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: Runtime Error)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int number_n, i, j, min_temp = Integer.MAX_VALUE, temp = -1, temp_count = 0, max_count = 0;
    number_n = Integer.parseInt(sc.next());
    int[] number = new int[number_n];
    for (i = 0; i < number_n; i++) number[i] = Integer.parseInt(sc.next());
    for (i = 0; i < number_n; i++) {
      for(j = temp; j < number_n; j++) {
        if(j == temp) temp = -1;
        if(min_temp >= number[j]) {
          temp_count++;
          min_temp = number[j];
        } else if(temp == -1) {
          temp = i;
        }
      }
      if(temp == -1) break;
      if(max_count < temp_count) max_count = temp_count;
      temp_count = 0;
      min_temp = Integer.MAX_VALUE;
    }
    System.out.println(max_count);
  }
}