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>
using namespace std;
const long long MOD = 1e9 + 7;
long long q[(long long)1e6];
long long p[(long long)1e6];
long long st[(long long)1e6];
long long taken[(long long)1e6];
int main() {
  long long t;
  cin >> t;
  t++;
  while (--t) {
    long long takenl = 0;
    long long n;
    cin >> n;
    for (long long i = 0; i < n; i++) cin >> q[i];
    long long ret = 0;
    for (long long i = 0; i < n; i++) {
      if (q[i] < i + 1 || q[i] > n) {
        cout << -1 << endl;
        ret = 1;
        break;
      }
    }
    if (ret) continue;
    p[0] = q[0];
    st[0] = t;
    taken[takenl] = p[0];
    takenl++;
    long long pr = q[0];
    for (long long i = 1; i < n; i++) {
      if (q[i] != pr) {
        pr = q[i];
        p[i] = q[i];
        st[i] = t;
        taken[takenl] = p[i];
        takenl++;
      }
    }
    sort(taken, taken + takenl);
    long long takeni = 0;
    long long num = 1;
    for (long long i = 0; i < n; i++) {
      if (st[i] != t) {
        while (takeni < takenl && num == taken[takeni]) {
          num++;
          takeni++;
        }
        p[i] = num;
        num++;
      }
    }
    for (long long i = 0; i < n; i++) {
      cout << p[i] << ' ';
    }
    cout << endl;
  }
}