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 ints():
  return [int(x) for x in input().split(' ')]

def find_index(ranges, x, i, j):
  if i == j:
    return i
  if i == j - 1:
    return j if ranges[j][0] <= x else i
  m = (i + j) // 2
  a, b = ranges[m]
  if x < a:
    return find_index(ranges, x, i, m)
  if x > b:
    return find_index(ranges, x, m, j)
  return m

def remove_item(ranges, x):
  i = find_index(ranges, x, 0, len(ranges) - 1)
  a, b = ranges[i]
  if a == b:
    ranges.pop(i)
    return ranges
  if x == a:
    ranges[i][0] += 1
    return ranges
  if x == b:
    ranges[i][1] -= 1
    return ranges
  return ranges[0:i] + [[a, x - 1], [x + 1, b]] + ranges[i + 1:]

for _ in range(int(input())):
  n = int(input())
  q = ints()
  up = set([i + 1 for i in range(n)])
  down = [[1, n]]
  last = None
  for i in range(n):
    if q[i] == last:
      q[i] = 0
    else:
      up.remove(q[i])
      down = remove_item(down, q[i])
      last = q[i]

  up = list(up)
  up.sort()
  p = q[:]
  j = 0
  last = q[0]
  for i in range(n):
    if p[i] == 0:
      p[i] = up[j]
      j += 1
      k = find_index(down, last, 0, len(down) - 1)
      a, b = down[k]
      q[i] = b
      if a == b:
        down.pop(k)
      else:
        down[k][1] -= 1
    else:
      last = q[i]
  
  print(' '.join([str(x) for x in p]))
  print(' '.join([str(x) for x in q]))