Consider the following operations performed on a PriorityQueue PQ that is initially empty $($i$.$e$.$ it has no elements, like an empty waiting room at a hospital$).$

PQ$.$add$($b$,0)$

PQ$.$add$($c$,2)$

PQ$.$add$($a$,1)$

PQ$.$remove$()$

PQ$.$add$($e$,4)$

PQ$.$add$($d$,3)$

This has produced a modified priority queue PQ$.$

Match each of the following operations on this modified priority queue PQ to their output. $($That is$,$ consider each of the following operations as the seventh operation after the six above; they are themselves not cumulative.$)$

You can$/$should assume that lower numbers have "higher priority"; that is$,$ when you remove, you want to find the element with the lowest numeric value associated with it$.$

PQ$.$remove$()$

PQ$.$size$()$