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.Scanner;
import java.util.Arrays;
import java.util.ArrayList;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt();
		int ans=n;
		long[] a=new long[n];
		long min=Long.MAX_VALUE;
		for(int i=0; i<n; i++){
			a[i] =sc.nextLong();
			if(i!=0){
				if(a[i]<=a[i-1]){
					if(min<a[i-1]){
						ans--;
					}
					min=a[i-1];
				}else{
					ans--;
				}
			}
		}
		System.out.println(ans);
	}
}