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.*;
 
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<>();
    list.add(Integer.parseInt(sc.nextLine()));
    
    for(int i = 1; i < N; i++){
      int a = Integer.parseInt(sc.nextLine());
      int lb = 0;
      int ub = list.size()-1;
      if(a <= list.get(ub)){
        list.add(a);
        ub++;
      }else if(a > list.get(lb)){
      }else{
        int mid = 0;
        while(ub-lb > 1){
          mid = (ub+lb)/2;
          if(a > list.get(mid)){
            ub = mid;
          }else{
            lb = mid;
          }
        }
        list.set(mid, a);
      }
    }
    System.out.println(list.size());
  }
}