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.Scanner;
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 i,j,ans=0,min=n+1;
		for(i=0;i<n;i++)a[i]=sc.nextInt();
		int cnt=0;
		for(i=0;i<n-1;i++) {
			cnt++;
			ans=0;
			for(j=i+1;j<n;j++) {
			if(a[i]>=a[j])
				ans++;
			}
			ans+=cnt;
			min=Math.min(ans,min);
		}
		System.out.println(min);		
    }
}