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 com.company;
 
    import java.io.*;
    import java.math.BigInteger;
    import java.util.*;
 
    public class Main {
 
        public static void main(String[] args) {
            Main main = new Main();
            main.solve();
        }
 
        BufferedReader in;
//        PrintWriter out;
        StringTokenizer tok;
 
        String readString() {
            while (!tok.hasMoreTokens()) {
                String line;
                try {
                    line = in.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) return null;
                tok = new StringTokenizer(line);
            }
            return tok.nextToken();
        }
 
        public void solve() {
//            Scanner in = null;
////            PrintWriter out = null;
//            PrintStream out = System.out;
//            try {
//                in = new Scanner(new File("input.txt"));
////                out = new PrintWriter(new File("output.txt"));
//                throw new FileNotFoundException();
//            }
//            catch (FileNotFoundException e) {
//                in = new Scanner(System.in);
//
////                out = new PrintWriter(System.out);
//            }
 
 
 
            tok = new StringTokenizer("");
            in = new BufferedReader(new InputStreamReader(System.in));
            PrintStream out = System.out;
 
            int n = Integer.parseInt(readString());//in.nextInt();
 
            if (n == -1) {
                return;
            }
            Set<Integer> unknown = new TreeSet();
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                unknown.add(i + 1);
                result[i] = 0;
            }
            while (true) {
                Integer a = unknown.iterator().next();
                if (a == -1) {
                    return;
                }
                unknown.remove(a);
                if (!unknown.iterator().hasNext()) {
                    unknown.add(a);
                    break;
                }
                Integer b = unknown.iterator().next();
                if (b == -1) {
                    return;
                }
                unknown.remove(b);
                out.println(String.format("? %d %d", a, b));
                out.flush();
                int amodb = Integer.parseInt(readString());//in.nextInt();
                out.println(String.format("? %d %d", b, a));
                out.flush();
                int bmoda = Integer.parseInt(readString());//in.nextInt();
                if (amodb > bmoda) {
                    result[a - 1] = amodb;
                    unknown.add(b);
                } else {
                    result[b - 1] = bmoda;
                    unknown.add(a);
                }
            }
            result[unknown.iterator().next() - 1] = n;
 
            out.print("! ");
            for (int i = 0; i < n; i++) {
                out.print(result[i] + " ");
            }
            out.println();
            out.flush();
 
//            out.close();
        }
 
    }