Suppose you have a stack $$ of size $50.$ Numbers $1$ to $10$ are pushed into the stack, before five numbers are

popped from the stack. The next numbers $11$ to $20$ are pushed into the stack before five numbers are popped from

the stack again. This process is repeated until numbers $91$ to $100$ are pushed and five numbers are popped. Given

this information, answer the following items.

a$.$ After executing the last POP operation on the stack, how many numbers are in the stack?

b$.$ After all operations have been executed, what is the total number of times a stack overflow error occurred?

c$.$

After executing the last PUSH operation, what is the value of the head of the stack?

d$.$ Using set notation, describe the elements inside the stack.