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 <algorithm>
#include <cassert>
#include <iostream>
#include <string>
#include <vector>
using namespace std;

int N;

bool query(vector<bool> which) {
    cout << '?';

    for (int i = 1; i <= 2 * N; i++)
        if (which[i])
            cout << ' ' << i;

    cout << endl;
    string T;
    cin >> T;
    return T[0] == 'R';
}

int main() {
    ios::sync_with_stdio(false);

    cin >> N;
    vector<bool> which(2 * N + 1, false);

    for (int i = 1; i <= N; i++)
        which[i] = true;

    bool initial = query(which);
    int low = 2, high = N + 1;

    while (low < high) {
        int mid = (low + high) / 2;

        which.assign(2 * N + 1, false);

        for (int i = mid; i < mid + N; i++)
            which[i] = true;

        bool result = query(which);

        if (result == initial)
            low = mid + 1;
        else
            high = mid;
    }

    int start = low, end = low + N - 1;
    which.assign(2 * N + 1, false);

    for (int i = start; i < end; i++)
        which[i] = true;

    vector<bool> answer(2 * N + 1, false);

    for (int i = 1; i <= 2 * N; i++)
        if (start <= i && i < end) {
            which[i] = false;
            which[start - 1] = which[end] = true;
            answer[i] = !query(which);
            which[start - 1] = which[end] = false;
            which[i] = true;
        } else {
            which[i] = true;
            answer[i] = query(which);
            which[i] = false;
        }

    cout << "! ";

    for (int i = 1; i <= 2 * N; i++)
        cout << (answer[i] ? 'R' : 'B');

    cout << endl;
}