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:
//created by Whiplash99
import java.io.*;
import java.util.*;
public class C
{
    private static BufferedReader br;
    private static int N;
    private static int[] ans;
    private static ArrayDeque<Integer> list;
    private static void ask(int i, int j)
    {
        System.out.println("? "+i+" "+j);
        System.out.flush();
    }
    private static void solve() throws IOException
    {
        if(list.size()==0) return;
        if(list.size()==1)
        {
            int x=0;
            HashSet<Integer> set=new HashSet<>();
            for(int i=1;i<=N;i++)
            {
                set.add(i);
                x^=i;
            }
            for(int i=0;i<N;i++) x^=ans[i];

            int pos=list.poll();
            ans[pos]=x;
            return;
        }

        int count=list.size()/2;
        while (count-->0)
        {
            int a=list.poll();
            int b=list.poll();

            ask(a+1,b+1);
            int c=Integer.parseInt(br.readLine().trim());

            ask(b+1,a+1);
            int d=Integer.parseInt(br.readLine().trim());

            if(c>d)
            {
                ans[a]=c;
                list.add(b);
            }
            else
            {
                ans[b]=d;
                list.add(a);
            }
        }
        solve();
    }
    public static void main(String[] args) throws IOException
    {
        br=new BufferedReader(new InputStreamReader(System.in));

        int i;

        N=Integer.parseInt(br.readLine().trim());
        ans=new int[N]; list=new ArrayDeque<>();
        for(i=0;i<N;i++) list.add(i);

        solve();

        StringBuilder sb=new StringBuilder();
        sb.append("! ");
        for(i=0;i<N;i++) sb.append(ans[i]).append(" ");

        System.out.println(sb);
        System.out.flush();
    }
}