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;

const int maxn = 200;
string res[maxn];



string ask(vector<int>& vt) {
	cout << "? ";
	for(int i=0;i<vt.size();i++) cout << vt[i] + 1<<" ";
	
	cout << endl;
	fflush(stdout);
	string s;
	cin >> s;
	return s;
}

int main() {
	//freopen("inp.txt", "r", stdin);
//	ios::sync_with_stdio(false);
//	cin.tie(0);
	int n = 0;
	cin >> n;
	string last = " ";
		vector<int> vt;
	for(int i=0;i<n*2;i++) res[i] = "";
	
	
	
	for(int i=0;i<n;i++) vt.push_back(i);
	
	
	string f = ask(vt);
	int l = 0;
	int r = n;
	int pos = r;
	while (l <= r) {
		int g = (l + r) >> 1;
		vt.clear();
		for(int i=g; i < g + n; i++) vt.push_back(i);
		string t = ask(vt);
		if (t == f) {
			l = g + 1;
		} else {
			pos = g;
			r = g - 1;
		}
	}
	
	int cnt = n / 2;
	int cnt1 = n / 2;
	
	int ll = pos;
	int rr = pos + n - 2;
	for(int i=0; i < 2 * n ; i++) {
		if (i >= ll && i <= rr) {
			continue;
		} else {
			vt.clear();
			for(int j = ll; j<= rr;j++) vt.push_back(j);
			vt.push_back(i);
			res[i] = ask(vt);
		}
	}
	
	vt.clear();
	for(int i=0;i<2*n;i++) {
		if (res[i] != "") {
			if (res[i][0] == 'R') {
				if (cnt1 > 0) {
					vt.push_back(i);
					cnt1--;
				}
			} else {
				if (cnt > 0) {
					vt.push_back(i);
					cnt--;
				}
			}
		}
	}
	
	for(int i=ll;i<=rr;i++) {
		vector<int> vt1 = vt;
		vt1.push_back(i);
		res[i] = ask(vt1);
	}
	
	cout << "! ";
	for(int i=0;i<n*2;i++) {
		cout << res[i][0];
	}
	fflush(stdout);
	return 0;
}