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;
using System.Collections.Generic;

namespace atcoderBeginnerContest134
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Convert.ToInt32(Console.ReadLine());
            int[] A = new int[N];
            List<int> ls = new List<int>()
            {
                -1
            };
            for (int i = 0; i < N; ++i)
            {
                A[i] = Convert.ToInt32(Console.ReadLine());

                if (ls[ls.Count - 1] >= A[i])
                    ls.Add(A[i]);
                else if (ls[0] < A[i])
                    ls[0] = A[i];
                else
                {
                    int idx = BinarySearch(ls, A[i]);
                    while (ls[idx] == A[i])
                        ++idx;
                    ls[idx] = A[i];
                }
            }
            Console.WriteLine(ls.Count);
        }


        private static int BinarySearch(List<int> ls, int elem)
        {
            int ini = 0;
            int fin = ls.Count;

            while(ini < fin)
            {
                int md = (ini + fin) >> 1;
                if (ls[md] > elem)
                    ini = md + 1;
                else
                    fin = md; 
            }

            return fin;
        }
    }
}