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: Runtime Error)

_n = gets.to_i
as = readlines.map(&:to_i)

lasts = [as.shift]
minimum = lasts.first
maximum = lasts.first

until as.empty?
  current_num = as.shift

  if current_num <= minimum
    lasts.unshift(current_num)
    minimum = current_num
  elsif current_num > maximum
    lasts[-1] = current_num
    maximum = current_num
  else # minimum < current_num <= maximum
    target_index = (0..(lasts.size-1)).bsearch { |i| current_num <= lasts[i] }
    target_index -= 1
    lasts[target_index] = current_num
    # indexが0だった場合にはminimumが変化
    minimum = current_num if target_index == 0
  end
  # p lasts
end
puts lasts.size