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)

pub struct Poper<'a> {
	iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Poper<'a> {
	pub fn new(iter: std::str::SplitWhitespace) -> Poper {
		Poper { iter: iter }
	}
	pub fn read<T: std::str::FromStr>(&mut self) -> T
	where
		<T as std::str::FromStr>::Err: std::fmt::Debug,
	{
		self.iter.next().unwrap().parse().unwrap()
	}
}

fn main() {
	let input = {
		use std::io::Read;
		let mut s = String::new();
		std::io::stdin().read_to_string(&mut s).unwrap();
		s
	};
	let mut iter = Poper::new(input.split_whitespace());

	let n: usize = iter.read();
	let a_list: Vec<u64> = (0..n).into_iter().map(|_| iter.read()).collect();

	let mut x_list: Vec<u64> = Vec::new();

	for a in a_list {
		let t = x_list
			.iter()
			.enumerate()
			.map(|(i, &n)| (i, n))
			.find(|&(_, n)| n < a);
		match t {
			Some((i, _)) => {
				x_list[i] = a;
				x_list.sort_by(|q, w| w.cmp(q));
			}
			None => match x_list.binary_search_by(|q| a.cmp(q)) {
				Ok(i) => {
					x_list.insert(i, a);
				}
				Err(i) => {
					x_list.insert(i, a);
				}
			},
		}
	}

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