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.*;
import java.util.*;
public class code {
	static printer pw;
	static boolean[] visit;
	static ArrayList<Pair>[] adj;
	static ArrayList<Integer> list;
	static long max=01;
	static void dfs(int i, long c) {
		visit[i]=true;
		max=Math.max(c, max);
		for(Pair p: adj[i]) {
			if(!visit[p.x-1]) {
				dfs(p.x-1, c+1l*p.y);
			}
		}
	}
	public static double dist(Pair a, Pair b) {
		return Math.sqrt((a.x-b.x)*(a.x-b.x)+ (a.y-b.y)*(a.y-b.y));
	}
	public static boolean sign(int x) {
		return x>0;
	}
	static int test(int[] arr, int mid) {
		int ans=0;
		for(int i=1; i<arr.length; i++) {
			if(arr[i]==-1 && arr[i-1]!=-1) {
				if(Math.abs(mid-arr[i-1])>Math.abs(ans))
					ans=mid-arr[i-1];
			}
			if(arr[i]!=-1 && arr[i-1]==-1) {
				if(Math.abs(mid-arr[i])>Math.abs(ans))
					ans=mid-arr[i];
			}
		}
		return ans;
	}
	public static void main(String[] args) throws Exception {
		Scanner sc= new Scanner(System.in);
		pw = new printer();
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			int[] arr=sc.nextArr(n);
			int[] ans=new int[n];
			TreeSet<Integer> tree=new TreeSet<Integer>();
			for(int i=1; i<=n; i++)
				tree.add(i);
			for(int i=0; i<n; i++) {
				if(i==0 || arr[i]>arr[i-1]) {
					ans[i]=arr[i];
					tree.remove(ans[i]);
				}
			}
			boolean valid=true;
			for(int i=0; i<n; i++) {
				if(ans[i]==0) {
					int x=tree.first();
					if(x<=arr[i] && arr[i]>=arr[i-1]) {
						tree.remove(x);
						ans[i]=x;
					}else {
						valid=false;
						break;
					}
				}
			}
			if(!valid)
				pw.println(-1);
			else
				pw.printArr(ans);
		}
		pw.close();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public int[] nextArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}
		public Integer[] nextsort(int n) throws IOException{
			Integer[] arr=new Integer[n];
			for(int i=0; i<n; i++) 
				arr[i]=nextInt();
			return arr;
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
	}
	static class printer{
		PrintWriter pw;
		public printer() {
			pw=new PrintWriter(System.out);
		}
		public void print(String s) throws IOException{
			pw.print(s);
		}
		public void print(int s) throws IOException{
			pw.print(s);
		}
		public void print(long s) throws IOException{
			pw.print(s);
		}
		public void print(char s) throws IOException{
			pw.print(s);
		}
		public void print(Integer s) throws IOException{
			pw.print(s);
		}
		public void print(Long s) throws IOException{
			pw.print(s);
		}
		public void print(Character s) throws IOException{
			pw.print(s);
		}
		public void println(String s) throws IOException{
			pw.println(s);
		}
		public void println(int s) throws IOException{
			pw.println(s);
		}
		public void println(long s) throws IOException{
			pw.println(s);
		}
		public void println(char s) throws IOException{
			pw.println(s);
		}
		public void println(Integer s) throws IOException{
			pw.println(s);
		}
		public void println(Long s) throws IOException{
			pw.println(s);
		}
		public void println(Character s) throws IOException{
			pw.println(s);
		}
		public void printArr(int[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(Integer[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(long[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(Long[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(char[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(Character[] arr) throws IOException{
			for(int i=0; i<arr.length-1; i++)
				pw.print(arr[i]+" ");
			pw.println(arr[arr.length-1]);
		}
		public void printArr(ArrayList arr) throws IOException{
			for(int i=0; i<arr.size()-1; i++)
				pw.print(arr.get(i)+" ");
			pw.println(arr.get(arr.size()-1));
		}
		public void close() throws IOException{
			pw.close();
		}
		public void flush() throws IOException{
			pw.flush();
		}
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		public Pair(int a, int b) {
			this.x=a;
			this.y=b;
		}
		public int compareTo(Pair other) {
			return this.y-other.y;
		}
	}
	static class Triple implements Comparable<Triple>{
		int x;
		int y;
		boolean d;
		public Triple(int a, int b, boolean t) {
			this.x=a;
			this.y=b;
			this.d=t;
		}
		public int compareTo(Triple other) {
			if(this.d && !other.d) {
				return 1;
			}else if(!this.d && other.d) {
				return -1;
			}else {
				return this.y-other.y;
			}
		}
	}
}