Me and my friends are ordering a big pizza to share. As you
can imagine this is quite complicated, since everyone has
different wishes about what should be on the pizza. For
instance Gunnar wants bananas on the pizza, Emma doesn’t want
bananas but wants olives, Marc wants there to be tomatoes, and
so on. Fortunately, against all odds, we managed to come up
with a selection of toppings such that everyone had at least
$2/3$’s of their wishes
fulfilled, which we unanimously decided was good enough.
But then, disaster struck! We sent out Lukáš to buy the
pizza, but he accidentally lost the piece of paper on which we
had written down our carefully selected list of toppings. Now
we’re back at square one, and have to construct a new selection
of toppings. Given how long it took us to find the original
selection of toppings, we have decided to lower our standards a
bit and just try to find a selection such that everyone has
strictly more than $1/3$ of their wishes fulfilled.
Can you help us with this? If you do, you’ll get some
pizza!
Input
The first line of input contains an integer $1 \le N \le 10\, 000$, the number of
friends in the group (including yourself). Each of the next
$n$ lines contains the
list of wishes of one of the friends. This list starts with an
integer $1 \le w \le 30$,
the number of wishes this friend has, followed by a
spaceseparated list of wishes. Each wish is either “+<topping>” or “<topping>” where <topping> is the name of a topping,
indicating that this friend wants or does not want this
topping. Each topping name appears at most once in each
list.
Topping names are nonempty strings of up to $15$ lowercase English letters
‘a’‘z’.
There are at most $250$
different toppings.
Output
Output a list of toppings (without repetitions, separated by
spaces or newlines) such that each friend has strictly more
than $1/3$ of their wishes
fulfilled. You may assume that there exists a list such that
every friend has at least $2/3$ of their wishes fulfilled.
Your list of toppings is not allowed to contain any toppings
that are not mentioned in the input, nor is it allowed to
contain repetitions.
Sample Input 1 
Sample Output 1 
1
4 +zucchini +mozzarella +mushrooms artichoke

zucchini
mozzarella
mushrooms
artichoke

Sample Input 2 
Sample Output 2 
3
3 +redbeans +soylentgreen bluecheese
3 +redbeans soylentgreen +bluecheese
3 redbeans +soylentgreen +bluecheese

redbeans
soylentgreen
bluecheese
