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.util.*;

public class Q5 {

	static Scanner sc = new Scanner(System.in);
	static BufferedWriter bw =new BufferedWriter(new OutputStreamWriter(System.out));
	public static void main(String[] args) throws IOException {
		int t = sc.nextInt();
		while(t-->0) {
			solve();
		}
		bw.flush();
		bw.close();
		
	}
	
	public static void solve() throws IOException {
		
		int n = sc.nextInt();
		int[] arr = new int[n];
		TreeSet<Integer> set = new TreeSet<>();
		TreeSet<Integer> set2 = new TreeSet<>();
		
		int prev = -1;
		for(int i = 0;i < n;i++) {
			arr[i] = sc.nextInt();
			set.add(i + 1);
			set2.add(i + 1);
		}
		
		int[] min = getMin(set, arr, n);
		int[] max = getMax(set2, arr, n);
		
		print(min);
		print(max);
		
	}
	
	public static void print(int[] arr) throws IOException {
		for(int ix : arr)bw.write(String.valueOf(ix) + " ");
		bw.write("\n");
	}
	
	public static int[] getMax(TreeSet<Integer> set, int[] arr, int n) {
		
		int prev = -1;
		int[] ret = new int[n];
		
		for(int i = 0;i < n;i++) {
			int v = arr[i];
			if(v != prev) {
				prev = v;
				ret[i] = v;
				set.remove(v);
			}
			
			else {
				int a = -1;
				try {
				a = set.lower(prev);
				}catch(Exception e) {
					//System.out.println("curr : " + prev + " set: " + set);
					break;
				}
				ret[i] = a;
				set.remove(a);
			}
		}
		
		return ret;
		
	}
	
	public static int[] getMin(TreeSet<Integer> set, int[] arr, int n) {
		
		int prev = -1;
		int[] ret = new int[n];
		
		for(int i = 0;i < n;i++) {
			int v = arr[i];
			if(v != prev) {
				prev = v;
				ret[i] = v;
				set.remove(v);
			}
			
			else {
				int a = set.first();
				ret[i] = a;
				set.remove(a);
			}
		}
		
		return ret;
	}
}