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: Accepted)

# https://atcoder.jp/contests/abc006/tasks/abc006_4
 
class Array
  def lis
    b_ary = [self[0]]
    self[1..-1].each do |v|
      # 広義単調増加 { |x| x > v }
      # index = b_ary.bsearch_index { |x| x > v }
      # 狭義単調増加 { |x| x >= v }
      # index = b_ary.bsearch_index { |x| x >= v }
      # 広義単調減少 { |x| x < v }
      index = b_ary.bsearch_index  { |x| x < v }
      # 狭義単調減少 { |x| x <= v }
      # index = b_ary.bsearch_index { |x| x <= v }
      if index
        b_ary[index] = v
      else
        b_ary << v
      end
    end
    return b_ary.size
  end
end
 
n = gets.to_i
puts n.times.with_object([]) { |_i,obj| obj << gets.to_i }.lis