Problem: This is an interactive problem.

We hid from you a permutation p of length n, consisting of the elements from 1 to n. You want to guess it. To do that, you can give us 2 different indices i and j, and we will reply with p_{i} mod p_{j} (remainder of division p_{i} by p_{j}).

We have enough patience to answer at most 2 ⋅ n queries, so you should fit in this constraint. Can you do it?

As a reminder, a permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

Input

The only line of the input contains a single integer n (1 ≤ n ≤ 10^4) — length of the permutation.

Interaction

The interaction starts with reading n. 

Then you are allowed to make at most 2 ⋅ n queries in the following way: 

  * "? x y" (1 ≤ x, y ≤ n, x ≠ y). 



After each one, you should read an integer k, that equals p_x mod p_y. 

When you have guessed the permutation, print a single line "! " (without quotes), followed by array p and quit.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



Exit immediately after receiving "-1" and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.

Hack format

In the first line output n (1 ≤ n ≤ 10^4). In the second line print the permutation of n integers p_1, p_2, …, p_n.

Example

Input


3

1

2

1

0

Output


? 1 2

? 3 2

? 1 3

? 2 1

! 1 3 2

Solution (in JAVA):

Solution:
//make sure to make new file!
import java.io.*;
import java.util.*;

public class C669{
   
   public static void main(String[] args)throws IOException{
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter out = new PrintWriter(System.out);
      
      int n = Integer.parseInt(f.readLine());
      
      int[] answer = new int[n+1];
      
      
      int last = 1;
      for(int k = 2; k <= n; k++){
         out.println("? " + last + " " + k);
         out.flush();
      
         int q1 = Integer.parseInt(f.readLine());
         out.println("? " + k + " " + last);
         out.flush();
         
         int q2 = Integer.parseInt(f.readLine());
         
         if(q1 > q2){
            answer[last] = q1;
            last = k;
         } else {
            answer[k] = q2;
         }
      }
      
      answer[last] = n;
      
      StringJoiner sj = new StringJoiner(" ");
      sj.add("!");
      for(int k = 1; k <= n; k++){
         sj.add("" + answer[k]);
      }
      out.println(sj.toString());
      
      
      
      
      
      
      out.close();
   }
   
}