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)

pub 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()
}

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

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn bsearch(l: usize, r: usize, v: &Vec<u32>, a: u32) -> usize {
    if v[l] > a {
        return 0;
    }

    let ret: usize;
    if l + 1 >= r {
        ret = r;
    } else {
        let m = (l + r) / 2;
        if v[m] <= a {
            ret = bsearch(m, r, v, a);
        } else {
            ret = bsearch(l, m, v, a);
        }
    }
    ret
}

fn main() {
    let n: usize = read();
    let a: Vec<u32> = read_col(n);

    let mut v: Vec<u32> = vec![a[n - 1]];

    for i in (0..n - 1).rev() {
        let id = bsearch(0, v.len(), &v, a[i]);
        if id == v.len() {
            v.push(a[i]);
        } else {
            v[id] = a[i];
        }
    }

    println!("{}", v.len());
}