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;
vector<string> ans(200);
vector<int> Q(100);
string rea;
void f(){
  cout<<"?";
  for(int i=0;i<n;i++){
    if(Q[i]>2*n)Q[i]-=2*n;
    cout<<" "<<Q[i];
  }
  cout<<endl;
  cin>>rea;
  if(rea=="-1")exit(0);
}

string g(string s){
  return s.substr(0,1);
}
string h(string s){
  string t=g(s);
  if(t=="R")return "B";
  return "R";
}

signed main(){
  cin>>n;
  for(int i=0;i<n;i++)Q[i]=i+1;
  f();
  string ho=rea;
  int l=1,r=n+1;
  while(r-l>1){
    int m=(r+l)>>1;
    for(int i=0;i<n;i++)Q[i]=m+i;
    f();
    if(rea==ho)l=m;
    else r=m;
  }
  ans[l]=g(ho);
  ans[l+n]=h(ho);
  for(int i=l+1;i<l+n;i++){
    for(int j=0;j<n-1;j++){
      Q[j]=l+n+j+1;
    }
    Q[n-1]=i;
    f();
    ans[i]=g(rea);
  }
  for(int i=l+n+1;i<l+2*n;i++){
    for(int j=0;j<n-1;j++){
      Q[j]=l+1+j;
    }
    Q[n-1]=i;
    f();
    int t=i;
    if(t>2*n)t-=2*n;
    ans[t]=g(rea);
  }
  cout<<"! ";
  for(int i=1;i<=2*n;i++)cout<<ans[i];cout<<endl;
}