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.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
// import java.io.PrintWriter;     // System.out is a PrintWriter
import java.util.Arrays;
// import java.util.ArrayList;
// import java.util.Collections;    //  for ArrayList sorting mainly
// import java.util.HashMap;
// import java.util.HashSet;
import java.util.Random;
import java.util.StringTokenizer;

public class C {
    public static void main(String[] args) throws Exception {
        FastScanner scn = new FastScanner();
        int N = scn.nextInt(), ff = 0, ss = 1, qry = N;
        long[] arr = new long[N];
        long sum = (N * (N + 1L)) >> 1L, pSum = 0L;
        while (qry-- > 0 && ff < N && ss < N) {
            System.out.println("? " + (ff + 1) + " " + (ss + 1));
            int aMb = scn.nextInt();
            System.out.flush();
            System.out.println("? " + (ss + 1) + " " + (ff + 1));
            int bMa = scn.nextInt();
            System.out.flush();
            if (aMb < bMa) {
                arr[ss] = bMa;
                pSum += bMa;
                while (ss < N && (arr[ss] != 0) || (ss == ff))
                    ss++;
            } else if (bMa < aMb) {
                arr[ff] = aMb;
                pSum += aMb;
                while (ff < N && (arr[ff] != 0 )|| (ss == ff))
                    ff++;
            }
        }
        long leftOut = (sum - pSum);
        System.out.print("! ");
        for (int i = 0; i < N; i++) {
            if (arr[i] == 0) arr[i] = leftOut;
            System.out.print(arr[i] + " ");
        } System.out.println();
    }

    static class Pair implements Comparable<Pair> {
        int ff, ss; // default 0 --> first and second
        
        public Pair(int first, int second) {
            this.ff = first;
            this.ss = second;
        }

        @Override
        public int compareTo(Pair o) {
            if (ff != o.ff)
                return ff - o.ff;
            return ss - o.ss;
        }

        @Override
        public String toString() {
            return "[" + ff + ", " + ss + "]";
        }
    }

    static final Random random = new Random();

    static void ruffleSort(int[] arr) {
        for (int i = 0, N = arr.length; i < N; i++) {
            int randIdx = random.nextInt(N);
            // swap
            int temp = arr[randIdx];
            arr[randIdx] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr); // NOTE use quick-sort for primitive types, merge-sort for objects implementing Comparable/Comparator
    }
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        FastScanner() {
            this.br = new BufferedReader(new InputStreamReader(System.in));
            this.st = new StringTokenizer("");
        }
        FastScanner(String file) {
            try {
                java.io.File inpFile = new java.io.File(file);
                this.br = new BufferedReader(new java.io.FileReader(inpFile));
            } catch (FileNotFoundException err) {
                err.printStackTrace();
            }
            this.st = new StringTokenizer("");
        }

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException err) {
                    err.printStackTrace();
                }
            return st.nextToken();
        }

        String nextLine() {
            if (st.hasMoreTokens()) {
                return st.nextToken("").trim();
            }
            try {
                return br.readLine().trim();
            } catch (IOException err) {
                err.printStackTrace();
            }
            return "";
        }

        byte nextByte() {
            return Byte.parseByte(next());
        }

        short nextShort() {
            return Short.parseShort(next());
        }

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

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

        float nextFloat() {
            return Float.parseFloat(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] readIntArray(final int N) {
            int[] arr = new int[N];
            for (int i = 0; i < N; i++)
                arr[i] = nextInt();
            return arr;
        }
    }
}