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:
    // package CFpracHim;
    /**
     * @Author : lucent868
     * @Date : 5/8/21
     * @Time : 9:57 PM
     */

    import java.util.*;
    import java.io.*;
    import java.math.*;

    public class BoxCF {
        static InputReader in;
        static PrintWriter w;

        public static void main(String args[]) {
            new Thread(null, new Runnable() {
                public void run() {
                    try {
                        solve();
                        w.flush();
                        w.close();
                    } catch (Exception e) {
                        e.printStackTrace();
                    }
                }
            }, "1", 1 << 26).start();
        }

        public static void solve() {
            in = new InputReader(System.in);
            w = new PrintWriter(System.out);

            int t = in.nextInt();
            while (t-- > 0) {
                int n = in.nextInt();
                int a[] = in.nextIntArray(n);

                int ans[] = new int[n];


                TreeSet<Integer> ts = new TreeSet<>();
                for(int i =1;i<=n;i++)
                    ts.add(i);

                int mark[] = new int[100001];

                ans[0] = a[0];
                ts.remove(ans[0]);
                mark[ans[0]] = 1;

                for(int i=1;i<n;i++)
                {
                    if(a[i] > a[i-1])
                    {
                        ans[i] = a[i];
                    }
                    else
                    {
                        ans[i] = ts.pollFirst();
                    }

                    mark[ans[i]]++;
                    ts.remove(ans[i]);
                }
//                for(int i=1;i<=n;i++)
//                    w.print(mark[i]+ " ");
//                w.println();

                int f=0;
                int max = ans[0];
                for(int i=1;i<n;i++)
                {
                    max = Math.max(max, ans[i]);
//                 w.println(max);
                   if( max != a[i] || mark[i+1] !=1)
                   {
                       f=1;
                       break;
                   }

                }

                if(f == 1 || mark[1] != 1)
                {
                    w.println("-1");
                    continue;
                }




                StringBuilder sb = new StringBuilder("");
                for(int i:ans)
                    sb.append(i+" ");

                w.println(sb);


            }
        }

        static class InputReader {
            private final InputStream stream;
            private final byte[] buf = new byte[8192];
            private int curChar, numChars;
            private SpaceCharFilter filter;

            public InputReader(InputStream stream) {
                this.stream = stream;
            }

            public int read() {
                if (numChars == -1) {
                    throw new InputMismatchException();
                }
                if (curChar >= numChars) {
                    curChar = 0;
                    try {
                        numChars = stream.read(buf);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (numChars <= 0) {
                        return -1;
                    }
                }
                return buf[curChar++];
            }

            public String nextLine() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                } while (!isEndOfLine(c));
                return res.toString();
            }

            public String readString() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                } while (!isSpaceChar(c));
                return res.toString();
            }

            public long nextLong() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    res *= 10;
                    res += c - '0';
                    c = read();
                } while (!isSpaceChar(c));
                return res * sgn;
            }

            public int nextInt() {
                int c = read();
                while (isSpaceChar(c)) {
                    c = read();
                }
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    res *= 10;
                    res += c - '0';
                    c = read();
                } while (!isSpaceChar(c));
                return res * sgn;
            }

            public int[] nextIntArray(int n) {
                int[] arr = new int[n];
                for (int i = 0; i < n; i++) {
                    arr[i] = nextInt();
                }
                return arr;
            }

            public long[] nextLongArray(int n) {
                long[] arr = new long[n];
                for (int i = 0; i < n; i++) {
                    arr[i] = nextLong();
                }
                return arr;
            }

            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

            private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
            }

            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }
    }