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 Div2_669;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;

public class ProblemC {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        StringBuilder print=new StringBuilder();
        int n=Integer.parseInt(br.readLine());
        int ans[]=new int[n+1];
        HashSet<Integer> ind=new HashSet<>();
        HashSet<Integer> rem=new HashSet<>();
        for(int i=1;i<=n;i++){
            ind.add(i);
            rem.add(i);
        }
        for(int i=1;i<=n;i++){
            int j=-1,k=-1;
            for(int num:ind){
                if(j==-1){
                    j=num;
                }
                else if(k==-1){
                    k=num;
                }
                else{
                    break;
                }
            }
            if(k==-1){
                for(int num:rem){
                    ans[j]=num;
                }
                break;
            }
            System.out.println("? "+j+" "+k);
            System.out.flush();
            int f=Integer.parseInt(br.readLine());
            System.out.println("? "+k+" "+j);
            System.out.flush();
            int s=Integer.parseInt(br.readLine());
            if(f<s){
                ans[k]=s;
                ind.remove(k);
                rem.remove(s);
            }
            else{
                ans[j]=f;
                ind.remove(j);
                rem.remove(f);
            }
        }
        print.append("! ");
        for(int i=1;i<=n;i++){
            print.append(ans[i]).append(" ");
        }
        System.out.println(print.toString());
    }
}