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.text.Collator;
import java.util.*;

public class Solution {
  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
  public static void main(String[] args) throws Exception {
    int testCases = Integer.parseInt(br.readLine());
    for(int iter = 1; iter <= testCases; iter ++) {
      int n = Integer.parseInt(br.readLine());
      int[] nums = new int[n];
      var lines = br.readLine().split(" ");
      for(int i = 0; i < n; i ++)
        nums[i] = Integer.parseInt(lines[i]);
      solve(nums);
    }
    bw.flush();
    bw.close();
    br.close();
  }
  private static void solve(int[] nums) throws Exception {
    int n = nums.length;
    int[] maximum = new int[n];
    int[] minimum = new int[n];
    var maxSet = new TreeSet<Integer>();
    var minSet = new TreeSet<Integer>();
    boolean[] maxUsed = new boolean[n + 1];
    boolean[] minUsed = new boolean[n + 1];
    maxUsed[nums[0]] = true;
    minUsed[nums[0]] = true;
    maximum[0] = nums[0];
    minimum[0] = nums[0];
    for(int i = 1; i < n; i ++) {
      var num = nums[i];
      if(nums[i] != nums[i - 1]) {
        maximum[i] = num;
        minimum[i] = num;
        maxUsed[num] = true;
        minUsed[num] = true;
      }
    }
    for(int i = 1; i <= n; i ++) {
      if(!maxUsed[i]) maxSet.add(i);
      if(!minUsed[i]) minSet.add(i);
    }
    for(int i = 0; i < n; i ++) {
      if(maximum[i] == 0) {
        maximum[i] = maxSet.lower(nums[i]);
        maxSet.remove(maximum[i]);
      }
      if(minimum[i] == 0) {
        minimum[i] = minSet.first();
        minSet.remove(minimum[i]);
      }
    }
    print(minimum);
    print(maximum);
  }
  private static void print(int[] nums) throws Exception{
    var builder = new StringBuilder();
    for(int i = 0; i < nums.length - 1; i ++)
      builder.append(nums[i]).append(" ");
    builder.append(nums[nums.length - 1]).append("\n");
    bw.write(builder.toString());
  }
}