$(35$ points$)$ Given Node.java and SinglyLinkedList.java, answer the following questions:

a$.(15$ points$)$ Write a method that gets a SinglyLinkedList object of numbers and a value max and removes every number greater than max in the list.

Example: if list$=[5,10,15,7,3,27,14,1],$ max $=13,$ list should be shortened by the following method and becomes $[5,10,7,3,1]$:

public static void removeValuesLargerThanMax$($SinglyLinkedList list, int max$)\{...\}$

b$.(20$ points$)$ Bob has n pens labeled by $1,2,3,...,$ n$.$ He uses pen #$1$ for day $1$ of school, pen #$2$ for day $2,$ pen #$3$ for day $3,...$ and pen #n for day n of school. For day n$+1$ of school, he uses pen #$1$ again. And this process continues in a round$-$robin fashion! Assume that Bob loses a pen every k days; i$.$e$.$ he loses a pen on day k$,$ another one on day $2$k$,$ etc. Write a method using the given SinglyLinkedList that gets the values of n and k$,$ and returns the label of last remaining pen before Bob loses all its pens.

Example $1$: n $=5,$ k $=1,$ the last pen is #$5$ since Bob loses a pen every day and #$5$ is the last pen Bob uses.

Example $2$: n $=5,$ k $=2,$

After day $2,$ pens are $[1,3,4,5]$

After day $4,$ pens are $[1,3,5]$

After day $6,$ pens are $[3,5]$

After day $8,$ pens are $[3]$

Last pen is #$3$

public static int bobsLastPen$($int numberOfPens, int k$)\{...\}$

$4.(15$ points$)$ Solve part $($a$)$ of question $3$ using java.util.LinkedList; i$.$e$.$ implement the following method:

public static void removeValuesLargerThanMax$($LinkedList list, int max$)\{...\}$

$5.(20$ points$)$ Write a Java method that uses java.util.Stack class to implement the following method:

public static boolean isBalanced$($String input, char$[]$ openingSymbols, char$[]$ closingSymbols$)\{...\}$

The method checks whether the input string is made of balanced sequence of parentheses, brackets, braces, etc. For example, assuming that input is $"\{1+(2+3*[4^$x$])-7\}",$ openingSymbols is an array made of $(,[,$ and $\{,$ and closingSymbols is another array made of $),],$ and $\},$ the method must return true. However, if the input is $"\{1+(2+3*[4^$x$]\}-7)",$ with the same mentioned opening and closing symbols, the method must return false since the opening and closing symbols are not balanced.