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 <algorithm>
#include <vector>
#include <queue>
#include <string>

using ll = long long;

using namespace std;

int main() {
    int n;
    cin >> n;
    string t;
    cout << "?";
    for (int i=1; i<=n; i++) cout << ' ' << i;
    cout << endl;
    cin >> t;
    char f = t[0];
    int l = 1, r = n+1, m;
    while (r - l > 1) {
        m = (l + r) / 2;
        cout << "?";
        for (int i=m; i<m+n; i++) cout << ' ' << i;
        cout << endl;
        cin >> t;
        if (t[0] == f) l = m;
        else r = m;
    }
    string ans = "";
    for (int i=1; i<=2*n; i++) {
        cout << "? " << i;
        if (i < r || i >= r+n-1)
            for (int j=r; j<r+n-1; j++) cout << ' ' << j;
        else  {
            for (int j=1; j<=2*n; j++)
                if (j < r-1 || j >= r+n)
                    cout << ' ' << j;
        }
        cout << endl;
        cin >> t;
        ans += t[0];
    }
    cout << "! " +  ans << endl;
    return 0;
}