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

public class c1 {
    public static FScanner scan;
    public static PrintWriter out;
    public static void main(String[] args) {
        scan=new FScanner();
        out=new PrintWriter(new BufferedOutputStream(System.out));

        int t=1;
//        int t=scan.nextInt();
        while(t-->0) {

            int n=scan.nextInt(),next,max=1,left=n;
            int[] ans=new int[n];
            if(n==1) {
                out.println("! 1");
                break;
            }
            next=getNext(ans,max);
            while(next!=-1&&left>1) {
                out.println("? "+(next+1)+" "+(max+1));
                out.flush();
                int ans1=scan.nextInt();

                out.println("? "+(max+1)+" "+(next+1));
                out.flush();
                int ans2=scan.nextInt();

                if(ans1>ans2) ans[next]=ans1;
                else {
                    ans[max]=ans2;
                    max=next;
                } left--;
                next=getNext(ans,max);
            } ans[max]=n;

            out.print("! ");
            for(int c=0;c<n;c++) out.print(ans[c]+" ");
            out.println();
        }
        out.close();
    }

    static int getNext(int[] a,int max) {
        for(int c=0;c<a.length;c++) if(a[c]==0&&c!=max) return c;
        return -1;
    }

    //------------------------------------------------------------------------------------------------------------------

    //scanner
    public static class FScanner {
        BufferedReader br;
        StringTokenizer st;

        public FScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}