$9.[12\%]$ For each of the following problems, indicate which are in P and which are in NP$.$ For those you think are in P$,$ give an outline of the algorithm to solve them. For those you think are in NP$,$ explain why you think they are not solvable in polynomial time. $($Hint: think about an algorithm to solve these problems, and then determine if it is polynomial.$)$The Smarandache function, S$($k$),$ gives the smallest integer m$,$ so that m$!$ can be evenly divided by k$.$ For example, S$(9)=6$ because $6!=720$ and $9$ does not divide any smaller factorial. Calculate the Smarandache function for any number.You have to seat N children in the smallest number of rows in an auditorium. For each child, you have a list of who that child dislikes. Experience shows that if a child is in the same row or any row behind a child that he or she dislikes, he or she will throw things at the other child. Given this list, determine in which row to seat each child, or determine that they cannot be seated.You are in front of a wall that stretches infinitely in both directions. You know that there is a door in the wall, but it is dark, and you have only a dim flashlight that allows you to see no more than one step in either direction. Find the door