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.Collections.Generic;
using System.Linq;

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


            
            var N = int.Parse(Console.ReadLine());

            var input = new int[N];
            var currentLine = new int[N + 1];
            currentLine[1] = int.MinValue;
            var currentMin = int.MaxValue;
            int cnt = 1;
            int x;

            for(int i = N-1; i >=0; i--){
                x = int.Parse(Console.ReadLine());
                if(x > currentLine[1]){
                    currentLine[1] = x;
                }else if(x <= currentLine[cnt]){
                    cnt++;
                    currentLine[cnt] = x;
                }else{
                    for(int k = 2; k <= cnt; k++){
                        if(x > currentLine[k]){
                            currentLine[k] = x;
                            break;
                        }
                    }
                }
                /*
                for(int j = 1; j < cnt+1; j++){
                    Console.Write(currentLine[j] + ",");
                }
                */
                //Console.WriteLine();


            }


            Console.WriteLine(cnt);

            //Console.ReadKey();
           
        }


        public static long modder(){
            return (long)Math.Pow(10,9) + 7;
        }

        public static long GCD(long n, long m){
            
            if(m % n == 0) return n;
            else return GCD(m%n, n);

        }

        public static long LCD(long n, long m){

            return m * n / GCD(n,m);
        }
    }
}