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;

template<typename T>
void out(T x) { cout << x << endl; exit(0); }
#define watch(x) cout << (#x) << " is " << (x) << endl





using ll = long long;

const ll mod = 1e9+7;
const int maxn = 1e6 + 5;



int n;

map<string, int> MP;

int ask(vector<int> v) {
    assert((int)v.size() == n);
    cout<<"? ";
    for (int i: v) cout<<i+1<<" ";
    cout<<endl;
    string res;
    if (res == "-1") out("fk");
    cin>>res;
    return MP[res];
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);  cout.tie(0);
    MP["Red"] = 0;
    MP["Blue"] = 1;

    cin>>n;

    vector<int> v;
    for (int i=0; i<n; i++) {
	v.push_back(i);
    }

    int a0 = ask(v);
    int lo = 0;
    int hi = n;
    while (hi-lo>1) {
	int mid=(lo+hi)/2;
	vector<int> tmp;
	for (int i=0; i<n; i++) {
	    tmp.push_back(mid+i);
	}
	if (ask(tmp)==a0) {
	    lo = mid;
	} else {
	    hi = mid;
	}
    }


    vector<int> ans(2*n, -1);

    int i1 = lo;
    int i2 = i1+n;
    //watch(i1+1);
    
    
    ans[i1] = a0;
    ans[i2] = 1-a0;

    for (int i=0; i<2*n; i++) {
	if (ans[i] == -1) {
	    vector<int> v = {i};
	    if (i1<=i && i<=i2) {
		for (int j=0; j<i1; j++) {
		    v.push_back(j);
		}
		for (int j=i2+1; j<2*n; j++) {
		    v.push_back(j);
		}
	    } else {
		for (int j=i1+1; j<i2; j++) {
		    v.push_back(j);
		}
	    }
	    ans[i] = ask(v);
	}
    }


    cout<<"! ";
    for (int i: ans) {
	cout<<(i==0 ? "R" : "B");
    }
    cout<<endl;    
    return 0;
}