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.util.*;
import java.io.*;
 
public class Main2 {
	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; }}
	static long mod = (long)(1e9+7);
//	static long mod = 998244353;
//	static Scanner sc = new Scanner(System.in);
	static FastReader sc = new FastReader();
	static PrintWriter out = new PrintWriter(System.out);
	static long p2[] = new long[1000001];
	public static void main (String[] args) {
		int t = 1;
//    	t = sc.nextInt();
	    z : for(int tc=1;tc<=t;tc++) {
	    	int n = sc.nextInt();
	    	if(n == 1) {
	    		System.out.print("! 1");
		    	System.out.println();
		    	System.out.flush();
		    	continue;
	    	}
	    	int ans[] = new int[n+1];
	    	Arrays.fill(ans, -1);
	    	boolean is[] = new boolean[n+1];
	    	int i=1,j=2;
	    	while(i<=n && j<=n) {
	    		int x = query(i,j);
	    		int y = query(j,i);
	    		if(x>y) {
	    			ans[i] = x;
	    			if(i>j) i++;
	    			else i = j+1;
	    			is[x] = true;
	    		}
	    		else {
	    			ans[j] = y;
	    			if(j>i) j++;
	    			else j = i+1;
	    			is[y] = true;
	    		}
	    	}
	    	int val = -1;
	    	for(i=1;i<=n;i++) {
	    		if(!is[i]) val = i;
	    	}
	    	for(i=1;i<=n;i++) {
	    		if(ans[i] == -1) ans[i] = val;
	    	}
	    	System.out.print("! ");
	    	for(i=1;i<=n;i++) System.out.print(ans[i]+" ");
	    	System.out.println();
	    	System.out.flush();
	    }
		out.close();
	}
	private static int query(int i, int j) {
		System.out.println("? "+i+" "+j);
		int x = sc.nextInt();
		System.out.flush();
		return x;
	}
	static int gcd(int a,int b) { if(b==0) return a; return gcd(b,a%b); }
	private static void sort(int[] a) {List<Integer> k = new ArrayList<>();for(int val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);}
	private static void ini(List<Integer>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}}
	private static void init(List<int[]>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}}
	private static void sort(long[] a) {List<Long> k = new ArrayList<>();for(long val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);}
}