Problem: A permutation is a sequence of n integers from 1 to n, in which all numbers occur exactly once. For example, [1], [3, 5, 2, 1, 4], [1, 3, 2] are permutations, and [2, 3, 2], [4, 3, 1], [0] are not.

Polycarp was presented with a permutation p of numbers from 1 to n. However, when Polycarp came home, he noticed that in his pocket, the permutation p had turned into an array q according to the following rule: 

  * q_i = max(p_1, p_2, …, p_i). 



Now Polycarp wondered what lexicographically minimal and lexicographically maximal permutations could be presented to him.

An array a of length n is lexicographically smaller than an array b of length n if there is an index i (1 ≤ i ≤ n) such that the first i-1 elements of arrays a and b are the same, and the i-th element of the array a is less than the i-th element of the array b. For example, the array a=[1, 3, 2, 3] is lexicographically smaller than the array b=[1, 3, 4, 2].

For example, if n=7 and p=[3, 2, 4, 1, 7, 5, 6], then q=[3, 3, 4, 4, 7, 7, 7] and the following permutations could have been as p initially: 

  * [3, 1, 4, 2, 7, 5, 6] (lexicographically minimal permutation); 
  * [3, 1, 4, 2, 7, 6, 5]; 
  * [3, 2, 4, 1, 7, 5, 6]; 
  * [3, 2, 4, 1, 7, 6, 5] (lexicographically maximum permutation). 



For a given array q, find the lexicographically minimal and lexicographically maximal permutations that could have been originally presented to Polycarp.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line of each test case contains n integers q_1, q_2, …, q_n (1 ≤ q_i ≤ n).

It is guaranteed that the array q was obtained by applying the rule from the statement to some permutation p.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output two lines: 

  * on the first line output n integers — lexicographically minimal permutation that could have been originally presented to Polycarp; 
  * on the second line print n integers — lexicographically maximal permutation that could have been originally presented to Polycarp; 

Example

Input


4
7
3 3 4 4 7 7 7
4
1 2 3 4
7
3 4 5 5 5 7 7
1
1


Output


3 1 4 2 7 5 6 
3 2 4 1 7 6 5 
1 2 3 4 
1 2 3 4 
3 4 5 1 2 7 6 
3 4 5 2 1 7 6 
1 
1 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

    private static void run(Reader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }

        TreeSet<Integer> minT = new TreeSet<>();
        TreeSet<Integer> maxT = new TreeSet<>();
        for (int i = 1; i <= n; i++) {
            minT.add(i);
            maxT.add(i);
        }

        int[] min = new int[n];
        int[] max = new int[n];
        for (int i = 0; i < n; i++) {
            int now;
            if (maxT.contains(a[i])) {
                now = a[i];
            } else {
                now = maxT.lower(a[i]);
            }
            max[i] = now;
            maxT.remove(now);
        }

        for (int i = 0; i < n; i++) {
            int now;
            if (minT.contains(a[i])) {
                now = a[i];
            } else {
                now = minT.higher(0);
            }
            min[i] = now;
            minT.remove(now);
        }

        for (int i = 0; i < n; i++) {
            out.print(min[i]);
            out.print(' ');
        }
        out.println();
        for (int i = 0; i < n; i++) {
            out.print(max[i]);
            out.print(' ');
        }
        out.println();
    }

    public static void main(String[] args) throws IOException {
        Reader in = new Reader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            run(in, out);
        }

        out.flush();
        in.close();
        out.close();
    }

    static class Reader {
        BufferedReader reader;
        StringTokenizer st;

        Reader(InputStreamReader stream) {
            reader = new BufferedReader(stream, 32768);
            st = null;
        }

        void close() throws IOException {
            reader.close();
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        String nextLine() throws IOException {
            return reader.readLine();
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}