Problem: Permutation p is a sequence of integers p=[p_1, p_2, ..., p_n], consisting of n distinct (unique) positive integers between 1 and n, inclusive. For example, the following sequences are permutations: [3, 4, 1, 2], [1], [1, 2]. The following sequences are not permutations: [0], [1, 2, 1], [2, 3], [0, 1, 2].

The important key is in the locked box that you need to open. To open the box you need to enter secret code. Secret code is a permutation p of length n. 

You don't know this permutation, you only know the array q of prefix maximums of this permutation. Formally:

  * q_1=p_1, 
  * q_2=max(p_1, p_2), 
  * q_3=max(p_1, p_2,p_3), 
  * ... 
  * q_n=max(p_1, p_2,...,p_n). 



You want to construct any possible suitable permutation (i.e. any such permutation, that calculated q for this permutation is equal to the given array).

Input

The first line contains integer number t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

The first line of a test case contains one integer n (1 ≤ n ≤ 10^{5}) — the number of elements in the secret code permutation p.

The second line of a test case contains n integers q_1, q_2, ..., q_n (1 ≤ q_i ≤ n) — elements of the array q for secret permutation. It is guaranteed that q_i ≤ q_{i+1} for all i (1 ≤ i < n).

The sum of all values n over all the test cases in the input doesn't exceed 10^5.

Output

For each test case, print:

  * If it's impossible to find such a permutation p, print "-1" (without quotes). 
  * Otherwise, print n distinct integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n). If there are multiple possible answers, you can print any of them. 

Example

Input


4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1


Output


1 3 4 5 2 
-1
2 1 
1 

Note

In the first test case of the example answer [1,3,4,5,2] is the only possible answer:

  * q_{1} = p_{1} = 1; 
  * q_{2} = max(p_{1}, p_{2}) = 3; 
  * q_{3} = max(p_{1}, p_{2}, p_{3}) = 4; 
  * q_{4} = max(p_{1}, p_{2}, p_{3}, p_{4}) = 5; 
  * q_{5} = max(p_{1}, p_{2}, p_{3}, p_{4}, p_{5}) = 5. 



It can be proved that there are no answers for the second test case of the example.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  std::vector<unsigned long long> ans;
  bool *used, fik, fiks;
  unsigned long long *all, t, n, last;
  std::cin >> t;
  for (unsigned long long g = 0; g < t; g++) {
    std::cin >> n;
    fik = fiks = true;
    fiks = false;
    all = new unsigned long long[n];
    used = new bool[n];
    for (unsigned long long er = 0; er < n; er++) {
      std::cin >> all[er];
      all[er]--;
      used[er] = true;
    }
    last = 0;
    ans.push_back(all[0]);
    used[all[0]] = false;
    for (unsigned long long er = 1; er < n; er++) {
      if (all[er] != all[er - 1]) {
        ans.push_back(all[er]);
        used[all[er]] = false;
      } else {
        ans.push_back(all[er]);
        if (used[last]) {
          ans[ans.size() - 1] = last;
          last++;
        } else {
          fiks = true;
          for (last++; (last < all[er]) && (fiks); last++) {
            if (used[last]) {
              ans[ans.size() - 1] = last;
              used[last] = false;
              fiks = false;
            }
          }
        }
        if (fiks) {
          fik = false;
          er = n;
        }
        fiks = false;
      }
    }
    if (fik) {
      for (unsigned long long ger = 0; ger < n; ger++) {
        std::cout << ans[ger] + 1 << " ";
      }
    } else {
      std::cout << -1;
    }
    std::cout << std::endl;
    ans.clear();
    delete[] used;
    delete[] all;
  }
}