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:

/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
 public class Codechef{
    /*static int gcd(int a,int b){
        if(b!=0)
            return gcd(b,a%b);
        else return a;
        
    }*/
    
	public static void main (String[] args) throws java.lang.Exception{
	    Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt();
	    Stack<Integer> s=new Stack<>();
	    for(int i=1;i<=n;i++)
	        s.push(i);
	    int a=s.peek(),b=-1,d=0,e=0;
	    s.pop();
	    int c[]=new int[n+1];
	    Set<Integer> s1=new TreeSet<>();
	    if(n>1){
	        b=s.peek();
	        s.pop();
	    while(!s.isEmpty()){
	        System.out.println("?"+" "+a+" "+b);
	        System.out.flush();
	        d=sc.nextInt();
	        System.out.println("?"+" "+b+" "+a);
	        System.out.flush();
	        e=sc.nextInt();
	        if(d>e){
	             c[a]=d;
	             a=s.peek();
	             s.pop();
	             s1.add(d);
	        }
	           
            else{
                 c[b]=e;
	             b=s.peek();
	             s.pop();
	             s1.add(e);
            }
	        
	    }   System.out.println("?"+" "+a+" "+b);
	        System.out.flush();
	        d=sc.nextInt();
	        System.out.println("?"+" "+b+" "+a);
	        System.out.flush();
	        e=sc.nextInt();
	        
	    
	    if(d>e){
	             c[a]=d;
	             a=-1;
	             s1.add(d);
	        }
	           
            else{
                 c[b]=e;
                 b=-1;
                 s1.add(e);
	             
            }}
            for(int i=1;i<=n;i++)
                if(!s1.contains(i))
                d=i;
                if(a==-1)
                    c[b]=d;
                else c[a]=d;
            System.out.print("!"+" ");
            for(int i=1;i<=n;i++)
            System.out.print(c[i]+" ");
            System.out.println();
	        
	    }
 }