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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::collections::VecDeque;
use num::Num;

fn main() {
    input! {
        n: usize,
        a: [usize; n],
    }

    let mut v = VecDeque::new();

    v.push_back(a[0]);

    for &na in a.iter().skip(1) {
        if na <= v[0] {
            //println!("append {}", na);
            v.push_front(na);
            continue;
        } else {
            let index = upper_bound(&v, na - 1);
            //println!("{} -> {}", v[index-1], na);
            v[index - 1] = na;
        }
    }

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

fn upper_bound<T>(v: &VecDeque<T>, n: T) -> usize 
where T: Num + PartialEq + PartialOrd
{
    let mut left = -1;
    let mut right = v.len() as isize;
    
    while right - left > 1 {
        let mid = (left + right) / 2;
        if v[mid as usize] <= n {
            left = mid;
        } else {
            right = mid;
        }
    } 
    right as usize
}