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.io.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {

  public static class LowerBoundComparator<T extends Comparable<? super T>>
      implements Comparator<T>
  {
    public int compare(T x, T y)
    {
      return (x.compareTo(y) >= 0) ? 1 : -1;
    }
  }


  public static class UpperBoundComparator<T extends Comparable<? super T>>
      implements Comparator<T>
  {
    public int compare(T x, T y)
    {
      return (x.compareTo(y) > 0) ? 1 : -1;
    }
  }

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  private static final long MOD = 1000000007L;

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int n = sc.nextInt();
    int[] a = new int[n];

    List<Integer> groups = new ArrayList<>();

    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
    }

    for (int i = 0; i < n; i++) {
      int j = groups.size() - 1;
      while (0 <= j && groups.get(j) <= a[j]) {
        j--;
      }
      if (0 <= j) {
        groups.set(j, a[i]);
      } else {
        groups.add(0, a[i]);
      }
    }

    os.println(groups.size());
  }
}