Problem: This is an interactive task.

We have 2N balls arranged in a row, numbered 1, 2, 3, ..., 2N from left to right, where N is an odd number. Among them, there are N red balls and N blue balls.

While blindfolded, you are challenged to guess the color of every ball correctly, by asking at most 210 questions of the following form:

* You choose any N of the 2N balls and ask whether there are more red balls than blue balls or not among those N balls.



Now, let us begin.

Constraints

* 1 \leq N \leq 99
* N is an odd number.



* * *



Example

Input




Output

Solution (in CPP):

Solution:
#include<iostream>
using namespace std;
int N;
bool ask(int id)
{
	cout<<"?";
	for(int i=0;i<N;i++)cout<<" "<<id+i;
	cout<<endl;
	string s;cin>>s;
	return s=="Red";
}
int main()
{
	cin>>N;
	int L=1,R=N+1;
	bool l=ask(1);
	while(R-L>1)
	{
		int M=(L+R)/2;
		bool f=ask(M);
		if(l==f)L=M;
		else R=M;
	}
	string ans(2*N,' ');
	ans[L-1]=l?'R':'B';
	ans[L+N-1]=l?'B':'R';
	for(int i=1;i<=2*N;i++)
	{
		if(i==L||i==L+N)continue;
		if(L<i&&i<L+N)
		{
			cout<<"? "<<i;
			for(int j=1;j<L;j++)cout<<" "<<j;
			for(int j=L+N+1;j<=2*N;j++)cout<<" "<<j;
			cout<<endl;
		}
		else
		{
			cout<<"? "<<i;
			for(int j=L+1;j<L+N;j++)cout<<" "<<j;
			cout<<endl;
		}
		string s;cin>>s;
		ans[i-1]=s=="Red"?'R':'B';
	}
	cout<<"! "<<ans<<endl;
}