augment the scala code elow with the following methods: 1) def filter(p: Int => Boolean): IntSet Hint: start by defining the helper method filterAcc which takes an accumulator set as a second argument. This accumulator contains the ongoing result of the filtering. def filterAcc(p: Int => Boolean, acc: IntSet): IntSet 2) Using the method remove with the following implementations: def remove(i: Int): IntSet = this // for Empty IntSet def remove(i: Int): IntSet = // for NonEmpty IntSet if (i < elem) new NonEmpty(elem, left.remove(i), right) else if (elem < i) new NonEmpty(elem, left, right.remove(i)) else left.union(right) Write a method descending() which prints the IntSet elements in descending order. Hint: start by implementing the method max() which returns the max element in the set. 3) Write a Scala main method to test your implemented methods

abstract class IntSet { def incl(x: Int): IntSet def contains(x: Int): Boolean def union(other: IntSet): IntSet } object Empty extends IntSet { def incl(x: Int): IntSet = new NonEmpty(x, Empty, Empty) def contains(x: Int): Boolean = false def union(other: IntSet): IntSet = other override def toString(): String = "." } class NonEmpty(elem: Int, left: IntSet, right: IntSet) extends IntSet { def incl(x: Int): IntSet = { println(x) if (x < elem) new NonEmpty(elem, left incl x, right) else if (x > elem) new NonEmpty(elem, left, right incl x) else this } def contains(x: Int): Boolean = { if (x < elem) left contains x else if (x > elem) right contains x else true } def union(other: IntSet) = { right union (left union (other incl elem)) } override def toString(): String = { elem + " " + left.toString() + " " + right.toString } } object Hello { def main(args: Array[String]) = { println("hello world!") val B = Empty incl 4 incl 1 incl 5 incl 6 println(B) val C = Empty incl -1 incl 2 incl 10 incl 100 println(C) val D = B union C println (D) } }