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;
using ll = int64_t;
using ar2 = array<int, 2>;
template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using max_heap = priority_queue<T>;
const int maxn = 1e4 + 69;
int a[maxn], n;
int ask(int x, int y) {
  printf("? %d %d\n", x, y);
  fflush(stdout);
  int k;
  scanf("%d", &k);
  return k;
}
void solve(int x, int y) {
  int p = ask(x, y);
  int q = ask(y, x);
  if (p > q)
    a[x] = p;
  else
    a[y] = q;
}
void solve() {
  scanf("%d", &n);
  int i = 1, j = 2;
  while (j <= n) {
    solve(i, j);
    while (i <= n && a[i] != 0) ++i;
    while (j <= i) ++j;
    while (j <= n && a[j] != 0) ++j;
  }
  a[i] = n;
  printf("! ");
  for (i = 1; i <= n; ++i) printf("%d ", a[i]);
  puts("");
}
int main() {
  int tc = 1;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}