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;

const int N = 105;

int n, cnt = 0, red[2 * N];
string s;
vector<int> ve;

int ask() {
    cout << "? ";
    for (int &v : ve) {
        cout << v << " ";
    }
    cout << endl;
    cin >> s;
    return s == "Red";
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    for (int i = 1; i <= n; i++) {
        ve.push_back(i);
    }
    int beg = ask();
    int le = 1, ri = n;
    while (le <= ri) {
        int mi = (le + ri) / 2;
        ve.clear();
        for (int i = 1; i <= n; i++) {
            ve.push_back(mi + i);
        }
        if (ask() != beg) {
            ri = mi - 1;
        } else {
            le = mi + 1;
        }
    }
    ve.clear();
    red[le] = beg; red[le + n] = 1 - beg;
    for (int i = 1; i < n; i++) {
        ve.push_back(le + i);
    }
    for (int i = 1; i <= 2 * n; i++) {
        if (i < le || i > le + n) {
            ve.push_back(i);
            red[i] = ask();
            ve.pop_back();
        }
    }
    ve.clear();
    for (int i = 1; i <= 2 * n; i++) {
        if (i < le || i > le + n) {
            ve.push_back(i);
        }
    }
    for (int i = le + 1; i <= le + n - 1; i++) {
        ve.push_back(i);
        red[i] = ask();
        ve.pop_back();
    }
    cout << "! ";
    for (int i = 1; i <= 2 * n; i++) {
        cout << (red[i] ? 'R' : 'B');
    }
    cout << endl;
    return 0;
}