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.io.IOException;
import java.util.*;



//import javafx.util.Pair; 
//import java.util.concurrent.LinkedBlockingDeque;







    
  public class Codeforces {
     
        
        public static long mod = (long)Math.pow(10,9)+7 ;
        public static double epsilon=0.00000000008854;//value of epsilon
        public static InputReader sc = new InputReader(System.in);
        public static PrintWriter pw = new PrintWriter(System.out);
        
        
        public static int gcd(int a,int b){
            while(b>0){
                int t=b;
                b=a%b;
                a=t;
            }
            return a;
        }
        public static void main(String[] args) {
            // code starts..
            
                int n=sc.nextInt();
                int ans[]=new int[n];
                Deque<Integer> qu=new LinkedList<>();
                for(int i=0;i<n;i++){
                    qu.add(i+1);
                }
                int h[]=new int[n+1];
                while(qu.size()>1){
                    int a=qu.remove();
                    int b=qu.remove();
                    pw.println("? "+a+" "+b);
                    pw.flush();
                    int a1=sc.nextInt();
                    pw.println("? "+b+" "+a);
                    pw.flush();
                    int b1=sc.nextInt();
                    if(a1>b1){
                        ans[a-1]=a1;
                        h[a1]++;
                        qu.add(b);
                    }
                    else{
                        ans[b-1]=b1;
                        h[b1]++;
                        qu.add(a);
                    }
                }
                
                for(int i=1;i<=n;i++){
                    if(h[i]==0){
                        ans[qu.remove()-1]=i;
                        break;
                    }
                }
                pw.print("! ");
                for(int i=0;i<n;i++){
                    pw.print(ans[i]+" ");
                }
            
            // Code ends...
            pw.flush();
            pw.close();
        }
       
        public static Comparator<Long[]> column(int i){
            return 
            new Comparator<Long[]>() {
                @Override
                public int compare(Long[] o1, Long[] o2) {
                    return o1[i].compareTo(o2[i]);//for ascending
                    //return o2[i].compareTo(o1[i]);//for descending
                }
            };
        }
        public static Comparator<Integer[]> col(int i){
            return 
            new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    return o1[i].compareTo(o2[i]);//for ascending
                    //return o2[i].compareTo(o1[i]);//for descending
                }
            };
        }
        public static Comparator<Integer> des(){
            return 
            new Comparator<Integer>() {
                @Override
                public int compare(Integer o1, Integer o2) {
                    //return o1[i].compareTo(o2[i]);//for ascending
                    return o2.compareTo(o1);//for descending
                }
            };
        }
        
        
        
        
        public static String reverseString(String s){
            StringBuilder input1 = new StringBuilder(); 
            input1.append(s);  
            input1 = input1.reverse();
            return input1.toString();
        }
        public static int[] scanArray(int n){
            int a[]=new int [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
    
            return a;
        }
        public static long[] scanLongArray(int n){
            long a[]=new long [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLong();
    
            return a;
        }
        public static String [] scanStrings(int n){
            String a[]=new String [n];
            for(int i=0;i<n;i++)
            a[i]=sc.nextLine();
    
            return a;
        }
        public static class InputReader {
    
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, snumChars;
            private SpaceCharFilter filter;
    
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
    
            public int snext() {
                if (snumChars == -1)
                    throw new InputMismatchException();
                if (curChar >= snumChars) {
                    curChar = 0;
                    try {
                        snumChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (snumChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }
    
            public int nextInt() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public long nextLong() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = snext();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = snext();
                } while (!isSpaceChar(c));
                return res * sgn;
            }
    
            public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                    a[i] = nextInt();
                }
                return a;
            }
    
            public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                    c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
            }
    
            public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                    c = snext();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
            }
    
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
    
            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }
    
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
        
    }
    class SegmentTree{
    int s[],n;
    
    int li[];
    long qn[];
	SegmentTree(int a[],long q[]){
        n=a.length;
        qn=q;
        li=a;
		int l=(int)Math.ceil(Math.log(n)/Math.log(2));
		l=2*(int)Math.pow(2,l)-1;
		s=new int[l];
		createSegmentTreeUtil(a, 0, 0, a.length-1);
	}
	
	int createSegmentTreeUtil(int a[],int root,int l,int r){
		if(l==r)
		s[root]=l;
		else
		s[root]= Compare(createSegmentTreeUtil(a, 2*root+1, l, (l+r)/2), createSegmentTreeUtil(a,2*root+2, (l+r)/2+1,r));
		return s[root];
	}
	int getValue(int gl,int gr){
		return getValueUtil(0, 0, n-1, gl, gr);
	}
	int getValueUtil(int root,int l,int r,int gl,int gr){
		if(l>=gl&&r<=gr){
			return s[root];
		}
		if(l>gr||r<gl){
			return n;
		}
		return Compare(getValueUtil(2*root+1, l, (l+r)/2, gl, gr), getValueUtil(2*root+2, (l+r)/2+1, r, gl, gr));
	}
	void update(int p,int k){
		updateUtil(p, k,0,0,n-1);
	}
	int updateUtil(int p,int k,int root,int l,int r){
		if(l==r&&l==k){
			return s[root]=p;
		}
		else if(l>k||r<k)
		return s[root];
		else{
			return s[root]=Compare(updateUtil(p, k, 2*root+1, l, (l+r)/2), updateUtil(p, k, 2*root+2,(l+r)/2+1,r ));
		}
	}
	int Compare(int a,int b){
        if(a>=n&&b>=n){
            System.out.println("adfna");
        }
        
		if(a>=n){
            return b;
        }
        if(b>=n){
            return a;
        }
        if(li[a]==li[b]){
            if(qn[a]>qn[b]){
                return a;
            }
            else return b;
        }
        else if(li[a]<li[b])
        return b;
        else return a;


	}
}