Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_macros)]
macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut iter = $s.split_whitespace();
            let mut next = || { iter.next().unwrap() };
            input_inner!{next, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = std::io::stdin();
            let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
            let mut next = move || -> String{
                bytes
                    .by_ref()
                    .map(|r|r.unwrap() as char)
                    .skip_while(|c|c.is_whitespace())
                    .take_while(|c|!c.is_whitespace())
                    .collect()
            };
            input_inner!{next, $($r)*}
        };
    }

#[allow(unused_macros)]
macro_rules! input_inner {
        ($next:expr) => {};
        ($next:expr, ) => {};

        ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
            let $var = read_value!($next, $t);
            input_inner!{$next $($r)*}
        };

        ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
            let mut $var = read_value!($next, $t);
            input_inner!{$next $($r)*}
        };
    }

#[allow(unused_macros)]
macro_rules! read_value {
        ($next:expr, ( $($t:tt),* )) => {
            ( $(read_value!($next, $t)),* )
        };

        ($next:expr, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        };

        ($next:expr, chars) => {
            read_value!($next, String).chars().collect::<Vec<char>>()
        };

        ($next:expr, bytes) => {
            read_value!($next, String).into_bytes()
        };

        ($next:expr, usize1) => {
            read_value!($next, usize) - 1
        };

        ($next:expr, $t:ty) => {
            $next().parse::<$t>().expect("Parse error")
        };
    }

fn main() {
    input! {
            n: usize,
            numbers: [i32; n],
        }

    let mut colors = vec![0];
    let mut minimum_cache = 0;

    for i in 0..n {
        let current_number: i32 = numbers[i];
        let appropriate_index = find_appropriate_index(&colors, current_number);
        if appropriate_index.is_none() {
            minimum_cache = current_number;
            colors.push(current_number);
        } else {
            let idx = appropriate_index.unwrap();
            colors[idx] = current_number;
        }
    }

    // not sure
    println!("{}", colors.len() - 1);
}

fn find_appropriate_index(colors: &Vec<i32>, current_number: i32) -> Option<usize> {
    let appropriate_colors= colors.iter().enumerate().filter(|&(_, &x)| x < current_number).map(|(idx, &value)| (idx, value)).collect::<Vec<(usize, i32)>>();
    let answer_value = appropriate_colors.iter().map(|&(_, x)| x).min();
    let answer= appropriate_colors.iter().find(|&&(idx, x)| x == answer_value.unwrap_or(-1)).map(|&(idx, _)| idx);

    return answer;
}