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: Wrong Answer)

import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		while (in.hasNext()) {
			int N = in.nextInt();
			ArrayList<Integer> lmds = new ArrayList<Integer>();
			
			for (int i = 0; i < N; ++i) {
				int a = in.nextInt();
				
				int idx = Collections.binarySearch(lmds, a, Collections.reverseOrder());
				idx = Math.max(idx, -(idx + 1));
				
				if (idx >= lmds.size()) {
					lmds.add(a);
				} else {
					if (lmds.get(idx) == a) {
						lmds.add(idx, a);
					} else {
						lmds.set(idx, a);
					}
				}
				
			}

			System.out.println(lmds.size());
		}
	}

}