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 scanner = new Scanner(System.in);
        int N = scanner.nextInt();
		int color = 0;
      
        int[] A = new int[N];
        for(int i = 0; i < N; i++){
            A[i] = scanner.nextInt();
        }
      
        for(int i = 0; i < N; i++){
              
            if(A[i] == -1){
                continue;
            }
          
            int max_A = A[i];
            for(int j = 1; j < N-i; j++){
                if(A[i + j] == -1){
                    continue;
                }
              
                if(A[i + j] > max_A){
                    max_A = A[i + j];
                    A[i + j] = -1;
                }
            }
          
            color++;
        }
        
        System.out.println(color);
    }
}