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:
from os import path;import sys,time
mod = int(1e9 + 7)
from math import ceil, floor,gcd,log,log2 ,factorial,sqrt
from collections import defaultdict ,Counter , OrderedDict , deque;from itertools import combinations,permutations
# from string import ascii_lowercase ,ascii_uppercase
from bisect import *;from functools import reduce;from operator import mul;maxx = float('inf')
I = lambda :int(sys.stdin.buffer.readline())
lint = lambda :[int(x) for x in sys.stdin.buffer.readline().split()]
S = lambda: sys.stdin.readline().strip('\n')
grid = lambda  r :[lint() for i in range(r)]
localsys = 0
start_time = time.time()
#left shift --- num*(2**k) --(k - shift)
nCr = lambda n, r: reduce(mul, range(n - r + 1, n + 1), 1) // factorial(r)
def ceill(n,x):
    return (n+x -1 )//x
T =1
def make_set(v):
    parent[v] = v

def find_set(v):
    if v== parent[v]:
        return v
    return find_set(parent[v])

def union_sets(a , b):
    a = find_set(a)
    b = find_set(b)
    if a!= b:
        parent[b] = a
def lcs(x , y ):
    m , n = len(x) , len(y)
    dp = [[None]*(n+1) for _ in range(m+1)]
    for i in range(m+1):
        for j in range(n+1):
            if i == 0 or j == 0 :
                dp[i][j] = 0
            elif y[j-1] == x[i-1]:
                dp[i][j] = dp[i-1][j-1]+ 1
            else:
                dp[i][j] = max(dp[i-1][j], dp[i][j-1])
    return dp[m][n]

def solve():
    n = I()
    a, mini , maxi , rem1 , rem2, curr   = lint() , [] , [] , deque() , deque() , 0
    for i in a:
        if i == curr :
            maxi.append(rem1.pop());mini.append(rem2.popleft())
        else:
            for k in range(curr+1 , i):
                rem1.append(k);rem2.append(k)
            maxi.append(i);mini.append(i)
            curr = i
    print(*mini,'\n',*maxi)






def run():
    if (path.exists('input.txt')):
        sys.stdin=open('input.txt','r')
        sys.stdout=open('output.txt','w')


run()
T = I() if T else 1
for _ in range(T):
    solve()


if localsys:
    print("\n\nTime Elased :",time.time() - start_time,"seconds")