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<algorithm>
#include<vector>
using namespace std;
int n, U[210], chk[210];
char res[210];

int Query(vector<int> &A) {
	sort(A.begin(), A.end());
	printf("? ");
	for (auto &t : A)printf("%d ", t);
	puts("");
	fflush(stdout);
	char p[10];
	scanf("%s", p);
	if (p[0] == 'R')return 1;
	return 2;
}
int Query2(int a) {
	vector<int>T;
	for (int i = a; i < a + n; i++)T.push_back(i);
	return Query(T);
}
int main() {
	int i, j;
	scanf("%d", &n);
	U[1] = Query2(1);
	U[n + 1] = 3 - U[1];
	int b = 1, e = n + 1;
	while (b+1 < e) {
		int m = (b + e) >> 1;
		U[m] = Query2(m);
		if (U[b] == U[m])b = m;
		else e = m;
	}
	for (i = b + 1; i < b + n; i++)chk[i] = 1;
	for (i = 1; i <= n+n; i++)if (i<b || i>b + n)chk[i] = 2;
	for (i = 1; i <= n+n; i++) {
		int ck = 0;
		if (b <= i && i <= b + n) ck = 2;
		else ck = 1;
		vector<int>T;
		for (j = 1; j <= n+n; j++)if (chk[j] == ck)T.push_back(j);
		T.push_back(i);
		if (Query(T) == 1)res[i] = 'R';
		else res[i] = 'B';
	}
	printf("! %s\n", res + 1);
	fflush(stdout);
}