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.*;
import java.math.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		long n = sc.nextLong();
		List<Long> list = new ArrayList<>();
		List<Boolean> flagList = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			long a = sc.nextLong();
			list.add(a);
			flagList.add(true);
		}

		int result = 0;
		int total = 0;
		
		for (int i = 0; i < n; i++) {
			// System.out.println(flagList);
			if(total == n) break;
			if(!flagList.get(i)){
				continue;
			}
			long a = list.get(i);
			flagList.set(i ,false);
			total++;
			result++;
			for (int j = i+1; j < n; j++) {
				if(!flagList.get(j)){
					continue;
				}
				long currentA = list.get(j);
				if(a >= currentA){
					continue;
				}
				a = currentA;
				flagList.set(j ,false);
				total++;
			}
		}
		

		System.out.println(result);
	}
}