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.*;

/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

public class Main {
   public static void main(String[] args) throws IOException {
      BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      // Scanner sc = new Scanner(System.in);

      // int n = sc.nextInt();
      int n = Integer.parseInt(br.readLine());
      int[] p = new int[n];

      int i = 1;

      for (int j = 2; j <= n; j++) {
         String query = String.format("? %d %d", i, j);
         bw.write(query);
         bw.newLine();
         bw.flush();
//         System.out.format("? %d %d\n", i, j);
//         System.out.flush();

         // int k = sc.nextInt();
         int k = Integer.parseInt(br.readLine());

         query = String.format("? %d %d", j, i);
         bw.write(query);
         bw.newLine();
         bw.flush();
//         System.out.format("? %d %d\n", j, i);
//         System.out.flush();

         // int l = sc.nextInt();
         int l = Integer.parseInt(br.readLine());

         if (k > l) {
            p[i - 1] = k;
            i = j;
         } else {
            p[j - 1] = l;
         }
      }

      p[i - 1] = n;

      StringBuilder sb = new StringBuilder("!");

      for (int pp : p) {
         sb.append(' ');
         sb.append(pp);
      }

      bw.write(sb.toString());
      bw.newLine();
      bw.flush();
//      System.out.println(sb.toString());
//      System.out.flush();
   }
}