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 printArray(int[] a) {
	// 	for (int i = 0; i < a.length; i++) {
	// 		System.out.print(a[i] + ", ");
	// 	}
	// 	System.out.println();
	// }

	// public static<T> void printArrayT(T[] a) {
	// 	for (int i = 0; i < a.length; i++) {
	// 		System.out.print(a[i] + ", ");
	// 	}
	// 	System.out.println();
	// }

	// public static class Triple implements Comparable<Triple> {
	// 	public int A, B, C;
	// 	Triple(int A, int B, int C) {
	// 		this.A = A;
	// 		this.B = B;
	// 		this.C = C;
	// 	}

	// 	@Override
	// 	public String toString() {
	// 		return String.format("(%d, %d, %d)", A, B, C);
	// 	}

	// 	@Override
	// 	public int compareTo(Triple o) {
	// 		int a = this.A - o.A;
	// 		if (a != 0) return a;
	// 		int b = this.B - o.B;
	// 		if (b != 0) return b;
	// 		return this.C - o.C;
	// 	}
	// }

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		for (int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
		}
		int color = 0;
		TreeMap<Integer, Integer> map = new TreeMap<>();
		for (int i = N - 1; i >= 0; i--) {
			int value = A[i];
			Map.Entry<Integer, Integer> entry = map.ceilingEntry(value + 1);
			if (entry != null) {
				if (entry.getValue() == 1) {
					map.remove(entry.getKey());
				} else {
					map.put(entry.getKey(), entry.getValue() - 1);
				}
			} else {
				color++;
			}
			if (map.containsKey(value)) {
				map.put(value, map.get(value) + 1);
			} else {
				map.put(value, 1);
			}
	}
		System.out.println(color);
	}
}