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>
#define DIM 200
using namespace std;

int v[DIM];
char sol[DIM];
int n,i;

int ask (int v[]){

    cout<<"? ";
    for (int i=1;i<=n;i++)
        cout<<v[i]<<" ";

    cout<<"\n";

    string ans;
    cin>>ans;
    if (ans == "Red")
        return 1;
    return 0;

}

int main (){

    cin>>n;

    for (i=1;i<=n;i++)
        v[i] = i;
    int val = ask (v);


    int st = 1, dr = n+1;
    while (st + 1 < dr){
        int mid = (st+dr)>>1;

        for (i=mid;i<=mid+n-1;i++)
            v[i-mid+1] = i;

        if (ask(v) == val)
            st = mid;
        else dr = mid;
    }

    if (val){
        sol[st] = 'R';
        sol[st+n] = 'B';
    } else {
        sol[st] = 'B';
        sol[st+n] = 'R';
    }

    /// st+1...st+n-1 nr de R e egal cu nr de B

    for (i=1;i<n;i++)
        v[i] = st+i;

    for (i=1;i<st;i++){

        v[n] = i;
        if (ask(v))
            sol[i] = 'R';
        else sol[i] = 'B';

    }

    for (i=st+n+1;i<=2*n;i++){
        v[n] = i;
        if (ask(v))
            sol[i] = 'R';
        else sol[i] = 'B';
    }

    /// mai trb sa determin partea aia in care R = B
    int k = 0;
    for (i=1;i<st;i++)
        v[++k] = i;
    for (i=st+n+1;i<=2*n;i++)
        v[++k] = i;


    for (i=st+1;i<st+n;i++){
        v[n] = i;
        if (ask(v))
            sol[i] = 'R';
        else sol[i] = 'B';
    }


    cout<<"! ";
    for (i=1;i<=2*n;i++)
        cout<<sol[i];

    cout<<"\n";

    return 0;
}