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 <iostream>
#include <string>

using namespace std;

int n, N, i, j, p, u, k, m;
char t;
string s;

char culoare(int k) {
    cout << "?";
    for (i = k; i < k + n; ++i) {
        cout << ' ' << i;
    }
    cout << "\n";
    cin >> s;
    return s[0];
}

int main() {
    cin >> n;
    N = 2 * n;
    p = 1;
    u = n;
    t = culoare(1);
    while (p <= u) {
        m = (p + u) >> 1;
        if (culoare(m) == t) {
            k = m;
            p = m + 1;
        } else {
            u = m - 1;
        }
    }
    string v(N, '.');
    v[k - 1] = t;
    v[k + n - 1] = (t == 'R' ? 'B' : 'R');
    for (j = k + 1; j < k + n; ++j) {
        cout << "? " << j;
        for (i = 1; i < k; ++i) {
            cout << ' ' << i;
        }
        for (i = k + n + 1; i <= N; ++i) {
            cout << ' ' << i;
        }
        cout << "\n";
        cin >> s;
        v[j - 1] = s[0];
    }
    for (j = 1; j < k; ++j) {
        cout << "? " << j;
        for (i = k + 1; i < k + n; ++i) {
            cout << ' ' << i;
        }
        cout << "\n";
        cin >> s;
        v[j - 1] = s[0];
    }
    for (j = k + n + 1; j <= N; ++j) {
        cout << "? " << j;
        for (i = k + 1; i < k + n; ++i) {
            cout << ' ' << i;
        }
        cout << "\n";
        cin >> s;
        v[j - 1] = s[0];
    }
    cout << "! " << v << "\n";
    return 0;
}