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.IOException;
import java.io.InputStreamReader;
import java.util.Deque;
import java.util.LinkedList;
import java.util.StringTokenizer;

public final class CodeForces {
    private static FastReader fr;
    public static void main(String[] args) {
        fr = new FastReader();
        int n = fr.nextInt();
        int[] arr = solve(n);
        StringBuilder sb = new StringBuilder();
        for(int i=0; i<arr.length; i++)
            sb.append(arr[i]).append(" ");
        System.out.println("! " + sb.toString());
        System.out.flush();
        fr.close();
    }

    private static int[] solve(int n) {
        Deque<Integer> q = new LinkedList<>();
        for(int i=1; i<=n; i++)
            q.add(i);
        int filled = 0;
        int[] ans = new int[n];
        if(n == 1) {
            ans[0] = 1;
            return ans;
        }
        while(filled != n) {
            int a = q.poll();
            int b = q.poll();
            System.out.println("? " + a + " " + b);
            System.out.flush();
            int remain1 = fr.nextInt();
            System.out.println("? " + b + " " + a);
            System.out.flush();
            int remain2 = fr.nextInt();
            if(remain1 > remain2) {
                ans[a-1] = remain1;
                q.add(b);
            } else {
                ans[b-1] = remain2;
                q.add(a);
            }
            if(q.size() == 1) {
                ans[q.poll()-1] = n;
                break;
            }
        }
        return ans;
    }

    static class FastReader {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while(!st.hasMoreTokens()) {
                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());
        }

        int[] readIntArray(int n) {
            int[] arr = new int[n];
            for(int i=0; i<n; i++)
                arr[i] = nextInt();
            return arr;
        }

        long[] readLongArray(int n) {
            long[] arr = new long[n];
            for(int i=0; i<n; i++)
                arr[i] = nextLong();
            return arr;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}