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)

N = gets.to_i
as = readlines.map(&:to_i)
lasts = [as.shift]
minimum = lasts.first
until as.empty?
  current_num = as.shift
  if current_num <= minimum
    lasts << current_num
    minimum = current_num
  else
    lasts.sort!
    # p current_num
    temp = (0..lasts.size-1).bsearch { |i| lasts[i] >= current_num }
    if temp.nil?
      index = -1
    else
      index = temp - 1
    end
    lasts[index] = current_num
    minimum = lasts[0..1].min
  end
  # p lasts
end
# p lasts
puts lasts.size