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.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];
        int[] B = new int[N];
        int colorCount = N-1;
        int min = 1000000000;
        for(int i=0;i<N;i++){
            B[i] = -1;
            A[i] = sc.nextInt();
        }

        for(int i=0;i<N;i++){
            if (A[i] <= min){
                min = A[i];
                B[colorCount] = A[i];
                colorCount--;
            } else {
                for(int j=N-1;j > -1;j--){
                    if(A[i] > B[j]){
                        B[j] = A[i];
                        break;
                    }
                }
            }
        }
        System.out.println(N -1- colorCount);

    }

}