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.util.Arrays;
public class Main{

static int maxn = (int)2e5+10;
static int[] f = new int[maxn];
public int maxArea(int[] height) {
     int length = height.length;
     if(length<=1) return -1;
     int i=0,j=length-1;
     int maxx = 0 ;
     while(i<j){
     	int h = Math.min(height[i],height[j]);
     	maxx = Math.max(maxx,(j-i)*h);
     	if(height[i]<height[j]) i++;
     	else j--;
     }
     return maxx;
}
public static void main(String[] args){	    
	     Scanner in  = new Scanner(System.in);
	     int t;
          t = in.nextInt();
         for(int k=1;k<=t;k++){
             int n;
             n = in.nextInt();
             int[] a = new int[n+1];
             int[] ans1 = new int[n+1];int[] ans2 = new int[n+1];
             int[] cnt1 = new int[n+1];   int[] cnt2 = new int[n+1];
             int c1 = 0,f1 =1,c2=0;
             for(int j=1;j<=n;j++) a[j] = in.nextInt();
             for(int j=1;j<=n;j++){
                 if(a[j]!=a[j-1]){
                    ans1[j] = ans2 [j]  = a[j];
                    for(int f = a[j-1]+1;f<a[j];f++){
                         cnt1[++c1] = f;
                         cnt2[++c2] = f;
                    }
                 }
                 else{
                    ans1[j] = cnt1[f1];f1++;
                    ans2[j] =  cnt2[c2];c2--;
                 }
             }
             for(int j=1;j<=n;j++) System.out.print(ans1[j] + " ");
             System.out.println();
              for(int j=1;j<=n;j++) System.out.print(ans2[j] + " ");
             System.out.println();  
          }
 	}
}