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 maxn 110
#define LL long long
#define pb push_back
#define mp make_pair
#define fi first
#define se second
typedef pair<int,LL> pii;
const int inf=0x3f3f3f3f;
const int mod=1e9+7;
const int tot=1<<15;

int n;
int t[maxn],x[maxn],y[maxn],s[maxn];
int qry(int p){
	printf("? ");
	if(p==0){
		for(int i=1;i<n;i++) printf("%d ",t[i]);
		printf("%d\n",t[n]);
	}else if(p==1){
		for(int i=1;i<n;i++) printf("%d ",x[i]);
		printf("%d\n",x[n]);
	}else{
		for(int i=1;i<n;i++) printf("%d ",y[i]);
		printf("%d\n",y[n]);
	}
	fflush(stdout);
	string s;
	cin>>s;
	if(s=="Red") return 1;
	else return -1;
} 

int a,b,beg,en;

int main(){
	//freopen("test.txt","r",stdin);
	
	cin>>n;

	
	int l=1,r=n+1,mid;
	for(int i=1;i<=n;i++) t[i]=i;
	a=qry(0);b=-1*a;
	while(l<r-1){
		mid=(l+r)>>1;
		for(int i=1;i<=n;i++) t[i]=mid+i-1;
		int tt=qry(0);
		if(tt!=a){
			r=mid;
		}else{
			l=mid;
		}
	}
	s[l]=a;s[l+n]=b;
	beg=l;en=l+n;
	int cnt=0;
	
	for(int i=1;i<n;i++) x[i]=i+beg;
//	cerr<<"beg=="<<beg<<" "<<en<<endl;
	
	for(int i=1;i<=2*n;i++)if(i<beg||i>en){
		x[n]=i;
		s[i]=qry(1);
		t[++cnt]=i;
	}
	
	for(int i=1;i<=2*n;i++)if(i>beg&&i<en){
		t[n]=i;
		s[i]=qry(0);
	}
	
	printf("! ");
	for(int i=1;i<2*n;i++) printf("%c",(s[i]==1)?'R':'B');
	printf("%c\n",(s[2*n]==1)?'R':'B');

	
	return 0;
}