CF1406E.Deleting Numbers

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 $a \gt 1$ must hold.

Write a program, that will find the value of $x$.

这是一个交互式问题。

存在一个未知整数 $x$（满足 $1\le x\le n$），你需要找出 $x$。

初始时，你拥有一个整数集合 $\{1, 2, \ldots, n\}$。你可以执行以下操作，至多 $10000$ 次：

• A a：查询当前集合中是 $a$ 的倍数的元素个数；
• B a：查询当前集合中是 $a$ 的倍数的元素个数，然后将这些倍数全部从集合中删除；但 $x$ 永远不会被删除（即使它是 $a$ 的倍数）。执行该操作时，要求 $a > 1$；
• C a：表示你已确定 $x = a$。该操作只能执行一次。

注意：在类型 B 的操作中，必须满足 $a > 1$。

请编写一个程序，找出 $x$ 的值。

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.

第一行包含一个整数 $n$（$1\le n\le 10^5$）。输入的其余部分将在交互过程中给出。

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.

注意：为了使样例更清晰，我们额外添加了空行。在交互过程中，你不应输出任何额外的空行。

在第一个测试中，$n=10$ 且 $x=4$。

初始集合为：${1,2,3,4,5,6,7,8,9,10}$。

在第一次操作中，你询问集合中有多少个数是 $4$ 的倍数，并将这些倍数删除。答案为 $2$，因为有两个数能被 $4$ 整除：${4,8}$。其中 $8$ 将被删除，但 $4$ 不会删除，因为数 $x$ 永远不会被删除。此时集合变为 ${1,2,3,4,5,6,7,9,10}$。

在第二次操作中，你询问集合中有多少个数是 $2$ 的倍数。答案为 $4$，因为有四个数能被 $2$ 整除：${2,4,6,10}$。

在第三次操作中，你询问集合中有多少个数是 $8$ 的倍数。答案为 $0$，因为当前集合中没有任何数能被 $8$ 整除。

在第四次操作中，你确定 $x=4$，即为正确答案。