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;

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

    a.reverse();

    let ans = lis(&a, 100001);
    println!("{}", ans);
}

fn lis(v: &Vec<usize>, max_n: usize) -> usize {
    let inf = 10usize.pow(10);
    let mut dp = vec![inf; max_n];

    for i in 0..v.len() {
        let index = upper_bound(&dp, v[i]);
        dp[index] = v[i];
    }

    lower_bound(&dp, inf)
}

fn upper_bound<T>(v: &Vec<T>, n: T) -> usize 
where T: 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
}
fn lower_bound<T>(v: &Vec<T>, n: T) -> usize
where
    T: 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
}