Restoring the Permutation
Description
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:
- $q_i = \max(p_1, p_2, \ldots, p_i)$.
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 $i$ ($1 \le i \le n$) 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.
The first line contains one integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains $n$ integers $q_1, q_2, \ldots, q_n$ ($1 \le q_i \le n$).
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 $2 \cdot 10^5$.
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;
Input
The first line contains one integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains $n$ integers $q_1, q_2, \ldots, q_n$ ($1 \le q_i \le n$).
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 $2 \cdot 10^5$.
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;
Samples
4
7
3 3 4 4 7 7 7
4
1 2 3 4
7
3 4 5 5 5 7 7
1
1
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