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 <iostream>
#include <string>
#include <vector>
using namespace std;

int main(){
	int n;
	cin >> n;
	
	string ret = " ";
	for(int i = 0 ; i < 2*n ; i ++){
		ret += " ";
	}
	cout << "?";
	for(int i = 1 ; i <= n ; i ++){
		cout << " " << i;
	}
	cout << endl;
	fflush(stdout);
	
	string in;
	cin >> in;
	string left = in;
	int l = 2, r = n+1;
	while(l<r){
		int m = (l+r)/2;
		cout << "?";
		for(int i = 1 ; i <= n ; i ++){
			cout << " " << m+i-1;
		}
		cout << endl;
		fflush(stdout);
		cin >> in;
		if(in == left)l = m+1;
		else r = m;
	}
	vector<int> A,B;
	A.push_back(l-1);
	B.push_back(l+n-1);
	ret[l-1] = 'A';
	ret[l+n-1] = 'B';
	for(int i = 1 ; i <= 2*n ; i ++){
		if(l-1 <= i && i <= l+n-1)continue;
		cout << "?";
		for(int j = 0 ; j <= n-2 ; j ++){
			cout << " " << l+j;
		}
		cout << " " << i;
		cout << endl;
		fflush(stdout);
		cin >> in;
		if(in == left){
			ret[i] = 'A';
			A.push_back(i);
		}
		else{
			ret[i] = 'B';
			B.push_back(i);
		}
	}
	for(int i = l ; i <= l+n-2 ; i ++){
		cout << "?";
		for(int j = 0 ; j < (n-1)/2 ; j ++){
			cout << " " << A[j];
		}
		for(int j = 0 ; j < (n-1)/2 ; j ++){
			cout << " " << B[j];
		}
		cout << " " << i;
		cout << endl;
		fflush(stdout);
		cin >> in;
		if(in == left){
			ret[i] = 'A';
			A.push_back(i);
		}
		else{
			ret[i] = 'B';
			B.push_back(i);
		}
	}
	for(int i = 1 ; i <= 2*n ; i ++){
		if(left[0] == 'R'){
			if(ret[i] == 'A')ret[i] = 'R';
			else ret[i] = 'B';
		}
		else {
			if(ret[i] == 'A')ret[i] = 'B';
			else ret[i] = 'R';
		}
	}
	cout << "!" << ret << endl;
	fflush(stdout);
}