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.awt.dnd.InvalidDnDOperationException;
import java.io.*;
import java.lang.reflect.Array;
import java.nio.charset.CharsetEncoder;
import java.util.*;

public class Main {
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private static final boolean OFFLINE_WITHOUT_FILES = true;


    void solve() throws IOException {
        int n=readInt();
        int indexMaxValue=0;
        int [] answerArr=new int [n];
        boolean [] used=new boolean[n];
        boolean [] usedIndexes=new boolean[n];
        for (int i=1;i<n;++i){
            int firstValue=getValue(i,indexMaxValue);
            int secondValue=getValue(indexMaxValue,i);
            if (firstValue>secondValue){
                answerArr[i]=firstValue;
                used[firstValue-1]=true;
                usedIndexes[i]=true;
            }else{
                answerArr[indexMaxValue]=secondValue;
                used[secondValue-1]=true;
                usedIndexes[indexMaxValue]=true;
                indexMaxValue=i;
            }
        }
        boolean end=false;
        for (int i=0;i<n;++i){
            if (!usedIndexes[i]){
                for (int j=0;j<n;++j){
                    if (!used[j]){
                        answerArr[i]=j+1;
                        end=true;
                        break;
                    }
                }
            }
            if (end){
                break;
            }
        }
        out.print("! ");
        printDefaultArr(answerArr);

    }

    int getValue(int i,int j) throws IOException {
        out.print('?');
        out.print(" "+(i+1)+" "+(j+1)+"\n");
        out.flush();
        int value=readInt();
        return value;
    }

    void printDefaultList(ArrayList <Integer> arr){
        for (Integer el:arr){
            out.print(el+" ");
        }
        out.println();
    }

    void printDefaultArr(int [] arr){
        for (int i=0;i<arr.length;++i){
            out.print(arr[i]+" ");
        }
        out.println();
    }

    public static void main(String[] args) {
        new Main();
    }

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    Main() {
        try {
            long timeStart = System.currentTimeMillis();
            if (ONLINE_JUDGE || OFFLINE_WITHOUT_FILES) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }

            tok = new StringTokenizer("");
            solve();
            out.close();
            long timeEnd = System.currentTimeMillis();
            System.err.println("time = " + (timeEnd - timeStart) + " compiled");
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String delimiter = " ";



    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (nextLine == null)
                return null;
            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    int[] sortArrayInt(int[] a) {
        Integer[] arr = new Integer[a.length];
        for (int i = 0; i < a.length; i++) {
            arr[i] = a[i];
        }
        Arrays.sort(arr);
        for (int i = 0; i < a.length; i++) {
            a[i] = arr[i];
        }
        return a;
    }

    void sortArrayLong(long[] a) {
        Long[] arr = new Long[a.length];
        for (int i = 0; i < a.length; i++) {
            arr[i] = a[i];
        }
        Arrays.sort(arr);
        for (int i = 0; i < a.length; i++) {
            a[i] = arr[i];
        }
    }
}