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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.stream.Collectors;

public class CF_669_C {

    public static void main(String[] args) {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
             BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out))) {
            int n = Integer.parseInt(br.readLine());
            List<Integer> unknowns = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                unknowns.add(i);
            }
            long[] result = new long[n+1];
            while (unknowns.size()>0) {
                List<Integer> unknownsNext = new ArrayList<>();
                for (int i = 0; i < unknowns.size()/2; i++) {
                    w.write("? " + unknowns.get(i*2) + " " + unknowns.get(i*2+1));
                    w.newLine();
                    w.flush();
                    int x = Integer.parseInt(br.readLine());
                    if (x==-1) {
                        return;
                    }
                    w.write("? " + unknowns.get(i*2+1) + " " + unknowns.get(i*2));
                    w.newLine();
                    w.flush();
                    int y = Integer.parseInt(br.readLine());
                    if (y==-1) {
                        return;
                    }
                    if (x > y) {
                        result[unknowns.get(i*2)] = x;
                        unknownsNext.add(unknowns.get(i*2+1));
                    } else {
                        result[unknowns.get(i*2+1)] = y;
                        unknownsNext.add(unknowns.get(i*2));
                    }
                }
                if (unknowns.size()%2==1 && unknowns.size()>1) {
                    unknownsNext.add(unknowns.get(unknowns.size()-1));
                } else if (unknowns.size()==1) {
                    for (int i = 0; i <= n; i++) {
                        if (result[i]==0) {
                            result[i] = n;
                        }
                    }
                }
                unknowns = unknownsNext;
            }
            // result
            w.write("! ");
            for (int i = 1; i <= n; i++) {
                w.write(result[i] + " ");
            }
            w.newLine();
            w.flush();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static void solve(long _n, List<Integer> a) {

    }
}