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 <cstdio>
#include <vector>

using namespace std;

int n;
char ch[10];

vector <int> v;

void ask(int st) {
	printf("? ");
	for (int i=st ; i<st+n ; i++) {
		printf("%d ", i);
	}
	printf("\n");
	fflush(stdout);
}

void ask2(int l, int r, int x) {
	printf("? %d ", x);
	for (int i=l ; i<=r ; i++) {
		printf("%d ", i);
	}
	printf("\n");
	fflush(stdout);
}

void ask3(int x) {
	printf("? %d ", x);
	for (int i=0 ; i<v.size() ; i++) {
		printf("%d ", v[i]);
	}
	printf("\n");
	fflush(stdout);
}

int main() {
	scanf("%d", &n);
	string sol = "";
	for (int i=0 ; i<=n*2 ; i++) {
		sol += "-";
	}
	string s;
	ask(1);
	scanf("%s", ch);
	s = ch;
	int l = 2;
	int r = n+1;
	string ans;
	int mid;
	while (l <= r) {
		mid = (l+r)/2;
		ask(mid);
		scanf("%s", ch);
		ans = ch;
		if (ans == s) {
			l = mid+1;
		} else {
			r = mid-1;
		}
	}
	if (ans != s) {
		mid--;
	}
	l = mid+1;
	r = mid+n-1;
	for (int i=1 ; i<=2*n ; i++) {
		if (i>=l and i<=r) continue;
		ask2(l, r, i);
		scanf("%s", ch);
		sol[i] = ch[0];
	}
	int red = (n-1) / 2;
	int blue = (n-1) / 2;
	for (int i=1 ; i<=n*2 ; i++) {
		if (sol[i] == 'R' and red) {
			red--;
			v.push_back(i);
		}
		if (sol[i] == 'B' and blue) {
			blue--;
			v.push_back(i);
		}
	}
	for (int i=1 ; i<=2*n ; i++) {
		if (sol[i] == '-') {
			ask3(i);
			scanf("%s", ch);
			sol[i] = ch[0];
		}
	}
	printf("! ");
	for (int i=1 ; i<=2*n ; i++) {
		printf("%c", sol[i]);
	}
	printf("\n");
	fflush(stdout);
	return 0;
}