# Deleting Numbers

## 题目描述

This 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 $x$ .

## 输入输出格式

### 输入格式

The 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.

### 输出格式

In 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 $n$ , $x$ ( $1 \leq x \leq n \leq 10^5$ ).

## 输入输出样例

### 输入样例 #1

10

2

4

0

### 输出样例 #1

B 4

A 2

A 8

C 4

## 说明

Note 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.