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 main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N; cin >> N;
    vector<char> ans(2*N+1);
    cout << '?';
    for (int i=1;i<=N;++i) cout << ' ' << i;
    cout << endl;
    string left,S; cin >> left;
    int lb=1,ub=N+1;
    while(ub-lb>1){
        int mid=(ub+lb)>>1;
        cout << '?';
        for (int i=0;i<N;++i) cout << ' ' << mid+i;
        cout << endl; cin >> S;
        (S==left?lb:ub)=mid;
    }
    ans[lb]=left[0],ans[lb+N]=(left[0]=='R'?'B':'R');
    vector<int> half,rest;
    for (int i=1;i<N;++i) half.emplace_back(lb+i);
    for (int i=1;i<lb;++i){
        cout << "? " << i;
        for (int i=0;i<N-1;++i) cout << ' ' << half[i];
        cout << endl; cin >> S;
        ans[i]=S[0]; rest.emplace_back(i);
    }
    for (int i=lb+N+1;i<=2*N;++i){
        cout << "? " << i;
        for (int i=0;i<N-1;++i) cout << ' ' << half[i];
        cout << endl; cin >> S;
        ans[i]=S[0]; rest.emplace_back(i);
    }
    for (int i=ub;i<lb+N;++i){
        cout << "? " << i;
        for (int i=0;i<N-1;++i) cout << ' ' << rest[i];
        cout << endl; cin >> S;
        ans[i]=S[0];
    }
    cout << "! ";
    for (int i=1;i<=2*N;++i) cout << ans[i];
    cout << endl;
}