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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.io.BufferedWriter;
import java.io.Writer;
import java.util.Scanner;
import java.io.OutputStreamWriter;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        int query(Scanner sc, int x, int y) {
            System.out.println("? " + x + " " + y);
            System.out.flush();
            return sc.nextInt();
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            Scanner sc = new Scanner(System.in);
            int n = sc.nextInt();
            TreeSet<Integer> remaining = new TreeSet<>();
            TreeSet<Integer> positions = new TreeSet<>();
            for (int i = 1; i <= n; i++) {
                remaining.add(i);
                positions.add(i);
            }

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

            for (int i = 1; i <= n; i++) {
                int x = positions.first();
                positions.remove(x);
                if (positions.isEmpty()) {
                    p[x] = remaining.first();
                    break;
                }

                int y = positions.first();
                positions.remove(y);

                int a = query(sc, x, y);
                int b = query(sc, y, x);

                if (a < b) {
                    p[y] = b;
                    positions.add(x);
                    remaining.remove(b);
                } else {
                    p[x] = a;
                    positions.add(y);
                    remaining.remove(a);
                }
            }
            System.out.print("! ");
            for(int i = 1; i <= n; i++) System.out.print(p[i] + " ");
            System.out.println();
            System.out.flush();
        }
    }

    static class InputReader {
        private InputStream stream;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

    }
}