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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int> > sas[10001];
int tab[10001];
int main() {
  int i;
  int n;
  cin >> n;
  int maxpos = 1;
  for (i = 2; i < n + 1; i++) {
    int answ, answ2;
    cout << "? " << i << " " << maxpos << "\n" << flush;
    cin >> answ;
    cout << "? " << maxpos << " " << i << "\n" << flush;
    cin >> answ2;
    if (answ < answ2) {
      sas[i].push_back({maxpos, answ2});
      maxpos = i;
    } else
      sas[maxpos].push_back({i, answ});
  }
  queue<int> Q;
  Q.push(maxpos);
  tab[maxpos] = n;
  while (Q.size()) {
    int v = Q.front();
    Q.pop();
    for (auto j : sas[v]) {
      if (tab[j.first]) continue;
      tab[j.first] = j.second;
      Q.push(j.first);
    }
  }
  cout << "! ";
  for (i = 1; i < n + 1; i++) cout << tab[i] << " ";
  cout << "\n" << flush;
  return 0;
}