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:
//package exercieses.div2_669;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class C {
    static FastReader reader;
    static int request(int i, int j) {
        System.out.println("? " + i +" " + j);
        System.out.flush();
        int p = reader.nextInt();
        return p;
    }

    static String solve(int n) {
        if(n == 1) {
            return "1";
        }
        boolean[] avail = new boolean[n+1];
        Arrays.fill(avail, true);
        int[] res = new int[n+1];
        Queue<Integer> untaken = new ArrayDeque<>(n);
        for(int i = 1; i <= n; i++) untaken.add(i);

        while(untaken.size() > 1) {
            int i = untaken.poll();
            int j = untaken.poll();
            int IModJ = request(i, j);
            int JModI = request(j, i);
            if(IModJ > JModI) {
                res[i] = IModJ;
                untaken.add(j);
                avail[res[i]] = false;
            } else {
                res[j] = JModI;
                untaken.add(i);
                avail[res[j]] = false;
            }
        }

        if(untaken.size() == 1) {
            int ind = untaken.poll();
            for(int i = 1; i <= n; i++) {
                if(avail[i]) {
                    res[ind] = i;
                    break;
                }
            }
        }
        StringBuilder resStr = new StringBuilder();
        for(int i = 1; i<= n; i++) resStr.append(res[i] + " ");
        resStr.deleteCharAt(resStr.length() - 1);
        return resStr.toString();
    }

    public static void main(String[] args) {
        reader = new FastReader();
        int n = reader.nextInt();
        String res = solve(n);
        System.out.println("! " + res);
        System.out.flush();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}