Interacdive Problem

有一个未知的数字 $x$，但已知 $1\le x < n$ 且 $2 < n\le 10^3$。可以向交互库提出询问： - `+ c`：使 $x\gets x+c$，并返回操作后 $\lfloor\frac{x}{n}\rfloor$ 的值。必须保证 $1\le c < n$。 在不超过 $10$ 次询问后，需要给出答案： - `! x`：表示你得到了**现在** $x$ 的值。

This problem is interactive. We decided to play a game with you and guess the number $ x $ ( $ 1 \le x < n $ ), where you know the number $ n $ . You can make queries like this: - + c: this command assigns $ x = x + c $ ( $ 1 \le c < n $ ) and then returns you the value $ \lfloor\frac{x}{n}\rfloor $ ( $ x $ divide by $ n $ and round down). You win if you guess the current number with no more than $ 10 $ queries.

The interaction begins by reading an integer $ n $ ( $ 2 < n \le 1000 $ ), which is written in the input data on its own line. Then you can make no more than $ 10 $ queries. To make a query, print on a separate line: - + c: this command will assign $ x = x + c $ ( $ 1 \le c < n $ ) and then print $ \lfloor\frac{x}{n}\rfloor $ (divide $ x $ by $ n $ and round down) on a separate line. Print the answer, like the queries, on a separate line. The answer doesn't count in number of queries. To output it, use the following format: - ! x: the current value of $ x $ . After that, your program should exit. You have to use a flush operation right after printing each line. For example, in C++ you should use the function fflush(stdout), in Java — System.out.flush(), in Pascal — flush(output) and in Python — sys.stdout.flush(). Note that the interactor is not responsive. To make a hack, use the following format: a single line must contain two numbers $ x $ and $ n $ , separated by a space.

3

1

+ 1

! 3

5

0

0

1

+ 1

+ 1

+ 1

! 5

10

0

0

1

2

+ 2

+ 2

+ 3

+ 8

! 20

In the first sample initially $ x = 2 $ . After the first query $ x = 3 $ , $ \lfloor\frac{x}{n}\rfloor = 1 $ . In the second sample also initially $ x = 2 $ . After the first query $ x = 3 $ , $ \lfloor\frac{x}{n}\rfloor = 0 $ . After the second query $ x = 4 $ , $ \lfloor\frac{x}{n}\rfloor = 0 $ . After the third query $ x=5 $ , $ \lfloor\frac{x}{n}\rfloor = 1 $ .