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 ABC134_E
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            var firstValue = long.Parse(Console.ReadLine());
            var list = new List<long>();
            list.Add(firstValue);
            for (long i = 0; i < N - 1; i++)
            {
                var A = long.Parse(Console.ReadLine());

                var flag = false;
                for (int j = 0; j < list.Count; j++)
                {
                    if (list[j] < A)
                    {
                        list[j] = A;
                        flag = true;
                        break;
                    }
                }
                if (!flag)
                {
                    list.Add(A);
                }
            }

            Console.WriteLine(list.Count);
        }
    }

    public class Node
    {
        public Node(long val)
        {
            Val = val;
        }

        public Node Left { get; set; }
        public Node Right { get; set; }

        public long Val { get; set; }

        public long GetRightVal()
        {
            if (Right == null)
                return Val;

            return Right.GetRightVal();
        }

        public void AddVal(long val)
        {
            if (Val >= val)
            {
                AddToLeft(val);
            }
            else if (Right == null || GetRightVal() < val)
            {
                AddToRight(val);
            }
            else
            {
                AddToLeft(val);
            }
        }

        public void AddToRight(long val)
        {
            if (Right == null)
            {
                Right = new Node(val);
            }
            else
            {
                Right.Val = val;
            }
        }

        public void AddToLeft(long val)
        {
            if (Left == null)
            {
                Left = new Node(val);
            }
            else
            {
                Left.AddVal(val);
            }
        }

        public long Count()
        {
            if (Left == null)
            {
                return 1;
            }
            else
            {
                return Left.Count() + 1;
            }
        }
    }
}