Write a program in C++ to build a calculator. Instead of a typical calculator which reads in-order expressions and evaluates them, build a calculator that takes in numbers and assigns the operations to yield the highest value expression. The current operations on the calculator only handle pairs of parentheses, and the operators for addition, subtraction, multiplication, and division. The calculator can rearrange the numbers if it helps find the optimal value. For example, the list 4.0 5.0 3.0 2.0 1.0 using the calculator should find the optimal expression yielding the maximum value to be:

4.0 * 5.0 * 3.0 * (2.0 + 1.0) = 180

Input from the keyboard a list of up to 10 floating-point values from -100000.0 to 100000.0. Output to the screen a single floating-point value rounded to a precision of two decimal places representing the highest value expression that the calculator could create by inserting the symbols ( ) + - * / into the given expression. Assume at least one number in the list and only the operators listed above. Refer to the sample output below.

Sample Runs (2):

Enter up to 10 floating-point values: 4.0 5.0 3.0 2.0 1.0

Maximum value: 180.00

Enter up to 10 floating-point values: 1.0 1.0 1.0 1.0 -1.0

Maximum Value: 5.00