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.*;
import java.util.*;

public class C {
    static int ask(int x,int y,Scanner sc,PrintWriter pw) throws IOException{
        pw.println("? " + (x+1) +" " + (y+1));
        pw.flush();
        int res = sc.nextInt();

        return res;
    }
    public static void main(String[] args)throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int[] arr = new int[n];
        int x = 0;
        int y = 1;
        TreeSet<Integer>tr = new TreeSet<>();
        TreeSet<Integer>tr2 = new TreeSet<>();
        for(int i=1;i<=n;i++)tr.add(i);
        for(int i=0;i<n;i++)tr2.add(i);
        for(int i=1;i<n;i++){
            y = i;
            if(x==y)continue;
            int a = ask(x,y,sc,pw);
            int b = ask(y,x,sc,pw);
            if(a>b){
                arr[x] = a;
                tr.remove(a);
                tr2.remove(x);
            }else{
                tr2.remove(y);
                arr[y] = b;
                tr.remove(b);
            }
            x = tr2.first();
        }
        pw.print("! ");
        for(int i=0;i<n;i++){
            pw.print((arr[i]==0)?tr.first() +" ":arr[i]+" ");
        }
        pw.println();
        pw.flush();
        pw.close();
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x,int y){
            this.x= x;
            this.y = y;
        }
        public int compareTo(Pair p){
            int max = Math.max(x,y);
            int max2 = Math.max(p.x,p.y);
            if(max==max2){
                int min = Math.min(x,y);
                int min2 = Math.min(p.x,p.y);
                return Long.compare(min,min2);
            }else{
                return Long.compare(max,max2);
            }
        }

        @Override
        public String toString() {
            return x+" " + y;
        }
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();

        }
    }
}