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 JAVA):

Solution:
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.StreamTokenizer;
import java.io.IOException;
import java.util.Arrays;
import java.io.PrintWriter;

public class Box {

	public static void main(String [] args) throws IOException {
		QuickInput in = new QuickInput();
		int t = in.nextInt();
		PrintWriter out = new PrintWriter(System.out);
		c : for (int u = 0; u < t; u++){
				int n = in.nextInt();
			
				boolean [] used = new boolean [n];
				Arrays.fill(used, false);
				int index = 0;
			
				int [] answer = new int [n];
				Arrays.fill(answer, 0);
			
				answer[0] = in.nextInt() - 1;
				used[answer[0]] = true;
				int MAX = answer[0];
			
				for (int i = 1; i < n; i++){
					int num = in.nextInt() - 1;
					if (num > MAX){
						answer[i] = num;
						used[num] = true;
						MAX = Math.max(MAX, answer[i]);
					} else {
						while(used[index] && index < num)
							index++;
						if (index == num){
							while(++i < n)
								in.nextInt();
							out.println(-1);
							continue c;
						} else {
							answer[i] = index;
							used[index] = true;
						}
					}
				}
				
				for (int nm : answer)
					out.print((nm + 1) + " ");
				out.println();
			}
		out.flush();
		out.close();
	}

}

class QuickInput {
	
	StreamTokenizer stk;
	
	QuickInput(){
		stk = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
	}
	
	int nextInt() throws IOException {
		stk.nextToken();
		return (int) stk.nval;
	}
	
}