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.PrintWriter;
    import java.util.*;
    public class d1  extends PrintWriter {

        static BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
        // static Scanner s=new Scanner(System.in);
        d1 () { super(System.out); }
        public static void main(String[] args) throws IOException{
            d1  d1=new d1 ();d1.main();d1.flush();

        }
        void main() throws IOException {
            BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
            StringBuffer sb = new StringBuffer();
            StringBuffer sb1 = new StringBuffer();
            PrintWriter out = new PrintWriter(System.out);
    //        Scanner s=new Scanner(System.in);
            String[] s1=s();
            int n=i(s1[0]);
            int[] ans=new int[n];
            HashMap<Integer,Integer> h=new HashMap<>();
            int flag=0;
            Queue<Integer> q=new LinkedList<>();;
            for(int i=0;i<n;i++){
                ans[i]=-1;
                q.add(i);
            }
            for(int j=0;j<n;j++){
             while(!q.isEmpty()&&q.size()>1){
           //      System.out.println("HI");
                int i=q.poll();
                int k=q.poll();
                 System.out.println("? "+(i+1)+" "+(k+1));
                 System.out.flush();     int mod1=i(s()[0]);

                 System.out.println("? "+(k+1)+" "+(i+1));
                 System.out.flush(); int mod2=i(s()[0]);

                 if(mod1>mod2){
                     ans[i]=mod1;q.add(k);
                     h.put(mod1,1);
                 }else{
                     ans[k]=mod2;q.add(i);
                     h.put(mod2,10);
                 }

             }
             if(h.size()==n-1||h.size()==n) break;
            }
          {      int sus=0;
              for(int i=1;i<=n;i++){
                  if(!h.containsKey(i)){
                      sus=i;break;
                  }
              }
                for(int i=0;i<n;i++){
                    if(ans[i]==-1){
                        ans[i]=sus;
                    }
                sb.append(ans[i]+" "); }
              System.out.print("! ");
              System.out.println(sb.toString());
          }
        }
        static long gcd(long a, long b) {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }
        static String[] s() throws IOException {
            return s.readLine().trim().split("\\s+");
        }

        static int i(String ss) {
            return Integer.parseInt(ss);
        }
        static long l(String ss) {
            return Long.parseLong(ss);
        }
    }
    class Student {
        int  l;long r;
        public Student(int l, long r) {
            this.l = l;
            this.r = r;
        }

        public String toString()
        {
            return this.l+" ";
        }
    }
    class Sortbyroll implements Comparator<Student> {

        public int compare(Student a, Student b){
            if(a.r<b.r) return -1;
            else if(a.r==b.r){
                if(a.r==b.r){
                    return 0;
                }
                if(a.r<b.r) return -1;
                return 1;}
            return 1;  }
    }