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,RB='R'+'B';

string reply;
char getreply(){
	cin >> reply;
	return reply[0];
}

void sendquestion(int s){
	int i;
	cout << "?";
	for(i=0; i<N; ++i){
		cout << " " << s+i;
	}
	cout << endl; cout.flush();
}

char c,ans[225];

int main(void){
	int i,j,p,l,r,m;
	cin >> N;
	l = 1; r = N+1;
	sendquestion(1); c = getreply();
	while(r-l>1){
		m = (l+r)/2;
		sendquestion(m);
		if(c == getreply()){
			l = m;
		}else{
			r = m;
		}
	}
	p = l;
	for(i=p; i<=p+N; ++i){
		cout << "?";
		for(j=p; j<=p+N; ++j){
			if(i==j){
				continue;
			}
			cout << " " << j;
		}
		cout << endl; cout.flush();
		ans[i-1] = RB-getreply();
	}
	for(i=1; i<=N*2; ++i){
		if(p<=i && i<=p+N){
			continue;
		}
		cout << "?";
		for(j=1; j<=p; ++j){
			if(i==j){
				continue;
			}
			cout << " " << j;
		}
		for(j=p+N; j<=N*2; ++j){
			if(i==j){
				continue;
			}
			cout << " " << j;
		}
		cout << endl; cout.flush();
		ans[i-1] = RB-getreply();
	}
	cout << "! ";
	for(i=0; i<N*2; ++i){
		cout << ans[i];
	}
	cout << endl; cout.flush();
	return 0;
}