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.*;
import java.io.*;

class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());
		int[] a = new int[n+1];
		for (int i=1; i<n+1; i++) {
			a[i] = Integer.parseInt(br.readLine());
		}

		int[] dp = new int[n+1];
		int max = 0;

		for (int i=1; i<n+1; i++) {
			dp[i] = 1;
			for (int j=0; j<i; j++) {
				if (a[j] < a[i]) {
					dp[i] = Math.max(dp[i],dp[j]+1);
				}
			}
			max = Math.max(max,dp[i]);
		}

		System.out.println(max);

		br.close();
	}
}