시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 512 MB 0 0 0 0.000%

## 문제

This problem was supposed to have a nice long legend about the Wild Wild West, but the author did not manage to write it in time, so use the power of your imagination!

Consider a number line. A player initially stands at the position $x = p$. At the beginning of each round, you can say either "+" or "-". After that, the player changes position according to what you said. More precisely, if you say $t$ and the player stood at position $x$, then he moves to position $x' = x + d_t$, where $d_+$ and $d_-$ are two integer constants.

You do not know the exact values $p$, $d_0$ and $d_1$, but you know that the player is either the Good, the Bad or the Ugly (yeah, imagination!):

• The Good player has $p = m$, $d_+ = 2$, $d_- = -1$;
• The Bad player has $p = -m$, $d_+ = 1$, $d_- = -2$;
• The Ugly player has either $p = m$ or $p = -m$ and either $d_+ = 1$ and $d_- = -1$ or $d_+ = -1$ and $d_- = 1$.

As you can see, the starting position of the player depends on some integer constant $m$ ($1 \le m \le 1000$)... unfortunately, you do not know it too.

After each round, the player tells you if he now stands at $x = 0$ or not.

It appears that, by playing several rounds, you can uniquely determine if the player is Good, Bad or Ugly. Do it in no more than $30 m$ rounds.

In each test, the values $m$, $p$, $d_+$ and $d_-$ are chosen according to the above rules. They are fixed in advance and don't change during the checking process.

## 프로토콜

This is an interactive problem.

If you want to play a round, print either "+" or "-" on a separate line. In response, you will get a line containing either $1$ if the player arrived at position $x = 0$, or $0$ if the player stands somewhere else.

If you are ready to guess the type of the player, print a line containing the character "!", a space and one of the words "good", "bad" or "ugly". After that, your program must terminate.

If after playing $30 m$ rounds you do not provide the answer, your solution will get a "Wrong Answer" outcome.

To prevent output buffering, flush the output buffer after each printed line.

## 예제 입력 1


0

1


## 예제 출력 1

-

-

! good


## 채점

• 예제는 채점하지 않는다.