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 rep(i,n) for(int i=0; i<(n); i++)
int n, ans[205], l, r, m;
bool lc, mc;
string s;
int main(){
	cin >> n; r = n;
	cout << '?';
	rep(i,n) cout << ' ' << i+1;
	cout << endl;
	cin >> s;
	lc = s == "Red";
	while(l+1 < r){
		m = (l+r) / 2;
		cout << '?';
		rep(i,n) cout << ' ' << i+m+1;
		cout << endl;
		cin >> s;
		mc = s == "Red";
		(lc == mc ? l : r) = m;
	}
	ans[l] = lc;
	ans[l+n] = !lc;
	rep(i,n*2){
		if(i == r-1 || i == r+n-1) continue;
		cout << '?';
		if(i < r || i >= r+n-1){
			rep(j,n-1) cout << ' ' << j+r+1;
			cout << ' ' << i+1 << endl;
		}else{
			rep(j,r-1) cout << ' ' << j+1;
			for(int j=r+n; j<n*2; j++) cout << ' ' << j+1;
			cout << ' ' << i+1 << endl;
		}
		cin >> s;
		ans[i] = s == "Red";
	}
	cout << "! ";
	rep(i,n*2) cout << (ans[i] ? "R" : "B");
	cout << endl;
}