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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        FastReader input = new FastReader();
        int test = input.nextInt();
        while (test-- > 0) {
            int n = input.nextInt();
            ArrayList<Integer> list = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                list.add(input.nextInt());
            }
            ArrayList<Integer> copy = new ArrayList<>(list);
            ArrayList<Integer> helper = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                helper.add(i + 1);
            }
            for (int i = 0; i < n - 1; i++) {
                if (list.get(i).equals(list.get(i + 1))) {
                    copy.set(i + 1, -1);
                }
            }
            for (int i = 0; i < n; i++) {
                helper.set(list.get(i) - 1, -1);
            }
            int m = 0;
//            System.out.println(copy);
            for (int i = 0; i < n; i++) {
                if (copy.get(i) == -1) {
                    while (helper.get(m) == -1) m++;
                    copy.set(i, helper.get(m));
                    m++;
                }
            }
            copy.forEach(x -> System.out.print(x + " "));
            System.out.println();
            helper = null;
            Stack<Integer> stack = new Stack<>();
            copy = new ArrayList<>(list);
            for (int i = 0; i < n - 1; i++) {
                if (list.get(i).equals(list.get(i + 1))) {
                    copy.set(i + 1, -1);
                }
            }
            int mn , mx = 0;
            for (int i = 0; i < n; i++) {
                if (copy.get(i) != -1){
                    mn = mx;
                    mx = copy.get(i);
                    for (int j = mn+1; j < mx; j++) {
                        stack.push(j);
                    }
                }
                else {
                    copy.set(i, stack.pop());
                }
            }
            copy.forEach(x -> System.out.print(x + " "));
            System.out.println();
        }
    }

    static class FastReader {
        final String del;
        private final BufferedReader input;
        private StringTokenizer tokenizer;

        public FastReader() {
            input = new BufferedReader(new InputStreamReader(System.in));
            del = " ";
        }

        public FastReader(String delimiter) {
            input = new BufferedReader(new InputStreamReader(System.in));
            del = delimiter;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
                try {
                    tokenizer = new StringTokenizer(input.readLine(), del);
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public String nextLine() {
            String res = null;
            try {
                res = input.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }
    }
}