Description

You are given the postorder and inorder traversal of a binary tree. Your job is to reconstruct the tree and print the preorder traversal of the tree.

Note

• Each vertex of the tree is labeled 1 ~ n distinctly.

Input

Each input is given in three lines.

The first line contains an integer n: The number of vertices of the binary tree.

The second line is the postorder traversal of the tree.

The last line is the inorder traversal of the tree.

Note

• For both traversals, each vertex is seperated by an empty space.

Restriction

• 1 ≤ n ≤ 2∗10⁵

 

Output

Output should be printed in one line. Containing the preorder traversal of the tree. Each vertex of the traversal should be seperated with an empty space.

Remember to print a ‘\n’ at the end of the output.

Do not include any spaces at the "end of line".

Sample Input  Download

Sample Output  Download

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