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 <bits/stdc++.h>
using namespace std;
#define all(V) V.begin(),V.end()
#define ll long long
#define MOD 1000000007

string st[200];

int main() {
	int N;
	cin >> N;
	cout << '?' << " ";
	for (int i = 1;i <= N;i++) {
		cout << i << " ";
	}
	cout << endl;
	string S, T;
	cin >> T;

	int same = N, oppo = 0, mid;
	while (same - oppo != 1) {
		mid = (same + oppo) / 2;

		cout << '?' << " ";
		for (int i = 1;i <= mid;i++) {
			cout << i << " ";
		}
		for (int i = N + mid + 1;i <= 2 * N;i++) {
			cout << i << " ";
		}
		cout << endl;

		cin >> S;
		if (S == T) {
			same = mid;
		}
		else {
			oppo = mid;
		}
	}
	

	for (int i = 1;i <= 2 * N;i++) {
		if (i <= oppo || i >= oppo + N + 2) {
			cout << '?' << " ";
			for (int j = oppo + 2;j <= oppo + N;j++) {
				cout << j << " ";
			}
			cout << i << endl;
		}
		else {
			cout << '?' << " ";
			for (int j = 1;j <= oppo;j++) {
				cout << j << " ";
			}
			for (int j = oppo + N + 2;j <= 2 * N;j++) {
				cout << j << " ";
			}
			cout << i << endl;
		}
		cin >> st[i];
	}

	cout << "! ";
	for (int i = 1;i <= 2 * N;i++) {
		cout << st[i][0];
	}
	cout << endl;
}