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.*;
public class Main
{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        ArrayList<Integer> list = new ArrayList();
        for(int i=0;i<N;i++){
            list.add(Integer.parseInt(sc.next()));
        }
        int result = 0;
        Iterator<Integer> it = list.iterator();
        while(it.hasNext()){
            //Iterator<Integer> it2 = list.iterator();
            int num = it.next();
            it.remove();
            result++;
            while(it.hasNext()){
                int num2 = it.next();
                if(num < num2){
                    it.remove();
                    num = num2;
                }
            }
            //it.remove();
            //result++;
            it = list.iterator();
        }
        System.out.println(result);
    }
}