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 main() {
  int n;
  cin >> n;
  auto ask = [&](int l) {
	       cout << '?';
	       for (int i = 0; i < n; i++) {
		 cout << ' ' << l + i;
	       }
	       cout << endl;
	       string res;
	       cin >> res;
	       return res.front();
	     };
  char ml = ask(1);
  int l = 1, r = n + 1;
  vector<char> ans(2 * n + 1);
  while (r - l > 1) {
    int mid = l + (r - l) / 2;
    if (ask(mid) == ml) {
      l = mid;
    } else {
      r = mid;
    }
  }
  ans[l] = ml;
  ans[l + n] = ml == 'R' ? 'B' : 'R';
  vector<int> r_index, b_index;
  if (ml == 'B') {
    b_index.push_back(l);
    r_index.push_back(l + n);
  } else {
    b_index.push_back(l + n);
    r_index.push_back(l);
  }
  auto ask2 = [&](int pos) {
		cout << '?';
		for (int i = 1; i < n; i++) {
		  cout << ' ' << l + i;
		}
		cout << ' ' << pos << endl;
		string res;
		cin >> res;
		return res.front();
	      };
 
  for (int i = 1; i <= 2 * n; ++i) {
    if (i < l ||  i > l + n) {
      ans[i] = ask2(i);
      if (ans[i] == 'B') {
	b_index.push_back(i);
      } else {
	r_index.push_back(i);
      }
    }
  }
  auto ask3 = [&](int pos) {
		cout << '?';
		for (int i = 0; i < (n - 1) / 2; ++i) {
		  cout << ' ' << b_index[i];
		  cout << ' ' << r_index[i];
		}
		cout << ' ' << pos << endl;
	        string res;
		cin >> res;
		return res.front();
	      };
  for (int i = l + 1; i < l + n; ++i) {
    ans[i] = ask3(i);
  }
 
  cout << "! ";  
  for (int i = 1; i <= 2 * n; i++) {
    cout << ans[i];
  }
  cout << endl;
  return 0;
}