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 PYTHON3):

Solution:
def per(l, arr):
    if arr[0] == arr[-1]:
        lex_min = [arr[0]] + [i for i in range(1, arr[0])]
        lex_max = [arr[0]] + [i for i in range(arr[0] - 1, 0, -1)]
    else:
        lex_min, lex_max = [arr[0]] + [0] * (l - 1), [arr[0]] + [0] * (l - 1)
        ls_min, ls_max = [i for i in range(1, arr[0])], [i for i in range(arr[0] - 1, 0, -1)]
        ind = 0
        for i in range(1, l):
            # print(f"ls_min: {ls_min} , ls_max: {ls_max}")
            if arr[i - 1] == arr[i]:
                lex_min[i], lex_max[i] = ls_min[ind], ls_max[ind]
                ind += 1
            else:
                lex_min[i], lex_max[i] = arr[i], arr[i]
                x = len(lex_min)
                ls_min[x:x] = [i for i in range(arr[i - 1] + 1, arr[i])]
                ls_max[ind:ind] = [i for i in range(arr[i] - 1, arr[i - 1], -1)]
            # print(f"MIN: {lex_min}")
            # print(f"MAX: {lex_max}")
    print(*lex_min)
    print(*lex_max)


for test in range(int(input())):
    n = int(input())
    lst = list(map(int, input().strip().split()))
    per(n, lst)