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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

	public static void main (String[] args)  {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		TreeSet<Color> set = new TreeSet<>();
		for (int i = 0; i < n; i++) {
		    Color x = new Color(n - i, sc.nextInt());
		    Color target = set.lower(x);
		    if (target != null) {
		        set.remove(target);
		    }
		    set.add(x);
		}
		System.out.println(set.size());
	}
	
	static class Color implements Comparable<Color> {
	    int idx;
	    int value;
	    
	    public Color (int idx, int value) {
	        this.idx = idx;
	        this.value = value;
	    }
	    
	    public int hashCode() {
	        return idx;
	    }
	    
	    public int compareTo(Color another) {
	        if (value == another.value) {
	            return idx - another.idx;
	        } else {
	            return value - another.value;
	        }
	    }
	    
	    public boolean equals(Object o) {
	        Color another = (Color)o;
	        return idx == another.idx && value == another.value;
	    }
	}
}