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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;


namespace SolutionCS
{

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

            int[] buf = new int[N];
            for (int i = 0; i < N; i++)
            {
                buf[i] = -1;
            }
            int count = 0;

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

                if ( count != 0 && buf[count - 1] >= v)
                {
                    buf[count] = v;
                    count++;
                }
                else
                {
                    if ( count > 32)
                    {
                        int start = 0;
                        int last = count;
                        int ind = (start + last) / 2;

                        for (int j = 0; j < 4; j++)
                        {
                            if(buf[ind] < v)
                            {
                                start = ind;
                            }
                            else
                            {
                                last = ind;
                            }
                        }

                        for (int j = 0; j < count / 16 + 15; j++)
                        {
                            if (buf[ind+j] < v)
                            {
                                buf[ind+j] = v;
                                break;
                            }
                        }
                    }
                    else
                    {
                        for (int j = 0; j < count; j++)
                        {
                            if (buf[j] < v)
                            {
                                buf[j] = v;
                                break;
                            }
                        }
                    }
                }
            }

            Console.WriteLine(count);
        }
    }
}