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.util.*;
import java.lang.*;
public class E
{  
    
    
    public static void main(String args[])
    {
        Scanner scan=new Scanner(System.in);
        int t=scan.nextInt();
        while(t--!=0){
                int n=scan.nextInt();
  int[] a=new int[n];
  
            for(int i=0;i<n;i++){
                a[i]=scan.nextInt();
            }
 
 
  PriorityQueue<Integer> minq=new PriorityQueue<Integer>();
  PriorityQueue<Integer> maxq=new PriorityQueue<Integer>(Collections.reverseOrder());
  List<Integer> minv=new ArrayList<Integer>();
            List<Integer> maxv=new ArrayList<Integer>();
            
 
  int prev=-1;
  int add=1;
  for(int i=0;i<n;i++)
  {
    if(a[i]!=prev){
        minv.add(a[i]);
        maxv.add(a[i]);
        while(add<a[i]) {minq.add(add); maxq.add(add); add++;}
        add++;
    }
    else{
        int mn=minq.poll();
        int mx=maxq.poll();
        minv.add(mn);
        maxv.add(mx);
    }
 
 
    prev=a[i];
  }
 
  //System.out.print(minq);
  for(int e:minv) System.out.print(e+" "); System.out.println();
  for(int e:maxv) System.out.print(e+" "); System.out.println();
        }
        }
        
    }