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: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.ListIterator;
import java.util.Scanner;
 
public class Main {
	private class Data implements Comparable<Data> {
		int index = 0;
		int num = 0;
		
		public Data(int index, int num) {
			this.index = index;
			this.num = num;
		}

		@Override
		public int compareTo(Data o) {
			return o.num - this.num;
		}
		
		
	}
	
	public void solve() {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();
		LinkedList<Data> list = new LinkedList<Data>();
		for (int i=0; i<N; i++) {
			list.add(new Data(i, in.nextInt()));
		}
		in.close();
		Collections.sort(list);
		
		int count = 0;
		
		while (true) {
			count++;
			ListIterator<Data> it = list.listIterator();
			Data top = it.next();
			it.remove();
			while (it.hasNext()) {
				Data next = it.next();
				if (top.index > next.index && top.num > next.num) {
					top = next;
					it.remove();
				}
			}
			
			if (list.size() == 0) {
				break;
			}
		}
		
		
		System.out.println(count);
	}
	
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}
 
}