# Problem I

Pizza Party!

You are co-organizing a computer science conference, and you
are in charge of a pizza party for the conference guests. Each
guest holds preferences over combinations of toppings, and
guests are seated in groups by table in the conference center
ballroom. One pizza is served to each table. You must make
sense of each table’s collective preferences by finding pizza
toppings that make all guests happy at a particular table.
Since you are paying by the topping, the conference organizers
wish to find the *minimal* set of
satisfying toppings for each table’s pizza.

Pizza preferences are specified as statements in either an
*absolute* or *implicative* form. An *absolute
preference* for `pepperoni` is a
statement that pepperoni must be on the pizza in order to
satisfy a particular guest. An *implicative
preference* is a conditional statement. For example, the
preference `if pepperoni and sausage then
mushroom` indicates that a pizza with both pepperoni and
sausage must also have mushrooms. Note that the implicative
preference says nothing about a preference for mushrooms when
either pepperoni or sausage are absent from the pizza.

Guests are already organized by table and each table’s preferences are aggregated. It is your job to find a topping assignment for the pizza at each table.

## Input

The first line of input consists of a single integer
$c$ ($1 \leq c \leq 1\, 000$), the number
of preferences for the pizza you are trying to create. This is
followed by $c$ lines
containing either an *absolute* or
*implicative* preference.

The name of each topping is a single word, not exceeding
$10$ characters in length,
consisting of only lowercase English letters. The words
`if`, `and`,
`or`, and `then` are not valid names for pizza
toppings.

*Absolute preferences* consist of a
single topping name. All *implicative
preferences* are either of the form `if` $t_1$
`and` $t_2$ `and`
$\ldots $ `and` $t_ k$
`then` $t_{k+1}$, *or*
`if` $t_1$ `or`
$t_2$ `or` $\ldots
$ `or` $t_ k$ `then`
$t_{k+1}$, where each of
$t_1, t_2, \ldots ,
t_{k+1}$ are topping names and $1 \leq k \leq 500$.

## Output

For the provided test case, print one line with a single integer $t$ — the minimal number of toppings for a pizza that satisfies all guests at the table.

Sample Input 1 | Sample Output 1 |
---|---|

4 peppers if spinach and olives then tomatoes spinach feta |
3 |

Sample Input 2 | Sample Output 2 |
---|---|

5 pepperoni pineapple if pepperoni and sausage then mushroom ham if pineapple and ham then bacon |
4 |

Sample Input 3 | Sample Output 3 |
---|---|

4 pepperoni sausage if pepperoni and sausage then mushrooms if mushrooms or peppers then cheese |
4 |