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();
		NavigableMap<Integer, Integer> s = new TreeMap();

		for (int i = 0; i < n; i++) {
			int a = sc.nextInt();
			if (s.isEmpty()) {
				s.put(a, 1);
				continue;
			}
			if (s.firstEntry().getKey() >= a) {
				s.put(a, s.getOrDefault(a, 0) + 1);
			} else {
				int v = s.lowerEntry(a).getValue();
				if (v > 1) {
					s.put(s.lowerEntry(a).getKey(), v - 1);
				} else {
					s.remove(s.lowerEntry(a).getKey());
				}
				if (s.containsKey(a)) {
					s.put(a, s.get(a) + 1);
				} else {
					s.put(a, 1);
				}
			}
		}

		int count = 0;
		for (Map.Entry<Integer, Integer> i : s.entrySet()) {
			count += i.getValue();
		}

		System.out.println(count);
	}
}