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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Comparator;
import java.util.PriorityQueue;

public class Main {

    public static void main(String[] args) throws Exception {
        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {
            int N = Integer.parseInt(reader.readLine());
            int[] A = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = Integer.parseInt(reader.readLine());
            }

            PriorityQueue<Integer> queue = new PriorityQueue<Integer>(new Comparator<Integer>() {
                @Override
                public int compare(Integer o1, Integer o2) {
                    return o2.compareTo(o1);
                }
            });

            for (int i = N - 1; i >= 0; i--) {
                Integer peek = queue.peek();
                if (peek == null || A[i] >= peek) {
                    queue.add(A[i]);
                    continue;
                } else {
                    queue.remove(peek);
                    queue.add(A[i]);
                }
            }

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

}