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: Accepted)

import java.util.*;

public class Main {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int n = scanner.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        List<Integer> list = new ArrayList<>();
        list.add(a[0]);
        for (int i = 1; i < n; i++) {
            int j = binarySearch(list, a[i]);
            if (j == -1) {
                list.add(0, a[i]);
            } else {
                list.set(j, a[i]);
            }
        }
        System.out.println(list.size());
    }

    static int binarySearch(List<Integer> list, int i) {
        int ok = -1, ng = list.size();
        while (Math.abs(ok - ng) > 1) {
            int mid = (ok + ng) / 2;
            if (list.get(mid) < i) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        return ok;
    }
}