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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace ABC134E
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var a = input.NextInt(n);

            // 最長増加部分列をできるだけ少ない数使って全体と同じ列を作る
            var count = 0;
            int i = 0;
            while (i < n)
            {
                if (a[i] >= int.MaxValue)
                {
                    i++;
                    continue;
                }

                var lis = LongestIncreasingSubsequence.Lis(a, i);
                foreach (var j in lis)
                {
                    a[j] = int.MaxValue;
                }

                count++;
            }

            // 一つの色では2つの数字しかぬれない
            Console.WriteLine(count);
        }

        class LongestIncreasingSubsequence
        {
            public static List<int> Lis(int[] nums, int begin)
            {
                var iss = new List<int>();
                var issi = new List<int>();

                iss.Add(nums[begin]);
                issi.Add(begin);
                for (int i = begin + 1; i < nums.Length; i++)
                {
                    if (iss[iss.Count() - 1] < nums[i])
                    {
                        iss.Add(nums[i]);
                        issi.Add(i);
                    }
                    else
                    {
                        var j = FindBound.LowerBound(iss, nums[i]);
                        if (iss[j] != nums[i])
                        {
                            iss[j] = nums[i];
                            issi[j] = i;
                        }
                    }
                }

                return issi;
            }
            /// <summary>
            /// 昇順ソート済みリストに対して、ある値以上/より大きい となるindexを探す
            /// </summary>
            class FindBound
            {
                /// <summary>
                /// Bound系の下請け
                /// </summary>
                /// <typeparam name="T"></typeparam>
                /// <param name="list"></param>
                /// <param name="v"></param>
                /// <param name="start"></param>
                /// <param name="end"></param>
                /// <returns></returns>
                static int findBound<T>(IList<T> list, T v, int start, int end, Func<T, T, bool> judge) where T : IComparable<T>
                {
                    int low = start;
                    int high = end;

                    if (low > high)
                    {
                        throw new ArgumentException();
                    }

                    while (low < high)
                    {
                        var mid = ((high - low) / 2) + low;
                        if (judge(v, list[mid]))
                        {
                            high = mid;
                        }
                        else
                        {
                            low = mid + 1;
                        }
                    }

                    return low;
                }

                /// <summary>
                /// v以上で最小のインデックスを返す
                /// </summary>
                /// <typeparam name="T"></typeparam>
                /// <param name="list"></param>
                /// <param name="v"></param>
                /// <param name="start"></param>
                /// <param name="end"></param>
                /// <returns></returns>
                public static int LowerBound<T>(IList<T> list, T v, int start, int end) where T : IComparable<T>
                {
                    return findBound(list, v, start, end, (x, y) => x.CompareTo(y) <= 0);
                }

                /// <summary>
                /// v以上で最小のインデックスを返す
                /// </summary>
                /// <typeparam name="T"></typeparam>
                /// <param name="list"></param>
                /// <param name="v"></param>
                /// <returns></returns>
                public static int LowerBound<T>(IList<T> list, T v) where T : IComparable<T>
                {
                    return LowerBound<T>(list, v, 0, list.Count());
                }

                /// <summary>
                /// vより大きな最小のインデックスを返す
                /// </summary>
                /// <typeparam name="T"></typeparam>
                /// <param name="list"></param>
                /// <param name="v"></param>
                /// <param name="start"></param>
                /// <param name="end"></param>
                /// <returns></returns>
                public static int UpperBound<T>(IList<T> list, T v, int start, int end) where T : IComparable<T>
                {
                    return findBound(list, v, start, end, (x, y) => x.CompareTo(y) < 0);
                }

                /// <summary>
                /// vより大きな最小のインデックスを返す
                /// </summary>
                /// <typeparam name="T"></typeparam>
                /// <param name="list"></param>
                /// <param name="v"></param>
                /// <returns></returns>
                public static int UpperBound<T>(IList<T> list, T v) where T : IComparable<T>
                {
                    return UpperBound(list, v, 0, list.Count());
                }
            }
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        /// <summary>
        /// 値を書き換え可能なTuple（ぐらいのイメージ）
        /// </summary>
        public class Pair<T, U> : IComparable<Pair<T, U>>, IEquatable<Pair<T, U>>
            where T : IComparable<T>
            where U : IComparable<U>
        {
            public T V1 { get; set; }
            public U V2 { get; set; }

            public Pair(T v1, U v2)
            {
                this.V1 = v1;
                this.V2 = v2;
            }

            public Pair(Pair<T, U> src) : this(src.V1, src.V2) { }

            public int CompareTo(Pair<T, U> other)
            {
                var r = this.V1.CompareTo(other.V1);
                if (r == 0) r = this.V2.CompareTo(other.V2);

                return r;
            }

            public bool Equals(Pair<T, U> other)
                => (other != null && this.CompareTo(other) == 0);

            public override string ToString()
                => $"{V1} {V2}";

            public override bool Equals(object obj)
                => Equals(obj as Pair<T, U>);

            public override int GetHashCode()
            {
                var hashCode = 1989511945;
                hashCode = hashCode * -1521134295 + V1.GetHashCode();
                hashCode = hashCode * -1521134295 + V2.GetHashCode();
                return hashCode;
            }

            public static bool operator ==(Pair<T, U> a, Pair<T, U> b)
            {
                if (object.ReferenceEquals(a, null))
                {
                    return object.ReferenceEquals(b, null);
                }

                return a.Equals(b);
            }

            public static bool operator !=(Pair<T, U> a, Pair<T, U> b)
                => !(a == b);
            public static bool operator <(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) < 0;
            public static bool operator <=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) <= 0;
            public static bool operator >(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) > 0;
            public static bool operator >=(Pair<T, U> a, Pair<T, U> b)
                => a.CompareTo(b) >= 0;
        }

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim()
                    .Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    queue.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any()
                => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read())
                {
                    return "";
                }

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                {
                    if (!Read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}