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>
const long long int mod = 1000000007;
const long long int MOD1 = (int)1e9 + 9;
const long long int MOD2 = 998244353;
const long double pi = atan2(0, -1);
const long double eps = 1e-9;
const int N = 2e5 + 5;
const int MAXR = 1000005;
long long int tests = 1;
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
long long int binarySearch(long long int l, long long int r, long long int k) {
  if (r >= l) {
    long long int mid = l + (r - l) / 2;
    if (mid * (mid + 1) == k) return 1;
    if (mid * (mid + 1) > k) return binarySearch(l, mid - 1, k);
    return binarySearch(mid + 1, r, k);
  }
  return 0;
}
bool sortinrev(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.first > b.first);
}
void swap(long long int *p1, long long int *p2) {
  long long int temp = *p1;
  *p1 = *p2;
  *p2 = temp;
}
long long int cbratt(long long int x) {
  long long int l = 0, r = MAXR;
  while (l != r) {
    long long int m = (l + r + 1) / 2;
    if (m * m * m > x)
      r = m - 1;
    else
      l = m;
  }
  return l;
}
int MaxSubArraySumReturn(int a[], int n) {
  int sum = 0, best = 0;
  for (long long int i = 0; i < n; i++) {
    sum = max(a[i], a[i] + sum);
    best = max(best, sum);
  }
  return best;
}
long long int totalDigits(long long int n) {
  long long int number_of_digits = 0;
  for (long long int i = 1; i <= n; i *= 10) number_of_digits += (n - i + 1);
  return number_of_digits;
}
int CeilIndex(std::vector<int> &v, int l, int r, int key) {
  while (r - l > 1) {
    int m = l + (r - l) / 2;
    if (v[m] >= key)
      r = m;
    else
      l = m;
  }
  return r;
}
int LongestIncreasingSubsequenceLength(std::vector<int> &v, int p) {
  if (v.size() == 0) return 0;
  std::vector<int> tail(v.size(), 0);
  int length = 1;
  tail[0] = v[0];
  for (size_t i = 1; i < v.size(); i++) {
    if (v[i] < tail[0])
      tail[0] = v[i];
    else if (v[i] > tail[length - 1])
      tail[length++] = v[i];
    else
      tail[CeilIndex(tail, -1, length - 1, v[i])] = v[i];
  }
  return (p - length);
}
long long int getPairsCount(long long int arr[], long long int n,
                            long long int sum) {
  int count = 0;
  map<int, int> mp;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      if (mp[i] == 0 && mp[j] == 0 && arr[i] + arr[j] == sum) {
        mp[i] = 1;
        mp[j] = 1;
        count++;
      }
    }
  }
  mp.clear();
  return count;
}
int main() {
  long long int n;
  cin >> n;
  long long int a[n + 1];
  long long int j = 1;
  for (long long int i = 2; i <= n; i++) {
    cout << "?"
         << " " << j << " " << i << endl;
    long long int x;
    cin >> x;
    cout << "?"
         << " " << i << " " << j << endl;
    long long int y;
    cin >> y;
    if (x > y) {
      long long int temp = x;
      a[j] = temp;
      j = i;
    } else {
      a[i] = y;
    }
  }
  a[j] = n;
  cout << "!"
       << " ";
  for (long long int i = 1; i <= n; i++) {
    cout << a[i] << " ";
  }
}