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.math.*;
import java.util.*;
import java.io.*;
  
public class E { 
  
    static int test = 10; // 0 for local testing, 1 for std input

    static BufferedReader in;
    static PrintWriter out = new PrintWriter(System.out);
    static String file = "../in";
    static int inf = 1_000_000;

    static void swap(int[]ary, int i, int j)
    {
        int t = ary[i];
        ary[i] = ary[j];
        ary[j] = t;
    }
    
    static String[] split() throws Exception
    {
        return in.readLine().split(" ");
        // String str = in.readLine();
        // System.out.println(str);
        // return str.split(" ");
    }

    static int readInt() throws Exception
    {
        return Integer.valueOf(in.readLine());
    }

    static int[] toIntArray() throws Exception
    {
        String[] sp = split();
        int n = sp.length;
        int[] ary = new int[n];
        for(int i = 0; i < n; i++) ary[i] = Integer.valueOf(sp[i]);
        return ary;
    }

    static long[] toLongArray() throws Exception
    {
        String[] sp = split();
        int n = sp.length;
        long[] ary = new long[n];
        for(int i = 0; i < n; i++) ary[i] = Long.valueOf(sp[i]);
        return ary;
    }    

    static long lcm(long a, long b)
    {
        long gcd = gcd(a, b);
        // System.out.println(a + ", " + b + "," + "gcd = " + gcd);
        return a * b / gcd;
    }

    static long gcd(long a, long b)
    {
        if(a == 0) return b;
        return gcd(b % a, a);
    }

    public static void main(String[] args) throws Exception
    {
        int _k = Integer.valueOf("1");
        if(test > 0) in = new BufferedReader(new InputStreamReader(System.in));
        else in = new BufferedReader(new FileReader(file));
        if(test < 0) {String[] str = in.readLine().split(" ");
            char[] cc = str[0].toCharArray();
        }

        
        
        /****************************************************/  
        /****************************************************/
        /****************************************************/
        /****************************************************/

        int t = readInt();
        while(t-- > 0)
        {
            int n = readInt();
            int[] ary = toIntArray();
            TreeSet<Integer> s1 = new TreeSet<>(), s2 = new TreeSet<>();
            for(int i = 1; i <= n; i++)
            {
                s1.add(i);
                s2.add(i);
            }

            int[] a = new int[n], b = new int[n];
            a[0] = ary[0];
            b[0] = ary[0];
            s1.remove(a[0]);
            s2.remove(b[0]);
            for(int i = 1; i < n; i++)
            {
                // System.out.println(s1);
                // System.out.println(s2);
                // System.out.println(Arrays.toString(a));
                // System.out.println(Arrays.toString(b));
                if(ary[i] != ary[i - 1])
                {
                    a[i] = ary[i];
                    b[i] = ary[i];
                    s1.remove(ary[i]);
                    s2.remove(ary[i]);
                }
                else
                {
                    a[i] = s1.first();
                    s1.remove(a[i]);
                    b[i] = s2.floor(ary[i]);
                    s2.remove(b[i]);
                }
            }

            for(int i  =0; i < n; i++)
            {
                out.printf("%d ", a[i]);
            }
            out.printf("\n");
            for(int i  =0; i < n; i++)
            {
                out.printf("%d ", b[i]);
            }
            out.printf("\n");

            
        }
        
        
        /****************************************************/
        /****************************************************/
        /****************************************************/
        /****************************************************/

        out.flush();
    }




    static boolean dfs(int pos, Map<Integer, List<Integer>> map, 
        boolean[] visited, boolean[] onstack,
        Stack<Character> stack)
    {
        if(onstack[pos]) return false;
        if(visited[pos]) return true;
        visited[pos] = true;
        onstack[pos] = true;
        for(int next : map.get(pos))
        {
            if(!dfs(next, map, visited, onstack, stack)) return false;
        }
        onstack[pos] = false;
        stack.push((char)('a' + pos));
        return true;
    }
}