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:
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
typedef long long ll;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
using namespace std;
const ll MAX_N=99;
ll N,A[MAX_N],c[MAX_N*2];
ll ask(){
	cout<<"?";
	REP(i,N){
		cout<<' '<<A[i]+1;
	}
	cout<<endl;
	ll res;
	string s;
	cin>>s;
	if(s[0]=='R'){
		res=0;
	}else{
		res=1;
	}
	return res;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>N;
	REP(i,N*2)c[i]=-1;
	REP(i,N)A[i]=i;
	ll flg=ask();
	ll lb=0,ub=N;
	while(ub-lb>1){
		ll m=(lb+ub)>>1;
		REP(i,N)A[i]=i+m;
		ll f=ask();
		if(f==flg){
			lb=m;
		}else{
			ub=m;
		}
	}
	c[lb]=flg;
	c[lb+N]=1-flg;
	A[0]=lb;
	A[1]=lb+N;
	REP(i,N-1){
		ll n=2;
		REP(j,N-1){
			if(j!=i){
				A[n++]=lb+1+j;
			}
		}
		ll f=ask();
		c[lb+i+1]=1-f;
	}
	ll rn=1,bn=1,n=2;
	REP(i,N-1){
		if(c[lb+1+i]==0){
			if(rn<(N-1)/2){
				rn++;
				A[n++]=lb+1+i;
			}
		}else{
			if(bn<(N-1)/2){
				bn++;
				A[n++]=lb+1+i;
			}
		}
	}
	REP(i,N*2){
		if(i<lb||i>=lb+N+1){
			A[N-1]=i;
			c[i]=ask();
		}
	}
	cout<<"! ";
	REP(i,N*2){
		cout<<(c[i]==0?'R':'B');
	}
	cout<<endl;
}