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: Time Limit Exceeded)

use std::io::prelude::*;

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

fn main() {
    let n: usize = input();
    let a: Vec<i32> = (0..n).map(|_| input()).collect();

    let mut l = 0;
    let mut r = n;
    while r - l > 1 {
        let m = (l + r) / 2;
        if check(m, &a) {
            r = m;
        } else {
            l = m;
        }
    }
    println!("{}", r);
}

fn check(m: usize, a: &Vec<i32>) -> bool {
    let mut v = vec![];
    let mut ok = true;
    for &a in a {
        if v.is_empty() || v[0] >= a {
            v.push(a);
            v.sort();
            if v.len() > m {
                ok = false;
                break;
            }
        } else {
            let mut l = -1;
            let mut r = v.len() as i32;
            while r - l > 1 {
                let m = ((l + r) / 2) as usize;
                if v[m] >= a {
                    r = m as i32;
                } else {
                    l = m as i32;
                }
            }
            v[l as usize] = a;
            v.sort();
        }
    }
    ok
}