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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    //const int MOD = 1000000007;
    static void Main(string[] args)
    {
        new Program().Solve();
    }

    void Solve()
    {
        int max = 101010;
        Scanner cin = new Scanner();
        int n = cin.NextInt();
        long[] a = new long[n];

        for (int i = 0; i < n; i++)
        {
            a[i] = cin.NextLong();
        }

        int inf = 1000000010;
        List<long> dp = new List<long>();

        // 単調減少列を考えるため、後ろからLIS作成
        foreach (var element in a.Reverse())
        {
            // 追加されている値より大きくして検索(a, a+1]?
            int index = BinarySearch.BinSearchIndex(element + 1, dp);
            if (index < dp.Count())
            {
                dp[index] = element;
            }
            else
            {
                dp.Add(element);
            }
        }        
        Console.WriteLine(dp.Count());
    }
}

public static class BinarySearch
{
    /// <summary>
    /// binary search
    /// </summary>
    /// <typeparam name="T">value type</typeparam>
    /// <param name="v">target value</param>
    /// <param name="list">searched list</param>
    /// <returns>index of target should be in.</returns>
    public static int BinSearchIndex<T>(T v, IEnumerable<T> list)
    where T : IComparable
    {
        int minRange = 0;
        int maxRange = list.Count();
        while (minRange != maxRange)
        {
            var center = (minRange + maxRange) / 2;
            if (list.ElementAt(center).CompareTo(v) < 0)
            {
                minRange = center + 1;
            }
            else
            {
                maxRange = center;
            }
        }

        return minRange;
    }
}


class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string Next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return Next();
        i = 0;
        return s[i++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public char[] ArrayChar()
    {
        return Next().ToCharArray();
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextInt() + add;
        }
        return Array;
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextLong() + add;
        }
        return Array;
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextDouble() + add;
        }
        return Array;
    }
}