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;

namespace AtCorder
{
	public class Program
	{
		const long MOD = 1000000007;
		static void Main(string[] args)
		{
			Scanner cin = new Scanner();
			int n = cin.Int();
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = cin.Int();
			}

			SortedList<int, long> sl = new SortedList<int, long>(n);
			sl.Add(a[n - 1], 1);
			for (int i = n - 2; i >= 0; --i) {
				if (sl.Keys[sl.Keys.Count() - 1] <= a[i]) {
					if (sl.ContainsKey(a[i])){
						sl[a[i]] += 1;
					} else {
						sl.Add(a[i], 1);
					}
				} else {
					int key = sl.Keys.First(x => x > a[i]);
					if (sl.ContainsKey(key)) {
						long num = sl[key];
						if (num == 1) {
							sl.Remove(key);
							if (sl.ContainsKey(a[i])) {
								sl[a[i]] += num;
							} else {
								sl.Add(a[i], num);
							}
						} else {
							sl[key] -= 1;
							if (sl.ContainsKey(a[i])) {
								sl[a[i]] += 1;
							} else {
								sl.Add(a[i], 1);
							}
						}
					} else {
						if (sl.ContainsKey(a[i])) {
							sl[a[i]] += 1;
						} else {
							sl.Add(a[i], 1);
						}
					}
				}
			}

			long ans = sl.Values.Sum();
			Console.WriteLine(ans);
		}
	}

	public class Scanner
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private string[] buf_;
		private int index_;
		
		public Scanner()
		{
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = Console.ReadLine();
			while (st == "") {
				st = Console.ReadLine();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int()
		{
			return int.Parse(Next());
		}
		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long Long()
		{
			return long.Parse(Next());
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double Double()
		{
			return double.Parse(Next());
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}
	}
}