1. Please draw a binary Merkles hash tree with 9 leaf nodes. The leaf nodes are labeled as Leaf1 to Leaf9, which correspond to the hash values of the files F1 to F9, respectively. Now please answer:

(a) For each node in the tree, please label clearly how the hash value is calculated based on its children; Please note that the number of leaf nodes is not power of 2. Therefore, you may need to change the way in which intermediate nodes are calculated. There are different ways to handle this. Please label clearly how you calculate each node.

(b) Now the creator of the file F6 needs to verify that his files hash value is integrated in the root of the tree. Please show the minimum number of hash values in the tree that the creator needs to accomplish the task. Please also show how the verification is accomplished.