There are three common ways to traverse the nodes of a binary tree:

• Preorder: First process the root, then the left subtree, and finally the right subtree.
• Inorder: First process the left subtree, then the root, and finally the right subtree.
• Postorder: First process the left subtree, then the right subtree, and finally the root.

There is a binary tree of \(n\) nodes with distinct labels. You are given the preorder and inorder traversals of the tree, and your task is to determine its postorder traversal.

Input

• The first input line has an integer \(n\): the number of nodes. The nodes are numbered \(1,2,…,n\).
• After this, there are two lines describing the preorder and inorder traversals of the tree. Both lines consist of \(n\) integers.
• You can assume that the input corresponds to a binary tree.

Output

• Print the postorder traversal of the tree.

Constraints

• \(1 \leq n \leq 10^5\)

Example

Sample input

5  
5 3 2 1 4  
3 5 1 2 4

Sample output

3 1 4 2 5