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)

use std::io::*;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let a: Vec<usize> = (0..n).map(|_| read()).collect();

    // 大きい順
    let mut vec: Vec<usize> = vec![];
    vec.push(a[0]);
    for i in 1..n {
        if vec[vec.len()-1] >= a[i] {
            vec.push(a[i]);
            continue;
        }
        let mut ok = vec.len();
        let mut ng = 0;
        while ng + 1 < ok {
            let mid = (ok + ng) / 2;
            if vec[mid] < a[i] {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        if vec[ng] < a[i] {
            vec[ng] = a[i];
        } else {
            vec[ng+1] = a[i];
        }
    }
    println!("{}", vec.len());
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}