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.*;

public class C{
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}
        public FastReader(String fileName) throws FileNotFoundException{br = new BufferedReader(new FileReader(fileName));}
        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());}
        char[][] readCharArray(int n,int m) {
            String str;
            char[][] arr = new char[n][m];
            for(int i=0;i<n;i++) {
                str=nextLine();
                for(int j=0;j<n;j++) {
                    arr[i][j]=str.charAt(j);
                }
            }
            return arr;
        }
        char[][] readCharArray(int n){
            return readCharArray(n,n);
        }
        int[] readArray(int n){int[] a=new int[n];for (int i=0; i<n; i++) a[i]=nextInt();return a;}
        long[] readLongArray(int n){long[] a=new long[n];for (int i=0; i<n; i++) a[i]=nextLong();return a;}
        String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
    }
    static void printArray(int[] arr){
        for(int x:arr){
        	if(x==0) System.out.print(arr.length+" ");
        	else System.out.print(x+" ");
        }
        System.out.println();
    }
    static final Random random=new Random();
    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        FastReader st = new FastReader();
        int n = st.nextInt();
        int[] arr = new int[n];
        int temp1,temp2;
        int i=1,j=0;
        while(i<n && j<n) {
        	System.out.println("? "+(j+1)+" "+(i+1));
        	temp1 = st.nextInt();
        	System.out.println("? "+(i+1)+" "+(j+1));
        	temp2 = st.nextInt();
        	if(temp2>temp1) {
        		arr[i]=temp2;i++;
        	}else {
        		arr[j]=temp1;j=i;
        	}
        	if(i==j) i++;
        }
        System.out.print("! ");
        printArray(arr);
    }
}