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 org.graalvm.compiler.nodes.calc.IntegerDivRemNode;

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

/* Name of the class has to be "Main" only if the class is public. */
public class q3
{
	public static void main (String[] args) throws java.lang.Exception
	{
        // your code goes here
        Scanner sc = new Scanner(System.in);
        int n= Integer.parseInt(sc.next());
        int i=1;int j= n;
        int[] arr = new int[n+1];
        int cnt=0;
        while(i>0 && i<=n && j>0 && j<=n && cnt<n-1)
        {
            System.out.println("?"+" "+i+" "+j);
            System.out.flush();
            int a = Integer.parseInt(sc.next());
            System.out.println("?"+" "+j+" "+i);
            System.out.flush();
            int b = Integer.parseInt(sc.next());
            if(a==-1 || b==-1)
            {
                return;
            }
            if(b>a)
            {
                arr[j]=b;
                j--;
            }
            else
            {
                arr[i]=a;
                i++;
            }
            cnt++;
        }
        if(arr[i]==0)
        {
            arr[i]=n;
        }
        else
        {
            arr[j]=n;
        }
        System.out.print("!"+" ");
        for(int it=1;it<=n;it++)
        {
            System.out.print(arr[it]+" ");
        }
        System.out.println("");
        
    }
}