Hi everyone. I'm not gonna lie to you - this is part of an assignment. However, I didn't come here to ask for code.

Right, my only question right now is how can I construct a binary tree from its in-order and post-order traversals?You are to determine the value of the leaf node in a given binary tree that is the terminal node of a path of least value from the root of the binary tree to any leaf. The value of a path is the sum of values of nodes along that path.

Input

The input file will contain a description of the binary tree given as the inorder and postorder traversal sequences of that tree. Your program will read two line (until end of file) from the input file. The first line will contain the sequence of values associated with an inorder traversal of the tree and the second line will contain the sequence of values associated with a postorder traversal of the tree. All values will be different, greater than zero and less than 10000. You may assume that no binary tree will have more than 10000 nodes or less than 1 node.

Output

For each tree description you should output the value of the leaf node of a path of least value. In the case of multiple paths of least value you should pick the one with the least value on the terminal node.

Sample Input

3 2 1 4 5 7 6

3 1 2 5 6 7 4

7 8 11 3 5 16 12 18

8 3 11 7 16 18 12 5

255

255

Sample Output

1

3

255

In-order: 3 2 1 4 5 7 6

Post-order: 3 1 2 5 6 7 4

Here's what I know so far in this example: 4 is the root, because it's the last element in the post-order sequence; 3 is the leftmost element, because it's the first element in the pre-order sequence.

However, I seem to have a hard time sorting out an algorithm to build the rest of the binary tree. Can you please point me in the right direction? Thank you in advance.