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.Scanner;

public class Main{
	public static void main(String args[]) {
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int[] a = new int[n];
		int[] DP = new int[n];
		int ans = 0;
		for (int i = 0; i < n; i++) {
			a[i] = scn.nextInt();
			DP[i] = 1;
			for (int j = 0; j < i; j++) {
				if (a[j] < a[i]) {
					DP[i] = Math.max(DP[i], DP[j]+1);
				}
			}
			ans = Math.max(ans, DP[i]);
		}
		System.out.println(ans);
		scn.close();
	}
}