A deque with heap order is a data structure consisting of a list of items, on which the following operations are possible:

push(x): Insert item x on the front end of the deque.

pop(): Remove the front item from the deque and return it.

inject(x): Insert item x on the rear end of the deque.

eject(): Remove the rear item from the deque and return it.

findMin(): Return the smallest item from the deque (breaking ties arbitrarily).

a. Describe how to support these operations in constant amortized time per operation.

b. Describe how to support these operations in constant worst-case time per operation.