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.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Collections;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int n = scanner.nextInt();
        final List<Integer> colors = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            final int next = scanner.nextInt();
            insert(colors, next);
        }

        System.out.println(colors.size());
    }

    private static void insert(final List<Integer> list, final int value) {

        int idx = Collections.binarySearch(list, value);

        if (idx < 0) {
            idx = -idx - 1;
            if (idx == 0) {
                list.add(0, value);
            } else {
                list.set(idx - 1, value);
            }
            return;
        }

        if (idx == 0) {
            list.add(0, value);
        } else {
            list.add(idx, value);
        }
    }
}