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.*;
import java.io.*;

public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		int tc,n,j,i,a[],b[],c[];
		Scanner sc=new Scanner(System.in);
		ArrayList<Integer> minp;
		TreeSet<Integer> maxp;
		HashSet<Integer> rem;
		
		tc=sc.nextInt();
		
		while(tc-->0)
		{
		    rem=new HashSet<>();
		    n=sc.nextInt();
		    for(i=0;i<n;i++)
		        rem.add(i+1);
		    
		    a=new int[n];
		    b=new int[n];
		    c=new int[n];
		    
		    for(i=0;i<n;i++)
		    {
	            a[i]=sc.nextInt();
	            b[i]=a[i];
	            c[i]=a[i];
	            
	            if(rem.contains(a[i]))
	                rem.remove(a[i]);
		    }
		    
		  //  System.out.println(rem);
		    
		    minp=new ArrayList<>();
		    maxp=new TreeSet<>();

		    for(int k:rem)
		    {
		        minp.add(k);
		        maxp.add(k);
		    }
	       Collections.sort(minp);
	       j=0;
	       
	       for(i=0;i<n;i++)
	       {
	           if(i>0&&a[i-1]==a[i])
	           {
	            b[i]=minp.get(j++);
	            c[i]=maxp.floor(a[i]);
	            maxp.remove(c[i]);
	           }
	       }
	       
	       prarray(b);
	       
	       prarray(c);
		}
	}
	public static void prarray(int a[])
	{
	    for(int i:a)
	        System.out.print(i+" ");
	   System.out.println();
	}
}