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)

// Practice AtCoder
// author: Leonardone @ NEETSDKASU

fn main() {
    let mut stdin = String::new();
    std::io::Read::read_to_string(
        &mut std::io::stdin(),
        &mut stdin).unwrap();
    let mut stdin = stdin.split_whitespace();
    let mut get = || stdin.next().unwrap();
    macro_rules! get {
        ($t:ty) => (get().parse::<$t>().unwrap());
        () => (get!(i64));
    }
    
    let n = get!(usize);
    let mut vs = vec![];
    for _ in 0 .. n {
        vs.push(get!());
    }
    
    let mut ws = vec![];
    ws.push(vs[n-1]);
    for i in 1 .. n {
    	let i = (n-1) - i;
        let v = vs[i];
        let mut lp = 0;
        let mut rp = ws.len();
        while lp < rp {
            let hp = (lp + rp) / 2;
            if ws[hp] <= v {
                lp = hp + 1;
            } else {
                rp = hp;
            }
        }
        if lp == ws.len() {
            ws.push(v);
        } else if ws[lp] <= v {
            ws.insert(lp+1, v);
        } else {
            ws[lp] = v;
            while lp > 0 && ws[lp-1] > ws[lp] {
                ws.swap(lp, lp-1);
                lp -= 1;
            }
            while lp+1 < ws.len() && ws[lp+1] < ws[lp] {
                ws.swap(lp, lp+1);
                lp += 1;
            }
        }
    }
    println!("{}", ws.len());
}