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 <bits/stdc++.h>
using namespace std;
int n,sol[205],st,dr,r,x,y;
int ask1(int pos)
{
	cout<<"?"<<" ";
	for(int i=pos;i<=pos+n-1;i++)
		cout<<i<<" ";
	cout<<endl;
	string ans;
	cin>>ans;
	if(ans=="Red")
		return 0;
	else
		return 1;
}
void ask2(int pos,int start)
{
	cout<<"?"<<" ";
	cout<<pos<<" ";
	for(int i=start;i<=start+n-2;i++)
	{
		if(i>2*n)
			cout<<i-2*n<<" ";
		else
			cout<<i<<" ";
	}
	cout<<endl;
	string ans;
	cin>>ans;
	if(ans=="Red")
		sol[pos]=0;
	else
		sol[pos]=1;
}
int main()
{
	cin>>n;
	if(n<=50)
	{
		for(int i=1;i<=n;i++)
		{
			x=ask1(i);
			y=ask1(i+1);
			if(x+y==1)
			{
				st=i+1;
				dr=i+n-1;
				//sol[i]=x;
				//sol[i+n]=y;
				break;
			}
		}
	}
	else
	{
		st=2;
		dr=n+1;
		x=ask1(1);
		while(st!=dr)
		{
			int mid=(st+dr)/2;
			y=ask1(mid);
			if(x!=y)
				dr=mid;
			else
				st=mid+1;
		}
		dr=st+n-2;
		//sol[st-1]=x;
		//sol[dr+1]=y;
	}
	//cout<<st<<" "<<dr<<"\n";
	//return 0;
	for(int i=1;i<=2*n;i++)
	{
		if(st<=i && i<=dr)
				ask2(i,dr+2);
		else
			ask2(i,st);
	}
	cout<<"!"<<" ";
	for(int i=1;i<=2*n;i++)
	{
		if(sol[i])
			cout<<"B";
		else
			cout<<"R";
	}
	cout<<endl;
	return 0;
}