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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;


public class Main {
    static int i,j,k,n,m,t,x,y,max=1000000;
    static long ans,a,b,c,d,e,l,r,sum,mi,ma,mod=1000000007 ;
    static String str;
    static char ch;
    static FastScanner fs = new FastScanner();

    public static void main(String[] args) {

        n = fs.nextInt();

        PrintWriter out = new PrintWriter(System.out);

        int [] vis = new int[n+1];
        int [] arr = new int[n+1];

        int maxIn = 1;

        for(i=2;i<=n;i++){
            out.println("? "+i+ " "+ maxIn);
            out.flush();
            x = fs.nextInt();

            if(x==-1)
                break;

            out.println("? "+maxIn+ " "+ i);
            out.flush();

            y = fs.nextInt();

            if(y==-1)
                break;

            if(y >x){
                arr[maxIn]=y;
                maxIn = i;
            }
            else{
                arr[i] = x;
            }

        }

        arr[maxIn] = n;

        out.print("! ");

        for(i=1;i<=n;i++){
            out.print(arr[i]+" ");
        }
        out.println();

        out.flush();

        out.close();
    }




    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                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());
        }
    }

    public static int[] readArray(int n){
        int[] arr = new int[n];

        for(int i=0;i<n;i++){
            arr[i] = fs.nextInt();
        }

        return arr;
    }

    public static int gcd(int a, int b)
    {
        if (a == 0)
            return b;

        return gcd(b%a, a);
    }

    //To be used with priority queues.
    static class Pair implements Comparable<Pair> {
        int first, second;
        int len;
        public Pair(int first, int second) {
            this.first=first;
            this.second=second;
            this.len=second-first+1;
        }

        public int compareTo(Pair o) {
            if (len!=o.len) {
                return -Long.compare(len, o.len);
            }
            else {
                return Long.compare(first, o.first);
            }
        }

    }

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

}