Consider a smart array that automatically expands on demand. (Like the java.util.ArrayList.) It starts with some given initial capacity of 100, and whenever it expands, it adds 50 to the current capacity. So, for example, at the 101st add, it expands to a capacity of 150. How many total units of work would be needed to add 1000 items to this smart array? Assume it takes one unit of work to write an item into an array location, and one unit of work to allocate a new array.