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.io.InvalidClassException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Stack;

public class _669C {
    static BufferedReader br;

    public static void main(String[] args) throws IOException, InvalidClassException {
        br = new BufferedReader(new InputStreamReader(System.in));
        int n = readInt();
        int arr[] = new int[n + 1];
        Stack<Integer> stack = new Stack<Integer>();
        for(int i = 1; i<=n; i++)stack.push(i);
        while(!stack.isEmpty()){
            int a = stack.pop();
            if(!stack.isEmpty()){
                int b = stack.pop();
                System.out.println("? "+a+" "+b);
                System.out.flush();
                int i1 = readInt();
                System.out.println("? "+b+" "+a);
                System.out.flush();
                int i2 = readInt();
                if(i1>i2){
                    arr[a] = i1;
                    stack.push(b);
                }else if(i1<i2){
                    arr[b] = i2;
                    stack.push(a);
                }
            }else{
                int flag[] = new int[n + 1];
                for(int i = 1; i <=n ;i++) flag[i]=-1;
                for(int i=1;i<=n;i++){
                    flag[arr[i]]=1;
                }
                for(int i = 1; i <=n ;i++) {
                    if(flag[i]==-1){
                        arr[a] = i;
                    }
                }
            }
        }
        System.out.print("! ");
        for(int i=1;i<=n;i++)System.out.print(arr[i]+" ");
        System.out.println();
    }

    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    static long[] readLongarray() throws IOException {
        String[] _arr_ = br.readLine().split(" ");
        long[] a = new long[_arr_.length];
        for (int i = 0; i < _arr_.length; i++) {
            a[i] = Long.parseLong(_arr_[i]);
        }
        return a;
    }

    static int[] readIntarray() throws IOException {
        String[] _arr_ = br.readLine().split(" ");
        int[] a = new int[_arr_.length];
        for (int i = 0; i < _arr_.length; i++) {
            a[i] = Integer.parseInt(_arr_[i]);
        }
        return a;
    }
}