Write a Haskell script for the following without using any built-in functions. You must write functions from scratch in order to use them.

Write a function data SF a = SS a FF invFac:: Integer -> SF Integer which returns the largest number whose factorial is no greater than the given number (what happens if the given number is negative?). Write a function data SF a = SS a FF invFac:: Integer -> SF Integer which returns the largest number whose factorial is no greater than the given number (what happens if the given number is negative?)