Design an NFA to recognize the following Python numerical literals and write code to implement your NFA $($or equivalent DFA$)($i$.$e$.$ state transitions, etc.$).$ If you just use a lot of if$-$else's to check this or that requirement, it's very difficult, if not impossible to prove your program is per spec $($the Python Language specification$).$

You cannot use built$-$in or $3$rd party functionalities that recognize numbers or build$/$interpret regular expressions, grammar, etc. You need to implement the tasks $$from scratch$.$

a$)$Recognize Python decimal integer literals.For simplicity, you can assume the input string$$s length $<=20.$ Your program should ask for user input as a string, and check if it can be a valid decimal integer or not. You also need to include your NFA design $($with unlimited digits allowed $-$ you can break this into a few smaller NFA parts, so it's not one humongous machine$)$ drawn using JFLAP.

b$)$Expand your program to recognize Python octal and hexadecimal integer literals. For simplicity, you can assume the input string$$s length $<=20.$ Your program should ask for user input as a string, and check if it can be a valid decimal$/$octal$/$hexadecimal integer or not. You also need to include your NFA design $($with unlimited digits allowed $-$ you can break this into a few smaller NFA's so it's not one humongous machine$)$ drawn using JFLAP.

$($PLZ INCLUDE THE NFA DIAGRAMS$)$