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;

int n;

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

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  int lo = 1, hi = n, k;
  char t = ask(1);
  while (lo <= hi) {
    int mid = (lo + hi) / 2;
    if (ask(mid) == t) {
      k = mid;
      lo = mid + 1;
    } else {
      hi = mid - 1;
    }
  }
  string ans(2 * n, '$');
  ans[k - 1] = t;
  ans[k + n - 1] = (t == 'R' ? 'B' : 'R');
  for (int j = k + 1; j < k + n; j++) {
    cout << "? " << j;
    for (int i = 1; i < k; i++) {
      cout << ' ' << i;
    }
    for (int i = k + n + 1; i <= 2 * n; i++) {
      cout << ' ' << i;
    }
    cout << endl;
    string s;
    cin >> s;
    ans[j - 1] = s[0];
  }
  for (int j = 1; j < k; j++) {
    cout << "? " << j;
    for (int i = k + 1; i < k + n; i++) {
      cout << ' ' << i;
    }
    cout << endl;
    string s;
    cin >> s;
    ans[j - 1] = s[0];
  }
  for (int j = k + n + 1; j <= 2 * n; j++) {
    cout << "? " << j;
    for (int i = k + 1; i < k + n; i++) {
      cout << ' ' << i;
    }
    cout << endl;
    string s;
    cin >> s;
    ans[j - 1] = s[0];
  }
  cout << "! " << ans << endl;
  return 0;
}