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>
int n, a[10001], b[10000], max_b, found, shit;
int main() {
  std::cin >> n;
  for (int i = 0; i < n; ++i) std::cin >> a[i];
  a[n] = a[n - 1];
  shit = 0;
  if (a[0] == 0) {
    b[0] = 1;
  } else {
    b[0] = 0;
  }
  max_b = b[0];
  for (int i = 1; i < n; ++i) {
    if (max_b + 2 < a[i]) {
      std::cout << max_b + 1 << a[i] << std::endl;
      std::cout << -1 << std::endl;
      shit = 1;
      break;
    }
    if (a[i - 1] < a[i]) {
      b[i] = a[i - 1];
      if (b[i] > max_b) {
        max_b = b[i];
      }
    } else {
      found = 0;
      for (int j = i - 1; j < n - 1; ++j) {
        if (found == 1) {
          break;
        }
        if ((a[j + 1] - a[j]) > 1) {
          for (int k = a[j] + 1; k < a[j + 1]; ++k) {
            if (k > max_b) {
              b[i] = k;
              max_b = b[i];
              found = 1;
              break;
            }
          }
        }
      }
      if (found == 0) {
        b[i] = a[n - 1] + 1;
        if (max_b > b[i]) {
          b[i] = max_b + 1;
          max_b = b[i];
        } else {
          max_b = b[i];
        }
      }
    }
  }
  if (shit == 0) {
    for (int i = 0; i < n; ++i) {
      std::cout << b[i] << " ";
    }
  }
}
