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.Text;
using System.Numerics;
using System.IO;


namespace SolutionCS
{
    class Entity : IComparable<Entity>
    {
        public Entity(int initial)
        {
            nowValue = initial;
        }

        int nowValue = -1;

        public bool TryAdd(int v)
        {
            if ( nowValue >= v)
            {
                return false;
            }

            nowValue = v;

            return true;
        }

        public int CompareTo(Entity e)
        {
            return -nowValue.CompareTo(e.nowValue);
        }
    }



    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            List<Entity> entity = new List<Entity>();

            for (int i = 0; i < N; i++)
            {
                int v = int.Parse(Console.ReadLine());

                if (entity.Count == 0 )
                {
                    entity.Add(new Entity(v));
                }
                else
                {
                    bool added = false;
                    foreach(Entity e in entity)
                    {
                        if (e.TryAdd(v))
                        {
                            added = true;
                            break;
                        }
                    }

                    if (!added)
                    {
                        entity.Add(new Entity(v));
                    }
                }
            }

            Console.WriteLine(entity.Count);
        }
    }
}