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;

namespace DPL1_D
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            var L = new Dictionary<int, int>();
            L[0] = int.Parse(Console.ReadLine());
            int length = 1;
            for (int i = 0; i < n-1; i++)
            {
                var t = int.Parse(Console.ReadLine());
                if (L[length - 1] < t)
                {
                    L[length++] = t;
                }
                else
                {
                    L[L.Values.TakeWhile(s => s < t).Count()] = t;
                }

            }
            Console.WriteLine(length);
        }
    }
}