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;

class WithIndex<T>
{
    public T Value;
    public int Index;
    public WithIndex(T value, int index)
    {
        this.Value = value;
        this.Index = index;
    }
}

static class Template
{
    public static int LineToInt()
    {
        return int.Parse(Console.ReadLine());
    }

    public static string[] LineToStrings()
    {
        return Console.ReadLine().Split();
    }

    public static int[] LineToInts()
    {
        return LineToStrings()
            .Select(s => int.Parse(s))
            .ToArray();
    }


    public static int[,] LinesToIntTable(int lineCount, int columnCount)
    {
        var value = new int[lineCount, columnCount];
        foreach (var y in Enumerable.Range(0, lineCount))
        {
            var ints = LineToInts();
            foreach (var x in Enumerable.Range(0, columnCount))
            {
                value[y, x] = ints[x];
            }
        }
        return value;
    }

    public static IEnumerable<WithIndex<T>> WithIndex<T>(this IEnumerable<T> sequence)
    {
        int index = 0;
        foreach (var item in sequence)
        {
            yield return new WithIndex<T>(item, index);
            index++;
        }
    }

    static void Main(string[] args)
    {
        var n = LineToInt();
        var numbers = new List<int>(n);
        foreach (var i in Enumerable.Range(0, n))
        {
            numbers.Add(LineToInt());
        }
        var colorNum = 1;
        var tasks = new List<List<int>>() { numbers };
        while (tasks.Any())
        {
            var task = tasks.First();
            var removed = new List<int>(task.Count); //大小関係がそろっている方
            for (int i = 0; i < task.Count - 1; i++)
            {
                if (task[i] < task[i + 1])
                {
                    removed.Add(task[i + 1]);
                    task.RemoveAt(i + 1);
                    //i--;
                }
            }
            if (removed.Any())
            {
                tasks.Add(removed);
                tasks.RemoveAt(0);
                colorNum++;
            }
            else
            {
                tasks.RemoveAt(0);
            }
        }
        Console.WriteLine(colorNum);
    }
}