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 PYTHON):

Solution:
from collections import defaultdict, deque, OrderedDict
import heapq

t = int(raw_input())

for _ in range(t):
    # n,m = map(int,input().split())
    n = int(raw_input())
    ans = 0
    arr = [int(i) for i in raw_input().split()]

    lex_min = [0 for i in range(n)]
    lex_max = [0 for i in range(n)]
    od_small = OrderedDict()
    od_big = OrderedDict()
    for i in range(1, n + 1):
        od_small[i] = i
        od_big[i] = i

    prev = arr[0]
    lex_min[0] = prev
    lex_max[0] = prev
    od_small.pop(prev)
    od_big.pop(prev)
    small = 1 if prev != 1 else 2
    big = prev - 1

    for i in range(1, n):
        # print(i)
        if arr[i] == prev:
            lex_min[i] = small
            lex_max[i] = big
            to_pop_s = small
            to_pop_g = big
            link_prev, link_next, key = od_small._OrderedDict__map[small]
            small = link_next[2]
            link_prev1, link_next1, key1 = od_big._OrderedDict__map[big]
            big = link_prev1[2]
            od_small.pop(to_pop_s)
            od_big.pop(to_pop_g)

        else:
            lex_min[i] = arr[i]
            lex_max[i] = arr[i]
            if small == arr[i]:
                link_prev, link_next, key = od_small._OrderedDict__map[small]
                small = link_next[2]

            link_prev1, link_next1, key1 = od_big._OrderedDict__map[arr[i]]
            big = link_prev1[2]
            od_small.pop(arr[i])
            od_big.pop(arr[i])

        prev = arr[i]
    print ' '.join(str(i) for i in lex_min)
    print ' '.join(str(i) for i in lex_max)