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:
/*********************
*  Author: xuziyuan  * 
*********************/

#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
#define LL long long
#define pii pair <int,int>
#define fi first
#define se second
#define pb push_back
#define mpr make_pair

using namespace std;

const LL MOD=1e9+7;

int n,lb,ub,mid;
string s,ans="",lst,fis;
vector <int> r,b;

bool check()
{
	cout.flush();
	cout<<"? ";
	for(int i=mid;i<=mid+n-1;i++) cout<<i<<' ';
	cout<<endl;
	cin>>s;
	if(s=="-1") exit(0);
	return s!=fis;
}

int main()
{
	cin>>n;
	cout.flush();
	cout<<"? ";
	repn(i,n) cout<<i<<' ';
	cout<<endl;
	cin>>s;
	fis=s;
	rep(i,n*2) ans.pb('a');
	lb=1;
	ub=n+1;
	while(lb<ub)
	{
		mid=(lb+ub)/2;
		if(check()) ub=mid;
		else lb=mid+1;
	}
	ub=lb+n-2;
	repn(i,n*2)
	{
		if(lb<=i&&i<=ub) continue;
		cout.flush();
		cout<<"? ";
		cout<<i<<' ';
		for(int j=lb;j<=ub;j++) cout<<j<<' ';
		cout<<endl;
		cin>>s;
		if(s=="-1") return 0;
		if(s[0]=='R') ans[i-1]='R';
		else ans[i-1]='B';
	}
	repn(i,n*2)
	{
		if(ans[i-1]=='R'&&r.size()<n/2) r.pb(i);
		if(ans[i-1]=='B'&&b.size()<n/2) b.pb(i);
	}
	//cout<<r.size()<<' '<<b.size()<<endl;
	for(int i=lb;i<=ub;i++)
	{
		cout.flush();
		cout<<"? ";
		cout<<i<<' ';
		rep(j,r.size()) cout<<r[j]<<' ';
		rep(j,b.size()) cout<<b[j]<<' ';
		cout<<endl;
		cin>>s;
		if(s=="-1") return 0;
		if(s[0]=='R') ans[i-1]='R';
		else ans[i-1]='B';
	}
	cout<<"! "<<ans<<endl;
	return 0;
}