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.ArrayList;
import java.util.StringTokenizer;

public class C_ChocolateBunny {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    private static StringTokenizer st;

    private static int readInt() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }

    private static String readToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public static void main(String[] args) throws IOException {
        solve();
        pw.close();
    }

    private static void solve() throws IOException {
        int n = readInt();
//        if (n == 1) {
//            pw.println("! 1");
//            return;
//        }

        int[] p = new int[n + 1];

        ArrayList<Integer> todo = new ArrayList<>();
        for (int i = 1; i <= n; i++) {
            todo.add(i);
        }

        while (todo.size() > 1) {
            ArrayList<Integer> nextTodo = new ArrayList<>();
            for (int i = 0, limit = todo.size() / 2 * 2; i < limit; i += 2) {
                int index = todo.get(i);
                int anotherIndex = todo.get(i + 1);
                pw.println("? " + index + " " + anotherIndex);
                pw.flush();
                int response1 = readInt();
                pw.println("? " + anotherIndex + " " + index);
                pw.flush();
                int response2 = readInt();
                if (response1 < response2) {
                    p[anotherIndex] = response2;
                    nextTodo.add(index);
                } else {
                    p[index] = response1;
                    nextTodo.add(anotherIndex);
                }
            }
            if (todo.size() % 2 == 1) {
                nextTodo.add(todo.get(todo.size() - 1));
            }
            todo = nextTodo;
        }
        p[todo.get(0)] = n;

        StringBuilder sb = new StringBuilder();
        sb.append("! ");
        for (int i = 1; i <= n; i++) {
            sb.append(p[i]).append(" ");
        }
        pw.println(sb);
    }
}