**Time limit:**1.00 s**Memory limit:**512 MB

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,\dots,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 \le n \le 10^5

# Example

Input:

5 5 3 2 1 4 3 5 1 2 4

Output:

3 1 4 2 5