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

*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.

**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`