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;

namespace ConsoleApp5
{
	class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			var sortedMaxList = new List<int>(n);	// 各色の最大値を要素とするリスト(降順)
			for (int i = 0; i < n; i++)
			{
				var num = int.Parse(Console.ReadLine());
				var index = sortedMaxList.FindIndex(x => x < num);
				if (index == -1)
				{
					sortedMaxList.Add(num);
				}
				else
				{
					sortedMaxList[index] = num;
				}
			}
			Console.WriteLine(sortedMaxList.Count);
		}
	}
}