Problem:
Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public class ABC
{
    //          long[] sp = Console.ReadLine().Split().Select(long .Parse).ToArray();
    //          int[] sp = Console.ReadLine().Split().Select(int.Parse).ToArray();
    public static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        int[] A = new int[N];
        List<int> maxint_eachValue = new List<int>();
        for (int i = 0; i < N; i++)
        {
            bool isAdded = false;
            int Avalue = int.Parse(Console.ReadLine());
            for (int listindex = maxint_eachValue.Count - 1; listindex >= 0; listindex--)
            {
                if (maxint_eachValue[listindex] < Avalue)
                {
                    maxint_eachValue.RemoveAt(listindex);
                    maxint_eachValue.Insert(listindex,Avalue);
                    isAdded = true;
                    break;
                }
            }
            if (!isAdded)
            {
                maxint_eachValue.Insert(0,Avalue);
            }

        }
        Console.WriteLine(maxint_eachValue.Count);
    }




}