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: Accepted)

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

namespace ConsoleApplication2
{
    //insertFirstを高速にし、Addを超低速にした逆順List
    public class RevList<T>
    {
        private List<T> arr;
        public RevList()
        {
            arr = new List<T>();
        }
        public void InsertFirst(T val)
        {
            arr.Add(val);
        }
        public void Add(T val)
        {
            arr.Insert(0, val);
        }
        public int Count
        {
            get
            {
                return arr.Count();
            }
        }
        public T this[int index]
        {
            set
            {
                arr[Count - index - 1] = value;
            }
            get
            {
                return this.arr[Count - index - 1];
            }
        }
    }
    class Program
    {

        static void Main(string[] args)
        {

            long n = int.Parse(Console.ReadLine());
            long[] a = new long[n];
            RevList<long> color = new RevList<long>();
            for (int i = 0; i < n; i++)
            {
                a[i] = int.Parse(Console.ReadLine());
            }

            color.Add(a[0]);

            for (int i = 1; i < n; i++)
            {
                int cnt = color.Count;
                if (a[i] <= color[0])
                {
                    color.InsertFirst(a[i]);
                }
                else if (a[i] > color[cnt - 1])
                {
                    color[cnt - 1] = a[i];
                }
                else
                {
                    //2分探査
                    int iS, iM, iL;
                    iS = 0;
                    iL = cnt - 1;


                    for (int j = 0; j < cnt; j++)
                    {
                        iM = (iS + iL) / 2;

                        if (iS == iM)
                        {
                            color[iS] = a[i];
                            break;
                        }
                        if (color[iM] >= a[i])
                        {
                            iL = iM;
                        }
                        else
                        {
                            iS = iM;
                        }
                    }
                }
            }
            Console.WriteLine(color.Count);
        }
    }
}