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 rep(i,l,r) for (int i=l,i##end=r;i<=i##end;++i)
#define per(i,r,l) for (int i=r,i##end=l;i>=i##end;--i)
#define ll long long
using namespace std;
int a[1003];
bool Q(int l1,int r1,int l2,int r2,int x){
    cout<<"? ";
    rep(i,l1,r1) cout<<i<<" ";
    if (l2) rep(i,l2,r2) cout<<i<<" ";
    if (x) cout<<x<<" "; cout<<endl;
    string s; cin>>s;
    cout.flush();
    return s[0]=='R';
}
int main(){
    int n,t=sqrt(n); cin>>n;
    int x=Q(1,n,0,0,0),l=2,r=n+1;
    while (l<=r){
        int m=l+r>>1;
        if (Q(m,m+n-1,0,0,0)==x) l=m+1;
        else r=m-1;
    }
    rep(i,1,2*n)
        if (i<l||i>=l+n-1) a[i]=Q(l,l+n-2,i,i,0);
        else a[i]=Q(1,l-2,l+n,2*n,i);
    cout<<"! ";
    rep(i,1,2*n) cout<<(a[i]?'R':'B');
    return 0;
}