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 ll long long

int main(){
    int N;
    cin >> N;
    
    cout << "?";
    for (int i = 1; i <= N; i++) cout << " " << i;
    cout << endl;
    string s;
    cin >> s;
    int l = 1;
    int r = N+1;
    while (r - l > 1) {
        int c = (l+r)/2;
        cout << "?";
        for (int i = c; i <= c+N-1; i++) cout << " " << i;
        cout << endl;
        string t;
        cin >> t;
        if (s == t) l = c;
        else r = c;
    }
    
    vector<char> ans(2*N+1);
    if (s == "Red") {
        ans[l] = 'R';
        ans[l+N] = 'B';
    }else {
        ans[l] = 'B';
        ans[l+N] = 'R';
    }
    
    for (int i = 1; i <= l-1; i++) {
        cout << "?";
        cout << " " << i;
        for (int j = l+1; j <= l+N-1; j++) cout << " " << j;
        cout << endl;
        string t;
        cin >> t;
        if (t == "Red") ans[i] = 'R';
        else ans[i] = 'B';
    }
    
    for (int i = l+N+1; i <= 2*N; i++) {
        cout << "?";
        cout << " " << i;
        for (int j = l+1; j <= l+N-1; j++) cout << " " << j;
        cout << endl;
        string t;
        cin >> t;
        if (t == "Red") ans[i] = 'R';
        else ans[i] = 'B';
    }
    
    for (int i = l+1; i <= l+N-1; i++) {
        cout << "?";
        cout << " " << i;
        for (int j = 1; j <= l-1; j++) cout << " " << j;
        for (int j = l+N+1; j <= 2*N; j++) cout << " " << j;
        cout << endl;
        string t;
        cin >> t;
        if (t == "Red") ans[i] = 'R';
        else ans[i] = 'B';
    }
    
    cout << "! ";
    for (int i = 1; i <= 2*N; i++) cout << ans[i];
    cout << endl;
    return 0;
}