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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using static System.Console;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        solve();
    }
    static int N;
    static int[] A;
    static void input()
    {
        N = int.Parse(ReadLine());
        A = new int[N];
        for(int i = 0; i < N; i++)
        {
            A[i] = int.Parse(ReadLine());
        }
    }
    static void solve()
    {
        input();
        int[] max = new int[1000000];
        int[] min = Enumerable.Repeat(int.MaxValue, 1000000).ToArray();
        int left = 0;
        for(int i = 0; i < N; i++)
        {
            bool flag = true;
            for (int l = left; l >= 0; l--)
            {
                if(A[i] > min[l])
                {
                    max[l] = Max(max[l], A[i]);
                    flag = false;
                    break;
                }
            }
            if (flag)
            {
                left++;
                min[left] = A[i];
                max[left] = A[i];
            }
        }
        WriteLine(left);
    }
}