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.Text;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

class AtCoder
{
    const int MOD = 1000000007;
    public void Slove()
    {
        var lst = new List<int>();
        var n = int.Parse(Console.ReadLine());
        foreach(int i in Enumerable.Range(0, n))
        {
            var num = int.Parse(Console.ReadLine());
            if(lst.Any())
            {
                int index = 0;
                for (int start = 0, end = lst.Count - 1; start <= end;)
                {
                    int mid = (start + end) / 2;

                    if (lst[mid] >= num)
                    {
                        end = mid - 1;
                    }
                    else
                    {
                        index = mid;
                        start = mid + 1;
                    }
                }
                if(lst[index] < num)
                    lst[index] = num;
                else
                    lst.Insert(0, num);
            }
            else
                lst.Add(num);
        }
        Console.WriteLine(lst.Count);
    }
    static void Main()
    {
        var ac = new AtCoder();
        ac.Slove();
    }
}