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;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = new List<int>();
            for (int i = 0; i < N; i++)
            {
                A.Add(int.Parse(Console.ReadLine()));
            }

            var min = new List<int>();
            min.Add(A[0]);

            for (int i = 1; i < N; i++)
            {
                for (int j = 0; j < min.Count; j++)
                {
                    if (A[i] > min[j])
                    {
                        min[j] = A[i];
                        break;
                    }

                    if (j + 1 == min.Count)
                    {
                        min.Add(A[i]);
                        break;
                    }
                }
            }

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