E. Deleting Numberstime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputThis is an interactive problem.There is an unknown integer x (1\le x\le n). You want to find x.At first, you have a set of integers \{1, 2, \ldots, n\}. You can perform the following operations no more than 10000 times:  A a: find how many numbers are multiples of a in the current set.  B a: find how many numbers are multiples of a in this set, and then delete all multiples of a, but x will never be deleted (even if it is a multiple of a). In this operation, a must be greater than 1.  C a: it means that you know that x=a. This operation can be only performed once. Remember that in the operation of type B a>1 must hold.Write a program, that will find the value of x.InputThe first line contains one integer n (1\le n\le 10^5). The remaining parts of the input will be given throughout the interaction process.InteractionIn each round, your program needs to print a line containing one uppercase letter A, B or C and an integer a (1\le a\le n for operations A and C, 2\le a\le n for operation B). This line desribes operation you make.If your operation has type C your program should terminate immediately.Else your program should read one line containing a single integer, which is the answer to your operation.After outputting each line, don't forget to flush the output. To do it use:  fflush(stdout) in C/C++;  System.out.flush() in Java;  sys.stdout.flush() in Python;  flush(output) in Pascal;  See the documentation for other languages. It is guaranteed, that the number x is fixed and won't change during the interaction process.Hacks:To make a hack, use such input format:The only line should contain two integers n, x (1 \leq x \leq n \leq 10^5).ExampleInput
10

2

4

0Output

B 4

A 2

A 8

C 4
NoteNote that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.In the first test n=10 and x=4.Initially the set is: \{1,2,3,4,5,6,7,8,9,10\}.In the first operation, you ask how many numbers are multiples of 4 and delete them. The answer is 2 because there are two numbers divisible by 4: \{4,8\}. 8 will be deleted but 4 won't, because the number x will never be deleted. Now the set is \{1,2,3,4,5,6,7,9,10\}.In the second operation, you ask how many numbers are multiples of 2. The answer is 4 because there are four numbers divisible by 2: \{2,4,6,10\}.In the third operation, you ask how many numbers are multiples of 8. The answer is 0 because there isn't any number divisible by 8 in the current set.In the fourth operation, you know that x=4, which is the right answer.
10

2

4

0
 B 4  A 2  A 8  C 4 
['interactive', 'math', 'number theory', '*2600']