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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n + 1];
        arr[0] = Integer.MAX_VALUE;
        int max = 0;
        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            if (arr[max] >= x) {
                max++;
                arr[max] = x;
               continue;
            }
            int left = 0;
            int right = max;
            while (right - left > 1) {
                int m = (left + right) / 2;
                if (arr[m] < x) {
                    right = m;
                } else {
                    left = m;
                }
            }
            arr[right] = x;
        }
        System.out.println(max);
        
    }
}