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;
using ll = long long;
template <class T>
using V = vector<T>;
template <class T, class U>
using P = pair<T, U>;
using vll = V<ll>;
using vii = V<int>;
using vvll = V<vll>;
using vvii = V<V<int> >;
using PII = P<int, int>;
using PLL = P<ll, ll>;
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class A, class B>
ostream& operator<<(ostream& out, const P<A, B>& p) {
  return out << '(' << p.first << ", " << p.second << ')';
}
template <class A>
ostream& operator<<(ostream& out, const V<A>& v) {
  out << '[';
  for (int i = 0; i < int(v.size()); i++) {
    if (i) out << ", ";
    out << v[i];
  }
  return out << ']';
}
template <class A, class B>
istream& operator>>(istream& in, P<A, B>& p) {
  return in >> p.first >> p.second;
}
template <class A>
istream& operator>>(istream& in, V<A>& v) {
  for (int i = 0; i < int(v.size()); i++) in >> v[i];
  return in;
}
const long long MOD = 1000000007;
const long long HIGHINF = (long long)1e18;
const int INF = (int)1e9;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  set<int> cand;
  for (ll i = 0; i < 1000001; i++) cand.insert(i);
  int n;
  cin >> n;
  vii a(n);
  cin >> a;
  for (ll i = 0; i < n; i++) {
    if (i + 1 < a[i]) {
      cout << -1 << '\n';
      return 0;
    }
    cand.erase(a[i]);
  }
  vii b(n, INF);
  for (ll i = 1; i < n; i++) {
    if (a[i - 1] != a[i]) b[i] = a[i - 1];
  }
  for (ll i = 0; i < n; i++) {
    if (b[i] == INF) {
      b[i] = *cand.begin();
      cand.erase(cand.begin());
    }
  }
  for (ll i = 0; i < n; i++) {
    if (i) cout << ' ';
    cout << b[i];
  }
  cout << '\n';
  return 0;
}
