Problem D
The
Uxuhul Voting System
Input: standard input
Output: standard output
Time Limit: 1 second
One of the world's first civilizations was that of the ancient Uxuhul indians, in the jungles
of Central America. The Uxuhul culture flourished for almost a thousand years,
with its golden era around 3200 BC. Each year high priests, representing
different parts of the realm, gathered in the capital to vote on important
matters. There were always exactly three issues to vote on, and each issue was
a simple yes/no question. The three issues were all decided in one single
voting round, in the following manner:
All the priests would gather in a large room, with a
table in the centre. On the table lie three flat stones, each with one white,
and one black side. Each stone represented an issue, with the black side up
symbolising the outcome 'no' and the white side the outcome 'yes'.
Initially all stones had the black side up, representing negative outcome on
all issues. In order of age, from youngest to oldest, each priest voted, by
turning exactly one stone, thus (temporarily) changing the outcome of one
issue. It was not allowed to skip the vote, each priest had to flip a stone.
The colours of the side facing up on the stones after the oldest priest had
flipped the stone of his choice, determined the final outcome of the voting on
the three issues.
The Uxuhul political life was rather complex, with a
lot of lobbying by different interest groups. Lobbying (and bribery), gave each
priest preferences between the eight different outcomes of the three issues.
Religious rules forced each priest to publicly state his preference order
between the eight outcomes, before the voting process started. Based on knowledge
of each other priest's preferences, it was possible for the priests to choose a
stone to flip in the way that it gained their interest best. As the Uxuhul were
advanced logicians, with deep knowledge of game theory, each priest was
actually able to vote in the optimal way!
Eventually, the complexity and rigidity of their
political system brought the Uxuhul culture to collapse. Today only ruins
remain of their cities and temples. Historians and archaeologists try to
understand more about their history by studying the results from their yearly
votes. However, only records of the priests' preferences remain, not the actual
outcomes of the votes. Now it is your task to find a way to recover the
outcomes.
The input begins with an integer n, 1<n<100,
the number of voting rounds. Starting on the next line, n problems
follow, one by one. Each voting starts with a line containing an integer m,
1<m<100, stating the number of voting priests. Then there are m
lines, defining the preference order for the outcomes of the three issues for
each voter, in order, starting with the voter who will begin the voting
procedure. The preferences for each outcome (NNN, NNY, NYN,
NYY, YNN, YNY, YYN, and YYY respectively,
where ‘N’ stands for no and ‘Y’ for yes), are given as an integer
in the range [1…8]. Lower numbers indicate higher preference. The
preferences for the eight outcomes are given in the same order as the
enumeration of the outcomes above.
For each of the n voting problems, output one
line describing the outcome of the votes for the three issues, 'Y' for
yes, and 'N' for no.
2 4 8 7 6 5 4 3 2 1 8 6 3 1 2 4 5 7 8 3 6 5 1 2 7 4 1 2 3 4 5 6 7 8 1 1 2 3 4 5 6 7 8 |
NYY NNY |
Swedish National Contest