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: Time Limit Exceeded)

io = STDIN
N=io.gets.to_i
ar=N.times.map{io.gets.to_i}
def calc(ar)
  chunk= ar.chunk_while{|i,j|i<j}.to_a
  return chunk.size if chunk.size<=2
  a0=chunk[0]
  a1=chunk[1]
  a2=chunk[2]
  if a0[-1]<a2[0]
    if chunk.size==3
      calc([a1,[a0,a2]].flatten)
    else
      calc([a1,[a0,a2],chunk[3..-1]].flatten)
    end
  else
    2+calc(chunk[2..-1].flatten)
  end
end
p calc(ar)