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 (1.42.0) (judge verdict: Accepted)

use std::collections::BTreeSet;
fn main() {
    proconio::input! {
        n: usize,
        a: [usize;n],
    }
    let mut s: BTreeSet<usize>=BTreeSet::new();
    for (i,a) in a.into_iter().enumerate() {
        if let Some(&v)=s.range(..a*n).rev().next() {
            s.remove(&v);
        }
        s.insert(a*n+i);
    }
    println!("{}",s.len());
}