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 sys import stdin,stdout
input = stdin.readline

for _ in range(int(input())):
    n = int(input())

    dic = {}
    for i in range(1,n+1):
        dic[i] = 0
    lis = list(map(int,input().split()))
    min_lis = [0]*n
    prev = min_lis[0]= lis[0]
    dic[prev] = 1
    i=0
    while i < n:
        if lis[i] > prev:
            prev = lis[i]
            min_lis[i] = prev
            dic[prev] = 1
        i+=1
        
    arr = [i for i in range(1,n+1) if dic[i]==0]

    arr2 = arr[:]
    max_lis = min_lis[:]
    
    i=0
    for j in range(n):
        if min_lis[j]==0:
            min_lis[j] = arr[i]
            i+=1
    print(*min_lis)
    # for i in min_lis:
    #     stdout.write(f'{i} ')
    # stdout.write('\n')
    
    stack = []
    i=0
    while i<len(arr)-1 and arr[i+1]<max_lis[0]:
        i+=1
    last = i
    curr = i
    # stack.insert(0,[i,i]) # curr,last
    for i in range(n):
        if len(stack)>0 and curr==stack[0][1]:
            curr = stack[0][0]
            stack.pop(0)
        if max_lis[i]==0:
            max_lis[i] = arr[curr]
            curr-=1
        else:
            if last<len(arr)-1 and max_lis[i]>arr[last+1]:
                stack.insert(0,[curr,last]) # curr,last
                j=last+1
                while j<len(arr)-1 and arr[j+1]<max_lis[i]:
                    j+=1
                last = j
                curr = j
        # print(last,curr,stack)
    print(*max_lis)