eprintln!("sum: {}, {}, {}", li + lj, lj + lk, lk + li);
                if li + lj > lk && lj + lk > li && lk + li > lj {
                    if li != lj && lj != lk && lk != li {
                        // eprintln!("{},{},{}", li, lj, lk);
                        // eprintln!("{},{},{}", i + 1, j + 1, k + 1);
                        ans += 1;
                        // let mut sorted = [li, lj, lk];
                        // sorted.sort();
                        // set.insert((sorted[0], sorted[1], sorted[2]));
                    }
                }
            }
        }
    }

    // println!("{:?}", set);
    // println!("{}", set.len());
    println!("{}", ans);
}

fn go(mid: usize, d: usize, use_num: usize, num753_cand: &mut Vec<usize>, n: usize) {}

// use lazy_static::lazy_static;
// use std::sync::Mutex;

// lazy_static! {
//     static ref VALUES: Mutex<Vec<i32>> = Mutex::default();
// }

// let mut values = VALUES.lock().unwrap();
// values.extend_from_slice(&[1, 2, 3, 4]);
// assert_eq!(&*values, &[1, 2, 3, 4]);