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.io.*;
import java.util.*;
 
public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      //begin
      int n = sc.nextInt();
      ArrayList<Integer> lowers = new ArrayList<Integer>();
      int colors = 1;
      lowers.add(sc.nextInt());
      for(int i = 1; i < n; i++)
      {
          int a = sc.nextInt();
          Collections.sort(lowers, Collections.reverseOrder());
          if(lowers.get(lowers.size() - 1) >= a)
          {
              colors++;
              lowers.add(a);
          }
          else
          {
            int j = 0;
            while(lowers.get(j) >= a)
                j++;
            lowers.set(j, a);
          }
      }
      out.println(colors);
      //end
      out.close();
   }
 
   public static PrintWriter out;
      
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
      long nextLong() {
          return Long.parseLong(next());
      }
      double nextDouble() {
          return Double.parseDouble(next());
      }
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }
   }
}