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.lang.*;
import java.util.*;

public class E1506 {
    public static void main(String[] args) throws IOException{
        StringBuffer ans = new StringBuffer();
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int t = Integer.parseInt(st.nextToken());
        for(int i = 0; i < t; i++){
            st = new StringTokenizer(f.readLine());
            int n = Integer.parseInt(st.nextToken());
            int[] arr = new int[n];
            st = new StringTokenizer(f.readLine());
            PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());
            PriorityQueue<Integer> pqr = new PriorityQueue<>();
            ArrayList<Integer> ft = new ArrayList<>();
            ArrayList<Integer> sc = new ArrayList<>();
            int curr = Integer.parseInt(st.nextToken());
            arr[0] = curr;
            ft.add(arr[0]);
            sc.add(arr[0]);
            for(int x = 1; x < curr; x++){
                pq.add(x);
                pqr.add(x);
            }
            for(int x = 1; x < n; x++){
                arr[x] = Integer.parseInt(st.nextToken());
                if(arr[x] != curr){
                    ft.add(arr[x]);
                    sc.add(arr[x]);
                    for(int y = curr+1; y < arr[x]; y++){
                        pq.add(y);
                        pqr.add(y);
                    }
                    curr = arr[x];
                }else{
                    ft.add(pq.poll());
                    sc.add(pqr.poll());
                }

            }
            for(int x : sc){
                ans.append(x).append(" ");
            }
            ans.append("\n");
            for(int x : ft){
                ans.append(x).append(" ");
            }
            ans.append("\n");
        }
        f.close();



        System.out.println(ans);
    }

}