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.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] A = new int[N];

        for(int i=0; i<N; i++){
            A[i] = sc.nextInt();
        }

        List<Integer> maxList = new ArrayList<>();

        A:for(int i=0; i<N; i++){
            //System.err.println(A[i]);
            maxList.sort(Comparator.reverseOrder());
            for(int j=0; j<maxList.size(); j++){
                //System.err.println(j + "(" + maxList.get(j) + ")" +  " : " + A[i]);
                if(A[i] > maxList.get(j)){
                    //System.err.println(j + "(" + maxList.get(j) + ")" +  " -> " + A[i]);
                    maxList.set(j, A[i]);
                    continue A;
                }
            }
            //System.err.println("add " + A[i]);
            maxList.add(A[i]);
        }

        int result = maxList.size();
        System.out.println(result);

    }
}