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 sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		int[] A = new int[n];
		for (int i = 0; i < n; i++) {
			A[i] = Integer.parseInt(sc.next());
		}
		
		int[] dp = new int[n];
		dp [0] = 0;
		int cnt = 0;
		
		for (int i = 1; i < n; i++) {
			if (dp [i] > dp[i-1]) {
				++cnt;
				dp[i] = Math.max(dp[i-1] , cnt);
			} else {
				dp[i] = dp[i-1];
				cnt = 0;
			}
		}
	
		System.out.println(dp[n-1]);
	}
}