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 {
    ( $($t:ty),* ) => {{
        let mut s = String::new();
        std::io::stdin().read_line(&mut s);
        let mut splits = s.trim().split_whitespace();
        ($( { splits.next().unwrap().parse::<$t>().unwrap() },)*)
    }}
}

fn lis(v: &Vec<u32>) -> usize {
    let mut seq = vec![];

    fn push(seq: &mut Vec<u32>, pos: usize, val: u32) {
        if seq.len() <= pos {
            seq.push(val);
        } else {
            seq[pos] = val;
        }
    }

    for val in v {
        match seq.binary_search(val) {
            Ok(pos) => {
                let mut right_pos = pos;
                for i in pos..(v.len() - 1) {
                    if v[pos] != *val {
                        right_pos = i - 1;
                    }
                }
                if v[v.len() - 1] == v[pos] {
                    right_pos = v.len() - 1;
                }

                push(&mut seq, right_pos, *val);
            },
            Err(pos) => {
                push(&mut seq, pos, *val);
            },
        }
    }
    
    return seq.len();

}

fn lds(v: &Vec<u32>) -> usize {
    let mut rev = v.clone();
    rev.reverse();
    return lis(&rev);
}

#[allow(unused_must_use)]
#[allow(unused_variables)]
fn solve() {
    let (n,) = input!(usize);
    let mut a = vec![];

    for _ in 0..n {
        let (tmp,) = input!(u32);
        a.push(tmp);
    }

    println!("{}", lds(&a));
}

fn main() {
    solve();
}