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;
int dn[299];
int query(int x){
  cout<<"?";
  for(int i=1;i<=n;i++)cout<<" "<<i+x;
  cout<<endl;
  cout.flush();
  string s;
  cin>>s;
  if(s[0]=='R')return 0;
  else return 1;
}
int query(vector<int> a){
  cout<<"?";
  for(auto i:a)cout<<" "<<i+1;
  cout<<endl;
  cout.flush();
  string s;
  cin>>s;
  if(s[0]=='R')return 0;
  else return 1;
}
vector<int>a[3];
void solve(int x){
  a[2].clear();
  int y=1-x;
  a[2]=a[x];
  for(auto i:a[y]){
    a[2].push_back(i);
    dn[i]=query(a[2]);
    a[2].pop_back();
  }
}
int main(){
  cin>>n;
  int s=query(0);
  int l=1,r=n-1,mid,ans=0;
  while(l<=r){
    mid=(l+r)>>1;
    int t=query(mid);
    if(t==s)ans=mid,l=mid+1;
    else r=mid-1;
  }
//  cout<<ans<<endl;
  dn[ans]=s;dn[ans+n]=1^s;
  for(int i=ans+1;i<ans+n;i++)a[0].push_back(i);
  for(int i=ans+n+1;i<ans+n+n;i++)a[1].push_back(i%(2*n));
  for(int i=0;i<2;i++)solve(i);
  cout<<"! ";
  for(int i=0;i<2*n;i++)cout<<(dn[i]?'B':'R');
  cout<<endl;
  return 0;
}