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: Accepted)

fn main() {
    let n: usize = read();
    let mut s: Vec<usize> = Vec::new();
    let a = (0..n).map(|_| read::<usize>());
    for aa in a {
        if s.is_empty() {
            s.push(aa);
            continue;
        }
        if s[0] >= aa {
            s.insert(0, aa);
            continue;
        }
        let mut lb = 0;
        let mut ub = s.len();
        while ub - lb > 1 {
            let mid = (ub + lb) / 2;
            if s[mid] < aa {
                lb = mid;
            } else {
                ub = mid;
            }
        }
        s[lb] = aa;
    }
    println!("{}", s.len());
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}