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;

class E
{
	static int Read() => int.Parse(Console.ReadLine());
	static void Main()
	{
		var a = Array.ConvertAll(new int[Read()], _ => Read());

		var l = new List<int>();
		int j;
		foreach (var v in a)
			if ((j = First(0, l.Count, i => l[i] < v)) < l.Count) l[j] = v;
			else l.Add(v);
		Console.WriteLine(l.Count);
	}

	static int First(int l, int r, Func<int, bool> f)
	{
		int m;
		while (l < r) if (f(m = l + (r - l - 1) / 2)) r = m; else l = m + 1;
		return r;
	}
}