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:
import io,os,sys
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
import heapq

T = int(input())
r = 1
while r<=T:
    n = int(input())
    arr = list(map(int, input().split()))

    minimum = [0]*n
    maximum = [0]*n
    minimum[0] = arr[0]
    maximum[0] = arr[0]

    for i in range(1,n):
        if arr[i]>arr[i-1]:
            minimum[i] = arr[i]
            maximum[i] = arr[i]

    minimumoccu = [False]*(n+1)
    maximumstack = []
    minimumoccu[arr[0]] = True
   
    count = 1
    for i in range(1,n):
        if minimum[i]>0: 
            minimumoccu[minimum[i]] = True
            continue
        while minimumoccu[count]: count += 1

        minimum[i] = count
        minimumoccu[count] = True

    lastchange = arr[0]
    maximumstack.append(1)
    maximumstack.append(arr[0]-1)


#    print(maximum)    
    for i in range(1,n):
#        print(maximumstack)
        if maximum[i]>0:
            maximumstack.append(lastchange+1)
            maximumstack.append(maximum[i]-1)
            lastchange = maximum[i]
        else:
            while maximumstack[-2]>maximumstack[-1]:
                maximumstack.pop()
                maximumstack.pop()
            maximum[i] = maximumstack[-1]
            maximumstack[-1] -= 1
        
        

    ans1 = " ".join(map(str,minimum))
    ans2 = " ".join(map(str,maximum))
    os.sys.stdout.write(str(ans1) + '\n')        
    os.sys.stdout.write(str(ans2) + '\n')




    r += 1