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:
//package round_710;


import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class E {
    static class InputReader {
        BufferedReader buffreader;
        StringTokenizer strtokenizer;
        public InputReader(InputStream inputstr) {
            buffreader = new BufferedReader(new InputStreamReader(inputstr), 1000000);strtokenizer = null; }
        //////////////////////////////////////////////////////////////////////////////////////////
        String next() {
            while (strtokenizer == null || !strtokenizer.hasMoreTokens()) {
                try { strtokenizer = new StringTokenizer(buffreader.readLine()); }
                catch (IOException e) { throw new RuntimeException(e); }
            }
            return strtokenizer.nextToken(); }
        ///////////////////////////////////////////////////////////////////////////////////////////
        public int nextInt() { return Integer.parseInt(next()); }
        public long nextLong() { return Long.parseLong(next()); }
        public double nextDouble() { return Double.parseDouble(next()); }
        public int[] nextIntArr(int n){
            int[] arr=new int[n];
            for (int i=0;i<n;i++){arr[i]=nextInt();}
            return arr;}
        public long[] nextLongArr(int n){
            long[] arr=new long[n];
            for (int i=0;i<n;i++){arr[i]=nextLong();}
            return arr;}
        public String[] nextStringArr(int n){
            String[] arr=new String[n];
            for (int i=0;i<n;i++){arr[i]=next();}
            return arr;}
    }
    static InputReader r = new InputReader(System.in);
    static PrintWriter pw = new PrintWriter(System.out);
    public static void main(String[] args){
        int t=r.nextInt();
        for (int v=0;v<t;v++) {
            int n = r.nextInt();
            int[] arr = r.nextIntArr(n);

            boolean[] used=new boolean[n+1];

            int[] base=new int[n];
            Arrays.fill(base,-1);
            base[0]=arr[0];used[arr[0]]=true;
            for (int i=1;i<arr.length;i++){
                if (arr[i]!=arr[i-1]){
                    base[i]=arr[i];
                    used[arr[i]]=true;
                }
            }
            int num=1;

            for (int i:base){
                if (i!=-1){
                    pw.print(i+" ");
                }
                else{
                    while (used[num]){
                        num++;
                    }
                    pw.print(num+" ");num++;
                }
            }
            pw.println();

            ArrayList<Integer> list=new ArrayList<>();
            for (int i=1;i<used.length;i++){
                if (!used[i]){
                    list.add(i);
                }
            }
            int z=0;
            for (int i:base){
                if (i!=-1){
                    pw.print(i+" ");
                    z=i;
                }
                else{
                    //Collections.sort(list);
                    int left=0;
                    int right=list.size()-1;
                    while (left<right){
                        int mid=(left+right+1)/2;
                        if (list.get(mid)<z){
                            left=mid;
                        }
                        else{
                            right=mid-1;
                        }
                    }
                    num=list.get(left);
                    list.remove(left);
                    pw.print(num+" ");
                }
            }
            pw.println();









        }
        pw.close();





    }
}