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 <cstdlib>
#include <vector>
#define llint long long

using namespace std;

llint n;
string s, res;
bool ans[205];

int main(void)
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	cin >> n;
	
	cout << "? ";
	for(int i = 1; i <= n; i++) cout << i << " ";
	cout << endl;
	cin >> s;
	
	llint ub = n+1, lb = 1, mid;
	while(ub-lb > 1){
		mid = (ub+lb)/2;
		cout << "? ";
		for(int j = 0; j < n; j++) cout << mid+j << " ";
		cout << endl;
		cin >> res;
		if(s == res) lb = mid;
		else ub = mid;
	}
	
	int pos = ub;
	ans[pos-1] = true;
	ans[pos-1+n] = false;
	
	for(int i = 1; i <= 2*n; i++){
		if(i < pos-1 || i > pos-1+n){
			cout << "? ";
			for(int j = pos; j <= pos-2+n; j++) cout << j << " ";
			cout << i << endl;
		}
		else{
			cout << "? ";
			for(int j = 1; j < pos-1; j++) cout << j << " ";
			for(int j = pos+n; j <= 2*n; j++) cout << j << " ";
			cout << i << endl;
		}
		cin >> res;
		ans[i] = (s == res);
	}
	
	cout << "! ";
	for(int i = 1; i <= 2*n; i++){
		if(ans[i]) cout << s[0];
		else{
			if(s[0] == 'R') cout << "B";
			else cout << "R";
		}
	}
	cout << endl;
	
	return 0;
}