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 Ruby (2.3.3) (judge verdict: Wrong Answer)

io = STDIN
N=io.gets.to_i
ar=N.times.map{io.gets.to_i}
if N>=3
  chunk= ar.chunk_while{|i,j|i<j}.to_a
  if chunk.size==2
    p 2
  else
    cnt = 0
    chunk.each_cons(3) do |a,b,c|
      if a.last < c.first
      else
        cnt+=1
      end
    end
    p cnt+2
  end
else
  if N==1
    puts 1
  else
    if ar[0]<ar[1]
      puts 1
    else
      puts 2
    end
  end
end