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 Coding {

    static long MOD = 1000000007;
    static long[] fact = new long[100002];
    static long[] pow2 = new long[100002];

    public static void main(String[] args) {
        BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        //precompute();
        try {
            int t = 1;
            while (t > 0) {
                int n = Integer.valueOf(bi.readLine());
                int[] ans = new int[n+1];
                for(int i=1;i<=n;++i) {
                    ans[i] = -1;
                }
                List<Integer> values = new ArrayList<>();
                List<Integer> indexes = new ArrayList<>();
                for(int i=1;i<=n;++i) {
                    values.add(i);
                    indexes.add(i);
                }
                boolean invalid = false;
                int[] left =  new int[n+1];
                for(int i=1;i<=n;++i) {
                    left[i] = -1;
                }
                while (!indexes.isEmpty()) {
                    if (indexes.size()==1) {
                        int val = 1;
                        for(int i=1;i<=n;++i) {
                            if (left[i]==-1) {
                                val = i;
                                break;
                            }
                        }
                        ans[indexes.get(0)] = val;
                        break;
                    }
                    int id1 = indexes.get(0);
                    int id2 = indexes.get(1);
                    writer.append("? " + id1 + " " + id2);
                    writer.append('\n');
                    writer.flush();
                    int k1 = Integer.valueOf(bi.readLine());
                    if (k1==-1) {
                        invalid = true;
                        break;
                    }
                    writer.append("? " + id2 + " " + id1);
                    writer.append('\n');
                    writer.flush();
                    int k2 = Integer.valueOf(bi.readLine());
                    if (k2==-1) {
                        invalid = true;
                        break;
                    }
                    if (k1>k2) {
                        ans[id1] = k1;
                        left[k1] = 1;
                        indexes.remove(0);
                    } else {
                        ans[id2] = k2;
                        left[k2] = 1;
                        indexes.remove(1);
                    }
                }
                if (invalid) {
                    break;
                }
                writer.append("!");
                for(int i=1;i<=n;++i) {
                    writer.append(" " + ans[i]);
                }
                writer.append('\n');
                writer.flush();
                t--;
            }
            writer.flush();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }



    private static int gcd(int a, int b) {
        if (a<b) {
            return gcd(b, a);
        }
        if (a%b==0) {
            return b;
        }
        return gcd(b, a%b);
    }

    private static void dfs(int cur, List<Integer>[] adj, long[] nodeCount, int parent) {
        for(int i=0;i<adj[cur].size();++i) {
            int nxt = adj[cur].get(i);
            if (nxt!=parent) {
                dfs(nxt, adj, nodeCount, cur);
                nodeCount[cur]+=nodeCount[nxt];
            }
        }
    }

    private static int findDist(int a, int b, int[] par) {
        Map<Integer, Integer> dist = new HashMap<>();
        int count = 0;
        dist.put(a, 0);
        while (par[a]!=-1) {
            a = par[a];
            count++;
            dist.put(a, count);
        }
        count=0;
        while(!dist.containsKey(b)) {
            b = par[b];
            count++;
        }
        return count+dist.get(b);
    }

    private static int findLongestPath(int cur, int prev, List<Integer>[] adj, int[] dep) {
        int diameter = 0;
        int highest = -1, second=-1;
        for(int i=0;i<adj[cur].size();++i) {
            int nxt = adj[cur].get(i);
            if (nxt!=prev) {
                diameter = Math.max(diameter, findLongestPath(nxt, cur, adj, dep));
                if (dep[nxt]>highest) {
                    second = highest;
                    highest = dep[nxt];
                } else if (dep[nxt]>second) {
                    second = dep[nxt];
                }
            }
        }
        diameter = Math.max(diameter, highest + second + 2);
        return diameter;
    }

    static long ncr(int n, int r) {
        long num = fact[n];
        long denom = (modExp(fact[r], MOD-2)*modExp(fact[n-r], MOD-2))%MOD;
        //System.out.println("num is " + num + " denom is" + denom);
        return (num*denom)%MOD;
    }

    static long modExp(long a, long b) {
        //System.out.println("a is " + a + " and b is " + b);
        if (a==1) return 1;
        long ans = 1;
        while (b!=0) {
            if (b%2==1) {
                ans = (ans*a)%MOD;
            }
            a = (a*a)%MOD;
            b/=2;
        }
        return ans;
    }

    private static void precompute() {
        fact[0] = 1;
        pow2[0] = 1;
        for(int i=1;i<=100000;++i) {
            fact[i] = (fact[i-1]*i)%MOD;
            pow2[i] = (pow2[i-1]*2)%MOD;
        }
    }
}