5. (25 pts) Stirling's approximation is used to estimate the value of natural logarithms of factorials of large numbers. The mathematical formula is. In (n!) = n lnn-n a. Write a function that meets the following specifications: def Simpson (N): N is a positive integer. The function should return both the estimated value of In(N!) and the percent error in the estimation based on the formula: error=1-[nln(n)-n]/In(N!) b. Write a function that meets the following specifications: def main(): Print lines of formatted output to the screen/console in the following format: In(500!) = 2605.3 (error = 0.15%) Notes: Output a similar formatted line only when error drops below values of 15%, 10%, 5%, 1% You can calculate the natural logarithm of a function with log () from the math module. You can calculate the factorial of an integer with factorial() from the math module