Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main {
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		int s=0,n=0;
		n=scan.nextInt();
		int List[]=new int[n];
		for(int i=0;i<n;i++){
			List[i]=scan.nextInt();
		}
		for(int i=0;i<n;i++){
			for(int j=i;0<=j;j--){
				if(j<i && List[j]<=List[i]){
					if(s<List[j]){
						s=List[j];
					}
				}
			}
		}
		System.out.println(s);
	}
}