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 <algorithm>
#include <iostream>
#include <string>
#include <random>
#include <cassert>
#include <cstring>
#include <chrono>

using namespace std;

typedef long long ll;

int n;

string Ask(const vector<int> a) {
  string s = "?";
  for (int x : a) {
    s += " " + to_string(x);
  }
  cout << s << endl;
  cout.flush();
  string result;
  cin >> result;
  return result;
}

string GetColor(int p) {
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    a[i] = p + i + 1;
  }
  return Ask(a);
}

string Other(string color) {
  if (color == "Red") return "Blue";
  return "Red";
}

string AskColor(int left, int what, int to) {
  vector<int> a;
  for (int i = 0; i < n; ++i) {
    if (left + i == what) continue;
    a.push_back(left + i + 1);
  }
  a.push_back(to + 1);
  return Ask(a);
}

int main()
{
  cin >> n;

  string leftColor = GetColor(0);

  int l = 0; int r = n;
  while (r - l > 1) {
    int m = (l + r) / 2;
    string curColor = GetColor(m);
    if (curColor != leftColor) {
      r = m;
    } else {
      l = m;
    }
  }

  string result(2 * n, ' ');
  result[l] = leftColor[0];
  r = l + n;
  result[r] = Other(leftColor)[0];

  for (int i = 0; i < 2 * n; ++i) {
    if (i == l || i == r) continue;
    string curColor;
    if (i < l || i > r) {
      curColor = AskColor(l, l, i);
    } else {
      curColor = Other(AskColor(l, i, r));
    }
    result[i] = curColor[0];
  }
  
  cout << "! " + result << endl;
  cout.flush();

  return 0;
}