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:
/**
 * 08-09-2020
 * Created by Himanshu
 **/

import java.util.*;
import java.io.*;
import java.math.*;

public class ChocolateBunny {

    static Scanner s = new Scanner(System.in);
    public static void main(String[] args) throws IOException {
        int n = s.nextInt();
        if (n == 1) {
            System.out.println("! 1");
            System.out.flush();
            return;
        }
        int [] arr = new int [n];
        int i=0,j=1;
        while (j < n) {
            int a = query(i+1,j+1);
            int b = query(j+1,i+1);
            if (a > b) {
                arr[i] = a;
                i = j;
            } else {
                arr[j] = b;
            }
            j++;
        }
        arr[i] = n;
        System.out.print("! ");
        for (i=0;i<n;i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
        System.out.flush();
    }
    private static int query (int x , int y) {
        System.out.println("? " + x + " " + y);
        System.out.flush();
        return s.nextInt();
    }
}