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: Wrong Answer)

# 昇順でソートされている前提
def priority_push(array:, num:)
  index = array.bsearch_index { |i| i <= num}
  if index.nil?
    array.push(num)
  else
    array.insert(index, num)
  end
end

# 昇順でソートされていて、indexに値がある前提
def priority_update(array:, index:, num:)
  array.delete_at(index)
  priority_push(array: array, num: num)
end

N = gets.to_i
arr = N.times.map{ gets.to_i }
stacks = [arr.shift]

arr.each do |i|
  overwrite_index = stacks.bsearch_index { |target| target < i }
  if overwrite_index.nil?
    priority_push(array: stacks, num: i)
  else
    p "overwrite_index: #{overwrite_index}"
    priority_update(array: stacks, index: overwrite_index, num: i)
  end
end
puts stacks.count