Problem D
Dunglish

A group of confused Dutchmen. Public domain.

Given a sentence in Dutch and a dictionary containing both correct translations as well as phonetic (incorrect) translations of individual words, find the translation of the sentence and indicate whether it is correct, or in case there is more than one find the total number of correct and incorrect translations. A sentence is correctly translated when each word of the sentence is correctly translated.

Input

The input consists of:

• One line with an integer $n$ ($1\le n\le 20$), the number of words in the Dutch sentence.

• One line with $n$ words, the Dutch sentence $s$.

• One line with an integer $m$ ($1\le m\le {10}^5$), the number of words in the dictionary.

• $m$ lines, each with three strings $d$, $e$ and $c$, a Dutch word, the English translation, and “correct” if this is the correct translation or “incorrect” otherwise.

A word consists of between $1$ and $20$ lowercase letters. Each word in $s$ appears at least once as a Dutch word in the dictionary, no word appears more than $8$ times as a Dutch word in the dictionary, and each combination of a Dutch and English word appears at most once.

Output

In case there is only a single translation of $s$, output one line with the translation followed by one line with “correct” or “incorrect”. In case there is more than one translation, output one line with the number of possible correct translations followed by “correct”, and one line with the number of possible incorrect translations followed by “incorrect”.

7
als mollen mollen mollen mollen mollen mollen
4
als when correct
mollen moles correct
mollen destroy correct
mollen mills incorrect

64 correct
665 incorrect

5
de zuigers zijn buiten werking
6
zijn are correct
banaan banana correct
de the correct
zuigers suckers incorrect
buiten out correct
werking working incorrect

the suckers are out working
incorrect