You cannot use any predefined functions for the calculation. The program must also use the 'while' function.

Calculate the factorial of an integer. The definition of a factorial is: $2)...(3)(2)(1).$

The algorithm must take into consideration the special case that the factorial of zero is $1$ by definition.

In addition to the above, the program must also verify that the number is not negative, which turns out to be

Invalid.

Run the program to calculate the factorial of the following values: $3,-4,1,0$ and $8.$