Pizza Anyone?

You are ordering one large pizza for yourself and your friends. Each friend tells you what they want on the pizza and what they do not want. Because there will be only one pizza, no one is likely to get everything they ask for. Your job is to order a single pizza that satisfies at least one request from every friend.

The pizza parlor offers the following toppings. You may independently include or omit each one:

Each friend gives you one line describing their preferences as a list of requests. A request +X means "the pizza must have topping X", and a request -X means "the pizza must not have topping X". A friend is satisfied when the pizza meets any one of that friend's requests. For example, +O-H+P; describes a friend who accepts the pizza if it has onions, or if it has no ham, or if it has pepperoni.

The input contains one or more pizza cases.

A pizza case is a group of 1 to 12 friend lines, one friend per line, followed by a line that contains a single period ..

Each friend line is a sequence of requests terminated by one semicolon ;. Each request is a sign character (+ or -) immediately followed by an uppercase topping code from A to P. A topping code may appear more than once on a line. There are no blank lines inside a case, and the input ends at end of file.

For each pizza case, print exactly one line.

When at least one pizza can satisfy every friend, several such pizzas may exist. Choose the pizza with the fewest toppings; if two or more pizzas tie for the fewest toppings, choose the one whose topping list is alphabetically smallest. Print Toppings: followed by the chosen toppings as uppercase letters in alphabetical order. If the chosen pizza has no toppings at all, print exactly Toppings: with nothing after it. For example, a pizza with anchovies, ham, lean ground beef and pepperoni is printed as Toppings: AHLP.

When no pizza can satisfy every friend, print exactly:

No pizza can satisfy these requests.