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;

bool query(vector<int> vec){
    cout<<"? ";
    for (auto c:vec){
        cout<<c<<" ";
    }
    cout<<endl;
    string s;
    cin>>s;
    return (s[0]=='R');
}

int ans[207],n; //-1 blue 1 red

bool check(vector<int> tmp){
    cout<<"? ";
    for (auto c:tmp){
        cout<<c<<" ";
    }
    cout<<endl;
    string s;
    cin>>s;
    return (s=="Red");
}

int mid_search(int l,int r,int val){
    if (l>=r-1) {return r;}
    int md=(l+r)>>1;
    vector<int> tmp;
    tmp.clear();
    for (int i=1;i<=n;++i){
        tmp.push_back(i+n*(i<=md));
    }
    if (check(tmp)!=val) return mid_search(l,md,val);
    else return mid_search(md,r,val);
}

int main(){
    cin>>n;
    vector<int> tmp;
    tmp.clear();
    for (int i=1;i<=n;++i) tmp.push_back(i);
    int u=check(tmp);
    int k=mid_search(0,n,u);
    int ans[207];
    for (int i=1;i<=2*n;++i){
        if (i<k||i>=n+k){
            vector<int> tmp;
            tmp.clear();
            for (int i=1;i<=n;++i){
                if (i==k) continue;
                tmp.push_back(i+n*(i<=k));
            }
            tmp.push_back(i);
            ans[i]=query(tmp);
        }
        else{
            vector<int> tmp;
            tmp.clear();
            for (int i=1;i<=n;++i){
                if (i==k) continue;
                tmp.push_back(i+n*(i>k));
            }
            tmp.push_back(i);
            ans[i]=query(tmp);
        }
    }
    cout<<"! ";
    for (int i=1;i<=2*n;++i){
        if (ans[i]) cout<<"R";
        else cout<<"B";
    }
    return 0; 
}