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: Time Limit Exceeded)

import java.util.*;
public class Main {
	public static void main(String args[]){
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int[] a=new int[n+5];
		for(int i=1;i<=n;i++)
			a[i]=in.nextInt();
		in.close();
		int[] dp=new int[n+5];
		Arrays.fill(dp,1);
		for(int i=2;i<=n;i++)
			for(int j=1;j<i;j++)
				if(a[j]<a[i])
					dp[i]=Math.max(dp[i],dp[j]+1);
		int ans=0;
		for(int i=1;i<=n;i++)
			ans=Math.max(dp[i],ans);
		System.out.println(ans);
	}

}