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 = read();
    let a: Vec<u32> = (0..n).map(|_| read()).collect();

    let mut min_value = Vec::new();
    for e in a.iter().rev() {
        let k = lower_bound(|&x| x>e, &min_value);
        if k == min_value.len() { min_value.push(e) }
        else { min_value[k] = e }
    }
    println!("{}", min_value.len());
}

fn lower_bound<T, F: Fn(&T)->bool>(f: F, a: &Vec<T>) -> usize {
    let mut l = 0;
    let mut r = a.len();
    while l != r {
        let m = (l+r) / 2;
        if f(&a[m]){ r = m   }
        else       { l = m+1 }
    }
    l
}

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