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:

import java.util.*;
import java.lang.*;
import java.io.*;
import java.awt.*;


 public class Main
{
     
 static Scanner scn = new Scanner(System.in);

public static void solve()
{
 
Set<Integer> set = new HashSet<>() ;

int n= scn.nextInt() ;

int[] ans  = new int[n+1];

int i = 1;int j =2 ; 


while(j<=n)
{
    System.out.println("? " + i+" " + j);int x = scn.nextInt() ;
    
    System.out.println("? " + j+" " + i);int y = scn.nextInt() ;
    
    if(x> y)
    {
        ans[i] =x ;i=j;j++ ;set.add(x) ;
    }
    else{
        ans[j] =y ;j++ ;set.add(y) ;
    }
    
    
    
}



int val =-1  ;
for( i = 1;i<= n ;i++ )
{
    if(!set.contains(i))
    {
        val = i ;break ;
    }
    
}
  
  
  for( i =1; i <= n ;i++)
  {
      if(ans[i] == 0){ans[i] =val ;break ; }
  }
  
  System.out.print("! ") ;
  
  for( i = 1; i<= n ;i++)System.out.print(ans[i] +" ") ;
  System.out.println()  ;
  
} // solve fn ends


public static void main (String[] args) throws java.lang.Exception
{
  

solve() ;
      
}


}