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 com.company.codeforces;


import javax.swing.*;
import java.util.*;

public class  Solution{
    public static void main(String[] args) {
          Scanner input=new Scanner(System.in);
          int t=input.nextInt();
          while (t-->0) {
              int n=input.nextInt();
              int a[]=new int[n];
              int c[]=new int[n+1];
              int k[]=new int[n+1];
              TreeSet<Integer> set=new TreeSet<>();

              for (int i = 0; i <n ; i++) {
                  a[i]=input.nextInt();
                  set.add(i+1);
              }

              int j=1;
              int min[]=new int[n];
              int max[]=new int[n];

              for (int i = 0; i <n ; i++) {
                  if (c[a[i]]==0){
                      min[i]=a[i];
                      c[a[i]]=1;
                  }else {
                      while (j<=n){
                          if (c[j]==0){
                              min[i]=j;
                              c[j]=1;
                              break;
                          }
                          j++;
                      }
                  }


                  //max
                  if (k[a[i]]==0){
                      max[i]=a[i];
                      k[a[i]]=1;


                  }else {
                      max[i]=set.lower(a[i]);
                  }
                  set.remove(max[i]);

              }
              for (int i = 0; i <n ; i++) {
                  System.out.print(min[i]+" ");
              }
              System.out.println();
              for (int i = 0; i <n ; i++) {
                  System.out.print(max[i]+" ");
              }
              System.out.println();




//              System.out.println(Arrays.toString(min));




          }
    }

}