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;
string tmp;
int n,flow,first,last,mid,pos,dfirst,dlast;
char f[1000001];
bool check(int x)
{
  cout<<'?'<<' '; 
  for (int i=x;i<=x+n-1;++i)
    cout<<i<<' ';
  cout<<endl;
  cin>>tmp;
  return ("Red"==tmp);
}
int main()
{
  cin>>n;
  first=1;
  last=n+1;
  dfirst=check(1);
  dlast=check(n+1);
  while (first+1<last)
    {
      mid=(first+last)/2;
      flow=check(mid);
      if (flow==dfirst)
	{
	  first=mid;
	  dfirst=flow;
	}
      else
	{
	  last=mid;
	  dlast=flow;
	}
    }
  pos=first;
  if (dfirst)
    {
      f[pos]='R';
      f[n+pos]='B';
    }
  else
    {
      f[pos]='B';
      f[n+pos]='R';
    }
  for (int i=pos+1;i<=n+pos-1;++i)
    {
      cout<<'?'<<' '<<i<<' ';
      for (int j=1;j<=pos-1;++j)
	cout<<j<<' ';
      for (int j=n+pos+1;j<=2*n;++j)
	cout<<j<<' ';
      cout<<endl;
      cin>>tmp;
      if (tmp=="Red")
	f[i]='R';
      else
	f[i]='B';
    }
  for (int i=1;i<=pos-1;++i)
    {
      cout<<'?'<<' '<<i<<' ';
      for (int j=pos+1;j<=n+pos-1;++j)
	cout<<j<<' ';
      cout<<endl;
      cin>>tmp;
      if (tmp=="Red")
	f[i]='R';
      else
	f[i]='B';
    }
  for (int i=n+pos+1;i<=2*n;++i)
    {
      cout<<'?'<<' '<<i<<' ';
      for (int j=pos+1;j<=n+pos-1;++j)
	cout<<j<<' ';
      cout<<endl;
      cin>>tmp;
      if (tmp=="Red")
	f[i]='R';
      else
	f[i]='B';
    }
  cout<<'!'<<' ';
  for (int i=1;i<=2*n;++i)
    cout<<f[i];
  cout<<endl;
  return 0;
}