Given the pre order traversal and in-order traversal of a binary treee. Build and print the post-order traveral of the given tree.

Input

• The first line contains: ~N~ as the number of vertices ~(N \le 80 000)~.
• The second line contains: ~N~ numbers, which are preorder browsing lists.
• The third line contains: ~N~ numbers as the inorder browse list.

Output

• Print out the postorder traversal .

Example Input

6
0 4 2 3 5 1
4 0 5 3 2 1

Example Output

4 5 3 1 2 0

Note