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.Linq;
using System.Text;

namespace ABC134
{
    class Program5
    {
        static void Main()
        {
            //greedy
            var N = int.Parse(Console.ReadLine());
            var list = new List<List<int>>();
            for (int i = 0; i < N; i++)
            {
                var num = int.Parse(Console.ReadLine());
                var canPush = false;
                foreach (var li in list)
                {
                    if (num <= li.Last())
                        continue;

                    li.Add(num);
                    canPush = true;
                    break;
                }
                if (!canPush)
                    list.Add(new List<int>() { num });
            }

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