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;
int main() {
  int N;
  cin >> N;
  if (N == 1) {
    cout << "! 1" << endl;
    return 0;
  }
  vector<int> res(N);
  for (;;) {
    int x = 0, y = 0;
    for (int i = 0; i < N; ++i) {
      if (x == 0 && res[i] == 0) {
        x = i + 1;
      } else if (res[i] == 0) {
        y = i + 1;
        break;
      }
    }
    if (y == 0) break;
    int z, w;
    cout << "? " << x << " " << y << endl;
    cin >> z;
    cout << "? " << y << " " << x << endl;
    cin >> w;
    if (z == 0) {
      res[y - 1] = w;
    } else if (w == 0) {
      res[x - 1] = z;
    } else if (z > w) {
      res[x - 1] = z;
    } else {
      res[y - 1] = w;
    }
  }
  set<int> a;
  for (int i = 1; i <= N; ++i) a.insert(i);
  for (auto x : res) a.erase(x);
  for (auto& x : res)
    if (x == 0) x = *a.begin();
  cout << "!";
  for (auto x : res) cout << " " << x;
  cout << endl;
}