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,i,j,b[205]={0},han[205]={0},pb;
char ou[10];

int que_a(int x){
    cout << "?";
        for(j=x;j<x+n;j++) cout << " " << j+1;
        cout << endl;
        cin >> ou;
        if(ou[0]=='-') return 0;
        if(ou[0]=='R') return 1;
        else return -1;
}

int que_b(int x){
    cout << "?";
        for(j=pb;j<=pb+n;j++) if(j!=x) cout << " " << j+1;
        cout << endl;
        cin >> ou;
        if(ou[0]=='-') return 0;
        if(ou[0]=='R') return -1;
        else return 1;
}

int que_c(int x){
    cout << "?";
        for(j=pb+n;j<2*n;j++) if(j!=x) cout << " " << j+1;
        for(j=0;j<=pb;j++) if(j!=x) cout << " " << j+1;
        cout << endl;
        cin >> ou;
        if(ou[0]=='-') return 0;
        if(ou[0]=='R') return -1;
        else return 1;
}

int main() {
	// your code goes here
    cin >> n;
    int l,r,mid;
    l=0; r=n;
    han[0]=que_a(0);
    han[n]=-han[0];
    while(r-l>1){
        mid=(l+r)/2;
        han[mid]=que_a(mid);
        if(han[l]==han[mid]) l=mid;
        else r=mid;
    }
    pb=l;
    b[pb]=han[pb];
    b[pb+n]=-han[pb];
    for(i=pb+1;i<pb+n;i++) b[i]=que_b(i);
    for(i=pb+n+1;i<2*n;i++) b[i]=que_c(i);
    for(i=0;i<pb;i++) b[i]=que_c(i);
    cout << "! ";
    for(i=0;i<2*n;i++){
        if(b[i]==1) cout << "R";
        else if(b[i]==-1) cout << "B";
        else cout << "0";
    }
    cout << endl;
	return 0;
}