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)

N = gets.chomp.to_i
a = []
N.times do
  a << gets.chomp.to_i
end

sorted = []
a.each do |n|
  # Early return
  if sorted.size == 0
    sorted.push(n)
    next
  end
  
  i = sorted.bsearch_index { |x| x >= n }
  if i == 0
    sorted.unshift(n)
  elsif i == nil
    sorted[sorted.size-1] = n
  else
    sorted[i-1] = n
  end
  
  # p "n: #{n}"
  # p "i: #{i}"
  # p sorted
end

p sorted.size