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;
using ll=long long;
#define fr(i,n) for(int i=0;i<(n);++i)
#define Fr(i,n) for(int i=1;i<=(n);++i)
#define ifr(i,n) for(int i=(n)-1;i>=0;--i)
#define iFr(i,n) for(int i=(n);i>0;--i)

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    istream& in(cin);
    ostream& out(cout);
    int n;
    string f,c;
    in>>n;
    cout<<"? ";
    Fr(i,n) cout<<i<<" ";
    cout<<endl;
    cin>>f;
    int l=0,r=n,m;
    while(r-l>1){
        m=(l+r)>>1;
        cout<<"? ";
        Fr(i,n) cout<<(i>m?i+n:i)<<" ";
        cout<<endl;
        cin>>c;
        if(c==f) r=m;
        else l=m;
    }
    vector<string> ans(2*n+1);
    ans[r]=f;
    ans[r+n]=(f=="Red"?"Blue":"Red");
    for(int i=r+1;i<r+n;++i){
        cout<<"? ";
        Fr(j,l) cout<<j<<" ";
        for(int j=r+n+1;j<=2*n;++j) cout<<j<<" ";
        cout<<i<<endl;
        cin>>ans[i];
    }
    Fr(j,l){
        cout<<"? ";
        for(int i=r+1;i<r+n;++i) cout<<i<<" ";
        cout<<j<<endl;
        cin>>ans[j];
    }
    for(int j=r+n+1;j<=2*n;++j){
        cout<<"? ";
        for(int i=r+1;i<r+n;++i) cout<<i<<" ";
        cout<<j<<endl;
        cin>>ans[j];
    }
    cout<<"! ";
    Fr(i,2*n) cout<<ans[i][0];
    cout<<endl;
}