E. Restoring the Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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.OutputFor 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; ExampleInput
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 

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  
['constructive algorithms', 'implementation', '*1500']