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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n;
  int arr[100005];
  int toUse[100005];
  memset(toUse, -1, sizeof(toUse));
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    toUse[arr[i]] = i;
  }
  if (arr[0] > 1) {
    cout << -1;
    return 0;
  }
  vector<int> ans;
  int prev;
  if (arr[0] == 0) {
    for (prev = 1;; prev++) {
      if (toUse[prev] < 0) break;
    }
    ans.push_back(prev);
    toUse[prev] = 9999999;
  } else if (arr[0] == 1) {
    for (prev = 1;; prev++) {
      if (toUse[prev] < 0) break;
    }
    ans.push_back(prev);
    toUse[prev] = 9999999;
  }
  for (int i = 1; i < n; i++) {
    if (arr[i] != arr[i - 1]) {
      if (toUse[arr[i - 1]] > i) {
        cout << -1;
        return 0;
      }
      int push = arr[i - 1];
      ans.push_back(push);
      toUse[push] = 9999999;
      prev = push;
    } else {
      int push = prev + 1;
      while (toUse[push] >= i) push++;
      ans.push_back(push);
      toUse[push] = 9999999;
      prev = push;
    }
  }
  for (auto& x : ans) cout << x << " ";
  return 0;
}
