Restoring the Permutation

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

inputFormat

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.

outputFormat

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

样例

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

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