Write/ scan clearly. Please explain your thinking process and any theorems or any external knowledge that would help understanding. Thank you.

4. Suppose Dr. WhyLie comes up to you and claims that he has invented a super-fast comparison based priority queue. The speed of the priority queue operations are as follows (n is the number of items currently in the priority queue): a. insert a new item in O(sqrt(log n)) time b. extract (remove and return) the smallest item from the priority queue in O(sqrt(log n)) time. Explain why Dr. WhyLie must be lying