Construct a recursive decent parser for the given grammar and demonstrate parsing steps by step for valid and invalid string.

EXP ::$=+$NUM $|-$NUM $|$ NUM

NUM : :$=$ NUM DIGITS $|$ DIGITS

DIGITS ::$=$ DIGIT $|$ DIGIT $.$ DIGIT

DIGIT ::$=0|1|2|3|4|5|6|7|8|9$

Input ends with $\text{'}$$$\text{'}$ end of string identifier

Valid Input String Example

$+9\mathrm{.}99$ $

Invalid Input String Examples

$++22\mathrm{.}2$$

provide clear, step by step explained solution