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: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++){
            list.add(sc.nextInt());
        }

        int[][] array = new int[n][2];

        for (int i :
                list) {
//            array
        }

        for (int i = 0; i < n; i++){
            array[i][0] = list.get(i);
            array[i][1] = 0;
        }

        for (int j : list) {
            for (int i = 0; i < n; i++) {
                if (array[i][0] == j) {
                    array[i][1] ++;
                }
            }
        }

        int max = 0;
        for (int i = 0; i < n; i++){
            if (max < array[i][1]){
                max = array[i][1];
            }
        }

        if (max <= 2){
            System.out.println("2");
        }else {
            System.out.println(max);
        }

    }
}