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.nextLine());
    List<Integer> list = new ArrayList<>();
    for(int i = 0; i < N; i++){
      list.add(Integer.parseInt(sc.nextLine()));
    }
    
    int count = 0;
    while(list.size() > 0){
      int a = list.get(0);
      list.remove(0);
      
      for(int i = 0; i < list.size(); i++){
        int b = list.get(i);
        if(a < b){
          a = b;
          list.remove(i);
          i--;
        }
      }
      count++;
    }
    System.out.println(count);
  }
}