Two teams, "Archimedians F.C." and "Pithagoreans F.C.", compete in the final of a football tournament, playing a two-game series. Each game ends with a certain number of goals scored by each team.
After these two games, a team is the winner of the series if they scored more goals in total than their opponent. Otherwise, if they finish with the same number of goals at the end of both games, the series must be decided in a third tiebreaker game.
Knowing the results of each of these two games (i.e., how many goals each team scored in each game), you are asked to write a program that determines which team won the series or if the series should go to a tiebreaker game.
A first line with two integers $$$A_1, P_1 (0 \leq A_1, P_1 \leq 31)$$$, which represent the number of goals scored by "Archimedians F.C." and "Pithagoreans F.C." in the first game, respectively.
Then, a second line, similar to the first, with two integers $$$A_2, P_2 (0 \leq A_2, P_2 \leq 31)$$$, indicating the number of goals scored by "Archimedians F.C." and "Pithagoreans F.C." in the second game, respectively.
A single line with a single character. In case the team "Archimedians F.C." wins the series, you should write A. If the team that wins the series is "Pithagoreans F.C.", you should print P, and if a tiebreaker game is needed to determine the series, you should print the character D.
3 1 1 1
A
4 3 1 3
P
2 4 2 0
D
In the first example, "Archimedians F.C." scored $$$3$$$ goals in the first game and $$$1$$$ goal in the second game, totaling $$$4$$$ goals in the series. On the other hand, "Pithagoreans F.C." scored $$$1$$$ goal in both games, totaling $$$2$$$ goals in the series. Therefore, "Archimedians F.C." emerged as the winning team of the series, and the answer is $$$\texttt{A}$$$.
