Problem:
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Reconstruction of a Tree

Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.

Input

In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.

In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.

In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.

Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.

Output

Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.

Constraints

$1 \leq n \leq 40$

Sample Input 1

5
1 2 3 4 5
3 2 4 1 5

Sample Output 1

3 4 2 5 1

Sample Input 2

4
1 2 3 4
1 2 3 4

Sample Output 2

4 3 2 1

Solution in Ruby (judge verdict: Accepted)

class Node
  attr_reader :id
  attr_accessor :left, :right

  def initialize(id)
    @id = id
  end
end

def tree(pre_ids, in_ids)
  return nil if pre_ids.none?

  root_id = pre_ids.first
  root = Node.new(root_id)
  return root if pre_ids.one?

  inorder_root_position = in_ids.find_index(root_id)
  left_in_ids = in_ids[0 .. inorder_root_position - 1]
  right_in_ids = in_ids[inorder_root_position + 1 .. -1]

  left_ids_count = inorder_root_position
  inorder_right_begin_position = left_ids_count + 1
  left_pre_ids = pre_ids[1, left_ids_count]
  right_pre_ids = pre_ids[inorder_right_begin_position .. -1]

  root.left = tree(left_pre_ids, left_in_ids)
  root.right = tree(right_pre_ids, right_in_ids)
  root
end

class TreeWalker
  def self.enum_node_postorder(node, &block)
    enum_node_postorder(node.left, &block) if node.left
    enum_node_postorder(node.right, &block) if node.right
    yield node
  end

  def initialize(root)
    @root = root
  end

  def enum_postorder(&block)
    self.class.enum_node_postorder(@root, &block)
  end
end

_ = gets.to_i
pre_ids = gets.chomp.split(' ').map(&:to_i)
in_ids = gets.chomp.split(' ').map(&:to_i)

root = tree(pre_ids, in_ids)
walker = TreeWalker.new(root)
puts walker.to_enum(:enum_postorder).map(&:id).join(' ')