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

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			long N = long.Parse(Console.ReadLine());
            long[] A = new long[N];
            for(long i = 0; i < N; i++)
            {
                A[i] = long.Parse(Console.ReadLine());
            }
            var List = new List<long>();
            List.Add(A[0]);
            int len = 1;
            for(int i = 1; i < N; i++)
            {
                //for (int j = 0; j < len; j++) Console.Write(List[j]);
                //Console.WriteLine(' ');
                if (List[len-1] >= A[i])
                {
                    List.Add(A[i]);
                    len++;
                }
                else if(List[0] < A[i])
                {
                    List[0] = A[i];
                }
                else
                {
                    int min = 0, max = len-1;
                    while (true)
                    {
                        if( (max-min) == 1)
                        {
                            List[max] = A[i];
                            break;
                        }
                        int mid = (min + max) / 2;
                        if (A[i] <= List[mid])
                        {
                            max = mid;
                        }
                        else
                        {
                            min = mid;
                        }
                    }
                }
            }

            //for (int i = 0; i < len; i++) Console.Write(List[i]);
            Console.WriteLine(List.Count);
            Console.ReadLine();

		}
	}
}