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: Time Limit Exceeded)

using System;

namespace question5
{
    class Program
    {
        static void Main(string[] args)
        {

            int n = int.Parse(Console.ReadLine());
            int[] a = new int[n];
            for (int i=0; i < n; i++)
            {
                a[i]= int.Parse(Console.ReadLine());
            }
            int[] b = new int[n];
            for (int i = 0; i < n; i++)
            {
                b[i] = 0;
            }
            int counter = 0;
            int currentnum = -1;
            int onecount = 0;
            int zerocount = 0;
            for (int k = 0; k < n; k++)
            {
                counter = 0;
                currentnum = -1;
                zerocount = 0;
                for (int i = 0; i < n; i++)
                {

                    if (b[i] == 0)
                    {
                        if (currentnum < a[i])
                        {

                            counter += 1;
                            currentnum = a[i];
                            b[i] = counter;
                        }
                        else zerocount ++;
                    }
                    //Console.WriteLine("aaaa{0}", zerocount);
                }
                if (zerocount == 0) break;

            }
            for (int k = 0; k < n; k++)
            {
                //Console.WriteLine(b[k]);
                if (b[k] == 1) onecount ++;
            }
            Console.WriteLine(onecount.ToString());
                Console.ReadLine();
        }
    }
}