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.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var num = Input.num;
        var ar = Input.ar1D(num);
        var dic = new Dictionary<int, int>();
        var d = 0;
        foreach (var a in ar.OrderBy(v => v))
            if (!dic.ContainsKey(a))
                dic[a] = ++d;
        for (var i = 0; i < num; i++)
            ar[i] = dic[ar[i]];
        var seg = new SegmentTree<int>(num+1, 0, Max);
        var res = new int[num + 1];
        for(var i = 0; i < num; i++)
        {
            var m = seg.Query(0, ar[i]);
            res[m + 1]++;
            seg.Update(ar[i], m + 1);
        }
        WriteLine(res.Max());
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static T[] create<T>(int n, Func<int, T> f)
        => Enumerable.Repeat(0, n).Select(f).ToArray();
    public static char[][] gred(int h)
        => create(h, _ => read.ToCharArray());
    public static int[] ar1D(int n)
        => create(n, _ => num);
    public static long[] arL1D(int n)
        => create(n, _ => numL);
    public static string[] strs(int n)
        => create(n, _ => read);
    public static int[][] ar2D(int n)
        => create(n, _ => ar);
    public static long[][] arL2D(int n)
        => create(n, _ => arL);
    public static List<T>[] edge<T>(int n)
        => create(n, _ => new List<T>());
    public static T GetValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        if (t == typeof(int[]))
            return (T)(object)ar;
        if (t == typeof(long[]))
            return (T)(object)arL;
        return default(T);
    }
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    private static Queue<string> sc;
    public static T Next<T>(){ sc = sc ?? new Queue<string>(); if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item);return GetValue<T>(sc.Dequeue()); }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}

public class SegmentTree<T>
{
    private readonly T[] item;
    private readonly int _num;
    private readonly Func<T, T, T> _func;
    private readonly Func<T, T, T> updateFunc;
    private readonly T _init;

    private int Parent(int index)
        => (index - 1) >> 1;
    private int Left(int index)
        => (index << 1) + 1;
    private int Right(int index)
        => (index + 1) << 1;
    public T this[int i]
    {
        get { return item[i + _num - 1]; }
        set { item[i + _num - 1] = value; }
    }

    public SegmentTree(int num, T init, Func<T, T, T> func, Func<T, T, T> updateFunc = null)
    {
        _func = func;
        _num = 1;
        _init = init;
        this.updateFunc = updateFunc ?? ((T val1, T val2) => val2);
        while (_num <= num)
            _num *= 2;
        item = new T[2 * _num - 1];
        for (var i = 0; i < 2 * _num - 1; i++)
            item[i] = init;
    }
    public void Update(int index, T value)
    {
        index += _num - 1;
        item[index] = updateFunc(item[index], value);
        while (index > 0)
        {
            index = Parent(index);
            item[index] = _func(item[Left(index)], item[Right(index)]);
        }
    }
    public void Update(int left, int right, T value)
        => Update(left, right, 0, 0, _num, value);
    private void Update(int left, int right, int k, int l, int r, T value)
    {
        if (r <= left || right <= l) return;
        if (left <= l && r <= right) item[k] = updateFunc(item[k], value);
        else
        {
            Update(left, right, Left(k), l, (l + r) >> 1, value);
            Update(left, right, Right(k), (l + r) >> 1, r, value);
        }
    }
    public void All_Update()
    {
        for (int i = _num - 2; i >= 0; i--)
            item[i] = _func(item[Left(i)], item[Right(i)]);
    }
    public T Query(int index)
    {
        index += _num - 1;
        var value = _func(_init, item[index]);
        while (index > 0)
        {
            index = Parent(index);
            value = _func(value, item[index]);
        }
        return value;
    }
    //[left,right)
    public T Query(int left, int right)
        => Query(left, right, 0, 0, _num);
    private T Query(int left, int right, int k, int l, int r)
    {
        if (r <= left || right <= l) return _init;
        if (left <= l && r <= right) return item[k];
        else
            return _func(Query(left, right, Left(k), l, (l + r) >> 1), Query(left, right, Right(k), (l + r) >> 1, r));
    }
}