Problem:
Longest Increasing Subsequence

For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.

An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.

Input

n
a0
a1
:
an-1

In the first line, an integer n is given. In the next n lines, elements of A are given.

Output

The length of the longest increasing subsequence of A.

Constraints

1 ≤ n ≤ 100000

0 ≤ ai ≤ 109

Sample Input 1

5
5
1
3
2
4

Sample Output 1

3

Sample Input 2

3
1
1
1

Sample Output 2

1

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var num = Input.num;
        var ar = Enumerable.Repeat(0, num).Select(v => Input.num).ToArray();
        var list = new List<int>() { ar[0] };
        for(var i = 1; i < num; i++)
        {
            if (list[list.Count - 1] < ar[i]) list.Add(ar[i]);
            else list[Search.LowerBound(list.ToArray(), ar[i])] = ar[i];
        }
        WriteLine(list.Count());
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public  
static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class Search
{
    public static int UpperBound<T>(T[] array,T value)
        where T:IComparable<T>
    {
        var low = 0;
        var high = array.Length;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) == 1) high = mid;
            else low = mid + 1;
        }
        return low;
    }

    public static int LowerBound<T>(T[] array,T value)
        where T : IComparable<T>
    {
        var low = 0;
        var high = array.Length;
        while (high > low)
        {
            var mid = (high + low) / 2;
            if (array[mid].CompareTo(value) != -1) high = mid;
            else low = mid + 1;
        }
        return low;
    }
}