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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static int LoadInt() { return int.Parse(Console.ReadLine()); }
        static int[] LoadIntArray() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray(); }

        static void Main(string[] args)
        {
            var N = LoadInt();
            var array = new List<int>();
            foreach(var i in Enumerable.Range(0,N))
            {
                array.Add(LoadInt());
            }

            var union = new UnionFind(N);
            foreach(var i in Enumerable.Range(0, N))
            {
                var tmp = array[i];
                for(var j=i+1; j<N; j++)
                {
                    if(tmp<array[j] && union.Data[j]==-1)
                    {
                        union.Unite(i, j);
                        tmp = array[j];
                    }
                }
            }
            var result = union.Data.Where(x => x < 0).Count();
            Console.WriteLine(result);
        }
    }

    /// <summary>
    /// union find, positive int only
    /// </summary>
    public class UnionFind
    {
        private int[] data;

        public UnionFind(int size)
        {
            data = new int[size];
            for (int i = 0; i < size; i++) data[i] = -1;
        }

        public int[] Data
        {
            get
            {
                return data;
            }
        }

        public bool Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);

            if (x != y)
            {
                if (data[y] < data[x])
                {
                    var tmp = y;
                    y = x;
                    x = tmp;
                }
                data[x] += data[y];
                data[y] = x;
            }
            return x != y;
        }

        public bool IsSameGroup(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public int Root(int x)
        {
            return data[x] < 0 ? x : data[x] = Root(data[x]);
        }
    }
}