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.util.Scanner;

public class Solution {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t, n;
        int xDel, yDel;
        int[] answer;
        int i = 1, j = 2;
        n = scanner.nextInt();
        answer = new int[n + 1];
        while (i <= n && j <= n) {
            System.out.println("? " + i + " " + j);
            System.out.flush();
            xDel = scanner.nextInt();
            System.out.println("? " + j + " " + i);
            System.out.flush();
            yDel = scanner.nextInt();
            if (xDel > yDel) {
                answer[i] = xDel;
                i = j;
                j++;
            } else {
                answer[j] = yDel;
                j++;
            }
        }
        if (answer[j - 1] == 0) {
            answer[j - 1] = n;
        } else if (answer[i] == 0){
            answer[i] = n;
        } else {
            answer[i - 1] = n;
        }
        System.out.print("! ");
        for (int k = 1; k < answer.length; k++) {
            System.out.print(answer[k] + " ");
        }
        scanner.close();
    }
}