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>
#define ll long long 
#define fi first
#define se second

using namespace std;

int n;
string t; 
char f; 

void flsh() {
    cout << endl;
}

int main() {
    cin >> n;
    cout << "?";
    for (int i = 1; i <= n; i++) 
        cout << ' ' << i;
    flsh();

    cin >> t;
    f = t[0];
    int st = 1, dr = n + 1, mid;
    while (st + 1 < dr) {
        mid = (st + dr) / 2;
        cout << "?";
        for (int i = mid; i < mid + n; i++) 
            cout << ' ' << i;
        flsh();

        cin >> t;
        if (t[0] == f) 
            st = mid;
        else dr = mid;
    }

    string ans = "";
    for (int i = 1; i <= 2 * n; i++) {
        cout << "? " << i;
        if (i >= dr + n - 1 || i < dr) {
            for (int j = dr; j < dr + n - 1; j++) 
                cout << ' ' << j;
        }
        else {
            for (int j = 1; j <= 2 * n; j++)
                if (j >= dr + n || j < dr - 1)
                    cout << ' ' << j;
        }
        flsh();
        
        cin >> t;
        ans += t[0];
    }

    cout << "! " +  ans;
    flsh();
    
    return 0;
}