Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
#include <bits/stdc++.h>
using namespace std;
int main() {
  vector<int> arr(100001);
  vector<int> b(100001);
  int i, n;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> arr[i];
  }
  if (arr[0] > 1) {
    cout << "-1\n";
    return 0;
  }
  vector<bool> present(n, false);
  vector<bool> f(n, false);
  deque<int> q;
  if (arr[0] == 0) {
    b[0] = 1;
    present[1] = false;
    q.push_back(0);
    f[0] = true;
  } else {
    b[0] = 0;
    present[0] = true;
  }
  int flag = 1;
  for (i = 1; i < n; i++) {
    if (arr[i] == arr[i - 1]) {
      b[i] = b[i - 1];
      f[i] = true;
      q.push_back(i);
      continue;
    }
    b[i] = arr[i - 1];
    present[arr[i - 1]] = true;
    for (int j = arr[i - 1] + 1; j < arr[i]; j++) {
      if (present[j] == false) {
        if (q.empty()) {
          flag = 0;
          break;
        }
        int index = q.front();
        q.pop_front();
        b[index] = j;
        f[index] = false;
      }
    }
    if (flag == 0) {
      break;
    }
  }
  if (flag == 0) {
    cout << -1 << "\n";
    return 0;
  }
  for (i = 0; i < n; i++) {
    cout << b[i] << " ";
  }
  return 0;
}
