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.*;

class Main{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        List<Integer> tops = new ArrayList<>();

        int prev = -1;
        int len = sc.nextInt();
        int color = 1;
        for(int i = 0; i < len; i++){
            int num = sc.nextInt();
            if(num <= prev){
                color++;
                tops.add(num);
                for(int j = num-1; j > 0; j--){
                    int index;
                    if((index = tops.indexOf(j)) != -1){
                        tops.set(index, num);
                        tops.remove(tops.size()-1);
                        color--;
                        break;
                    }
                }
            }
            prev = num;
        }

        System.out.println(color);
    }
}