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.*;
import java.util.stream.Collectors;


public class Main {

    private static final int INF = 1000000007;
    private static final int INF1 = Integer.MAX_VALUE;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Integer> list = new ArrayList<>();
        for(int tmp = 0; tmp < n; tmp++){
            list.add(sc.nextInt());
        }

        List<Integer> rest = new ArrayList<>();
        rest.add(list.get(n - 1));
        int max = list.get(n - 1);
        for(int tmp = n - 2; tmp >= 0; tmp--){
            int a = list.get(tmp);

            if(a > max){
                max = a;
            }

            if(max > a){
                rest.remove((Integer) max);
                if(rest.size() > 0) {
                    Collections.sort(rest);
                    rest.remove(rest.size() - 1);
                    
                }else{
                    max = a;
                }
            }

            rest.add(a);
        }

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