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>
#define mp make_pair
#define pb push_back
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define debug(x) cerr << #x << " " << x << '\n'
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pli = pair<ll,int>;
const int INF = 0x3f3f3f3f, N = 105;
const ll LINF = 1e18 + 5;
int col[N], n;
string t;
bool check(int x)
{
	cout << '?';
	for(int i=x;i<=x+n-1;i++)
		cout << ' ' << i;
	cout << '\n';
	fflush(stdout);
	cin >> t;
	return (t=="Red");
}
void solve(int l,int r,vector<int> s)
{
	for(int i=l;i<=r;i++)
	{
		cout << '?';
		cout << ' ' << i;
		for(int j : s) cout << ' ' << j;
		cout << '\n';
		fflush(stdout);
		cin >> t;
		col[i] = (t=="Red");
	}
}
int main()
{
 	cin >> n;
 	int l = 1, r = n + 1, p = -1;
 	bool lcol = check(l), pcol = 0;
 	while(l<=r)
 	{
 		int mid = (l+r) >> 1;
 		bool midcol = check(mid);
 		if(midcol==lcol) l = mid + 1, p = mid, pcol = lcol;
 		else r = mid - 1;
 	}
 	vector <int> s1, s2;
 	for(int i=p+1;i<=p+n-1;i++) s1.pb(i);
 	for(int i=1;i<=p-1;i++) s2.pb(i);
 	for(int i=p+n+1;i<=2*n;i++) s2.pb(i);
 	if(pcol) col[p] = 1, col[p+n] = 0;
 	else col[p] = 0, col[p+n] = 1;
 	solve(p+1,p+n-1,s2);
 	solve(1,p-1,s1);
 	solve(p+n+1,2*n,s1);
 	cout << "! ";
 	for(int i=1;i<=2*n;i++)
 	{
		if(col[i]) cout << 'R';
		else cout << 'B';
 	}
 	cout << '\n';
 	fflush(stdout);
	return 0;
}