Description:
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 $$$x$$$.
Input Format:
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.
Output Format:
None
Note:
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.