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_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  vector<long long int> v(n, 0);
  for (long long int i = 0; i < n; i++) cin >> v[i];
  long long int b[n];
  for (long long int i = 1; i < n; i++) {
    b[i] = -1;
    if (v[i] != v[i - 1]) b[i] = v[i - 1];
  }
  if (v[0] == 0) {
    b[0] = 1;
    long long int n0 = -1;
    bool f = true;
    for (long long int i = 1; i < n; i++) {
      if (v[i] > (i + 1)) f = false;
      if (v[i] != 0) {
        n0 = i;
        break;
      }
    }
    vector<long long int> e;
    for (long long int i = n0; i < n; i++) {
      for (long long int j = v[i] - 1; j >= v[i - 1] + 1; j--) {
        if (j != 1) e.push_back(j);
      }
    }
    long long int len = e.size() - 1;
    for (long long int i = 1; i < n; i++) {
      if (b[i] == -1 && len == -1)
        b[i] = 1;
      else if (b[i] == -1 && len > -1)
        b[i] = e[len--];
    }
    if (len > -1) f = false;
    if (f) {
      for (long long int i = 0; i < n; i++) cout << b[i] << " ";
      cout << endl;
    } else
      cout << "-1" << endl;
  } else if (v[0] == 1) {
    b[0] = 0;
    long long int n0 = -1;
    bool f = true;
    for (long long int i = 1; i < n; i++) {
      if (v[i] > (i + 1)) f = false;
      if (v[i] != 1) {
        n0 = i;
        break;
      }
    }
    b[n0] = 0;
    vector<long long int> e;
    for (long long int i = n0; i < n; i++) {
      for (long long int j = v[i] - 1; j >= v[i - 1] + 1; j--) {
        if (j != 1 && j != 0) e.push_back(j);
      }
    }
    long long int len = e.size() - 1;
    for (long long int i = 1; i < n; i++) {
      if (b[i] == -1 && len == -1)
        b[i] = 0;
      else if (b[i] == -1 && len > -1)
        b[i] = e[len--];
    }
    if (len > -1) f = false;
    if (f) {
      for (long long int i = 0; i < n; i++) cout << b[i] << " ";
      cout << endl;
    } else
      cout << "-1" << endl;
  } else
    cout << "-1" << endl;
}
