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<cstdio>
#include<algorithm>
using namespace std;
int cnt=0,j,n,aut,i,seq[105],col[205],anm,pr,l,r,mid;
char s[10];
int ask()
{
	cnt++;
	int i;
	printf("?");
	for(i=1;i<=n;i++)printf(" %d",seq[i]);
	printf("\n");fflush(stdout);
	scanf("%s",s);
	if(s[0]=='R')return 0;
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;i++)seq[i]=i;
	aut=ask();
	l=1;r=n+1;
	while(l+1<r)
	{
		mid=(l+r)/2;
		for(i=1;i<=n;i++)seq[i]=mid+i-1;
		anm=ask();
		if(anm==aut)l=mid;
		else r=mid;
	}
	pr=r;
	for(j=0;j<n-1;j++)seq[j+1]=pr+j;
	for(i=1;i<pr;i++)
	{
		seq[n]=i;
		col[i]=ask();
	}
	for(i=pr+n-1;i<=2*n;i++)
	{
		seq[n]=i;
		col[i]=ask();
	}
	for(i=1;i<pr-1;i++)seq[i]=i;
	for(i=pr+n;i<=2*n;i++)seq[i-n-1]=i;
	for(i=pr;i<pr+n-1;i++)
	{
		seq[n]=i;
		col[i]=ask();
	}
	printf("! ");
	for(i=1;i<=2*n;i++)printf("%c",(col[i]==0)?'R':'B');
	printf("\n");
	fflush(stdout);
	return 0;
}