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::{stdin, Read, StdinLock};
use std::str::FromStr;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read_<T: FromStr>(&mut self) -> Option<T> {
        let token = self
            .cin
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read_().unwrap()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n: i32 = sc.read();
    let mut array: Vec<i32> = vec![];
    for _ in 0..n {
        array.push(sc.read());
    }

    let mut result: Vec<i32> = vec![];
    for el in array {
        if result.len() == 0 || result[result.len() - 1] >= el {
            result.push(el);
        } else {
            let mut left = 0;
            let mut right = result.len();
            while left < right {
                let current = (left + right) / 2;
                if result[current as usize] < el {
                    right = current;
                } else {
                    left = current + 1;
                }
            }
            result[left as usize] = el;
        }
    }

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