F. Interacdive Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis 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.InteractionThe 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.ExamplesInput
3

1Output
+ 1

! 3Input
5

0

0

1
Output
+ 1

+ 1

+ 1

! 5
Input
10

0

0

1

2Output

+ 2

+ 2

+ 3

+ 8

! 20NoteIn 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.
3

1
+ 1  ! 3
['binary search', 'constructive algorithms', 'interactive', '*2000']