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.Scanner;
import java.util.TreeSet;

public class Main{
    static int n;
    final static int maxn =200000 + 10;
    static int[] arr = new int[maxn];
    static int[] vis = new int[maxn];
    static TreeSet<Integer> st = new TreeSet<>();
    public static void main(String[] args){
        Scanner cin = new Scanner(System.in);
        arr[0] = 0;
        int T = cin.nextInt();
        while(T-- != 0){
            n = cin.nextInt();
            for(int i = 1 ; i <= n ; i++ )
                arr[i] = cin.nextInt();
            int low = 1;
            for(int i = 1 ; i <= n ; i++ ){
                if(arr[i] != arr[i - 1]){
                    System.out.print(arr[i] + " ");
                    vis[arr[i]] = 1;
                }else{
                    while(vis[low] == 1) ++low;
                    vis[low] = 1;
                    System.out.print(low + " ");
                }
            }
            System.out.println();
            for(int i = 1 ; i <= n ; i++ ){
                if(arr[i] != arr[i - 1]){
                    System.out.print(arr[i] + " ");
                    for(int j = arr[i - 1] + 1 ; j < arr[i] ; j++ )
                        st.add(j);
                }else{
                    int val = st.last();
                    st.remove(val);
                    System.out.print(val + " ");
                }
            }
            System.out.println();
            st.clear();
            for(int i = 1 ; i <= n ; i++ )
                vis[i] = 0;
        }
    }
}