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.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Stack;

public class CFPractice {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int t = in.nextInt();
		for(int i = 0; i < t; i++) {
			// implementation starts here
			int lowest = 1, highest = 0, current = 0, size = in.nextInt();
			int[] q = new int[size], min = new int[size], max = new int[size];
			Queue<Integer> minQ = new LinkedList<Integer>();
			Stack<Integer> maxS = new Stack<Integer>();
			
			for(int j = 0; j < size; j++) {
				int val = in.nextInt();
				q[j] = val;	
				
				if(val > current) {
					minQ.add(val);
					min[j] = max[j] = val;
					for(int k = highest + 1; k < val; k++)
						maxS.add(k);
					current = highest = val;
				} else {
					while(minQ.peek() == lowest) {
						minQ.remove();
						lowest++;
					}
					min[j] = lowest;
					lowest++;
					max[j] = maxS.pop();
				}
			}
			
			for(int j: min)
				System.out.print(j + " ");
			System.out.println();
			for(int j: max)
				System.out.print(j + " ");
			System.out.println();
			
			// implementation ends here
		}
	}
}