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)

#![allow(dead_code)]
use std::io::*;

fn main(){
    let n: usize = read();
    let mut a: Vec<i32> = (0..n).map(|_| read()).collect();
    for i in 0..n{
        a[i] *= -1;
    }
    let mut b: Vec<i32> = vec![];
    for i in a{
        let t = upper_bound(&b, &i);
        match t{
            Some(j) =>{
                b[j] = i;
            },
            None => b.push(i),
        }
    }
    println!("{}", b.len());
}

fn upper_bound(a: &Vec<i32>, x: &i32) -> Option<usize>
{
    let mut ok: isize = a.len() as isize;
    let mut ng: isize = -1;
    if ok == 0 || a[ok as usize - 1] <= *x{
        None
    }else{
        while (ng - ok).abs() > 1{
            let mid = (ok + ng) / 2;
            if a[mid as usize] > *x{
                ok = mid;
            }else{
                ng = mid;
            }
        }
        Some(ok as usize)
    }
}

fn read<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()
}