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 C# (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

public class Hello{
    public static int N;
    public static int[] A;
    public static int[] memo;
    public static void Main(){
        N = int.Parse(Console.ReadLine());
        A = new int[N];
        memo = new int[N];
        for(int i=0; i<N; i++){
            A[i] = int.Parse(Console.ReadLine());
        }
        var ans = 0;
        //????????°????????????????????????????????????????????£????????£????????§????????´??°
        for(int i=0; i<N; i++){
            ans = Math.Max(ans, dfs(i));
        }
        Console.WriteLine(ans);
    }
    
    //???????¢??????¨????????????????????¢????????°??§?§£??????
    public static int dfs(int cur){
        if(memo[cur]>0) return memo[cur];
        //????????°??????????§???????????????????????????§??±??????1??§?????????
        var ret = 1;
        //?????¨?????????????????????????????????????????????????????????????????°????????????
        for(int j=cur; j<N; j++){
            if(A[cur]<A[j]){
                //?????????or????????????
                //???????????´?????????????????????????????´??°????????±??????1??????????????????????????´???????????¨??????????????????????????????????????????
                ret = Math.Max(ret, dfs(j)+1);
            }
        }
        memo[cur] = ret;
        return ret;
    }
}