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:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
What do you think? What do you think?
1st on Billboard, what do you think of it
Next is a Grammy, what do you think of it
However you think, I’m sorry, but shit, I have no fcking interest
*******************************
I'm standing on top of my Monopoly board
That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300iq as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class C2
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int[] res = new int[N+1];
         for(int i=2; i <= N; i+=2)
         {
            System.out.println("? "+(i-1)+" "+i);
            System.out.flush();
            int ab = Integer.parseInt(infile.readLine());
            System.out.println("? "+i+" "+(i-1));
            System.out.flush();
            int ba = Integer.parseInt(infile.readLine());
            if(ab > ba)
               res[i-1] = ab;
            else
               res[i] = ba;
         }
         ArrayList<Integer> ls = new ArrayList<Integer>();
         for(int i=1; i <= N; i++)
            if(res[i] == 0)
               ls.add(i);
         while(ls.size() >= 2)
         {
            for(int i=1; i < ls.size(); i+=2)
            {
               int a = ls.get(i);
               int b = ls.get(i-1);
               System.out.println("? "+a+" "+b);
               System.out.flush();
               int ab = Integer.parseInt(infile.readLine());
               System.out.println("? "+b+" "+a);
               System.out.flush();
               int ba = Integer.parseInt(infile.readLine());
               if(ab > ba)
                  res[a] = ab;
               else
                  res[b] = ba;
            }
            ArrayList<Integer> temp = new ArrayList<Integer>();
            for(int dex: ls)
               if(res[dex] == 0)
                  temp.add(dex);
            ls = temp;
         }
         if(ls.size() == 1)
         {
            HashSet<Integer> set = new HashSet<Integer>();
            for(int i=1; i <= N; i++)
               set.add(res[i]);
            for(int v=1; v <= N; v++)
               if(!set.contains(v))
               {
                  res[ls.get(0)] = v;
                  break;
               }
         }
         StringBuilder sb = new StringBuilder("! ");
         for(int i=1; i <= N; i++)
            sb.append(res[i]+" ");
         System.out.println(sb);
         System.out.flush();
      }
   }
   class Thing implements Comparable<Thing>
   {
      public int val;
      public int dex;
      
      public Thing(int a, int b)
      {
         val = a;
         dex = b;
      }
      public int compareTo(Thing oth)
      {
         return oth.val-val;
      }
   }