Write a recursive method called parenthesize that takes a String and an integer n as parameters and that prints the string inside n sets of parentheses. For example, this code:

parenthesize$("$Joe$",2)$;

System.out.println$()$; $//$ to complete line of output

parenthesize$("$The University of Washington", $6)$;

System.out.println$()$; $//$ to complete line of output

parenthesize$("$midterm$",1)$;

System.out.println$()$; $//$ to complete line of output

should produce these $3$ lines of output:

$(($Joe$))$

$(((((($The University of Washington$))))))$

$($midterm$)$

Your method should throw an IllegalArgumentException if passed a negative number. It could be passed $0,$ as in:

parenthesize$("$CS$143,$ Spring $2010",0)$;

System.out.println$()$; $//$ to complete line of output

In this case the output would have no $($i$.$e$.,0)$ parentheses:

CS$143,$ Spring $2010$

You are not allowed to construct any structured objects $($no array, ArrayList, String, StringBuilder, etc$)$ and you may not use a while loop, for loop, or do$/$while loop to solve this problem; you must use recursion.