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)

N = gets.to_i
class Node
    attr_accessor :index, :children, :parent, :sibling

    def initialize()
        @children = []
        @parent = nil
        @sibling = nil
    end

    def depth
        parent == nil ? 0 : parent.depth + 1
    end

    def degree
        children.length
    end

    def height
        if children.empty?
            0
        else
            children.map {|e| e.height }.max + 1
        end
    end

    def preorder_array
        left_array = children[0] == nil ? [] : children[0].preorder_array
        right_array = children[1] == nil ? [] : children[1].preorder_array
        [[self], [left_array], [right_array]].flatten
    end

    def inorder_array
        left_array = children[0] == nil ? [] : children[0].inorder_array
        right_array = children[1] == nil ? [] : children[1].inorder_array
        [[left_array], [self], [right_array]].flatten
    end

    def postorder_array
        left_array = children[0] == nil ? [] : children[0].postorder_array
        right_array = children[1] == nil ? [] : children[1].postorder_array
        [[left_array], [right_array], [self]].flatten
    end
end
preorders = gets.chomp.split(" ").map(&:to_i)
inorders = gets.chomp.split(" ").map(&:to_i)

def setNode(preorders, inorders, parent=nil)
    node = Node.new
    node.index = preorders[0]
    node.parent = parent
    left_num = inorders.index(node.index)
    right_num = preorders.length - left_num - 1
    left_node = (left_num == 0) ? nil : setNode(preorders[1..left_num], inorders[0..(left_num-1)], node)
    right_node = (right_num == 0) ? nil : setNode(preorders[(-right_num)..(-1)], inorders[(-right_num)..(-1)], node)
    node.children = [left_node, right_node]
    node
end

root_node = setNode(preorders, inorders)

puts root_node.postorder_array.map {|e|e.index}.join(" ")