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 <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
#include <sstream>

#include <memory>
#include <string>
#include <vector>
#include <queue>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <deque>
#include <algorithm>
#include <random>
#include <iomanip>
using namespace std;
// RRBBRB
// rrrbbb
int f(vector<int> q) {
	cout << "?";
	for (auto qq : q)
		cout << " " << qq + 1;
	cout << endl << flush;
	string s;
	cin >> s;
	if (s == "Red")
		return 1;
	else if (s == "Blue")
		return -1;
	else
		return 0;
}

int main(int argc, char *argv[]) {
	int n;
	cin >> n;
	int b = 0, e = n;
	vector<int> q;
	for (int i = 0; i < n; i++)
		q.push_back(i);
	int c0 = f(q);
	while (b < e) {
		int m = (b + e) / 2 + 1;
		q.clear();
		for (int i = m; i < n + m; i++)
			q.push_back(i);
		int cm = f(q);
		if (cm == c0) {
			b = m;
		}
		else {
			e = m - 1;
		}
	}
	vector<int> res(2 * n, 0);
	res[b] = c0;
	res[b + n] = -c0;
	q.clear();
	for (int i = b + 1; i < b + n; i++) 
		q.push_back(i);
	for (int i = 0; i < 2 * n; i++) {
		if (res[i] == 0 && (i < b || i > b + n)) {
			q.push_back(i);
			res[i] = f(q);
			q.pop_back();
		}	
	}
	for (int i = b + 1; i < b + n; i++) {
		q.clear();
		for (int j = b; j <= b + n; j++) {
			if (i == j) continue;
			q.push_back(j);
		}
		res[i] = -f(q);
	}
	cout << "! ";
	for (int i = 0; i < 2 * n; i++) {
		if (res[i] == 1)
			cout << "R";
		else
			cout << "B";
	}
	cout << endl << flush;

}