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 updateQuery(BIT,index,val):
    while index < len(BIT):
        BIT[index] += val
        index += index&-index

def sumQuery(BIT,index):
    total = 0
    while index > 0:
        total += BIT[index]
        index -= index&-index

    return total

def rangeQuery(BIT,l,r):
    return sumQuery(BIT,r)-sumQuery(BIT,l-1)

def findSmallest(BIT,x):
    low = 1
    high = x-1
    smallest = -1
    while low <= high:
        mid = (low+high)//2
        total = rangeQuery(BIT,1,mid)
        if total == mid:
            smallest = mid+1
            low = mid+1
        else:
            high = mid-1

    if smallest == -1:
        return 1
    
    return smallest

def findLargest(BIT,x):
    low = 1
    high = x
    largest = -1
    while low <= high:
        mid = (low+high)//2
        total = rangeQuery(BIT,mid,x)
        if total == x-mid+1:
            largest = mid-1
            high = mid-1
        else:
            low = mid+1

    return largest

def solve(arr,n,ans):
    BIT_small = [0]*(n+1)
    BIT_large = [0]*(n+1)
    minimal = []
    maximal = []
    curr_max = 0
    for i in arr:
        if i > curr_max:
            minimal.append(str(i))
            maximal.append(str(i))
            updateQuery(BIT_small,i,1)
            updateQuery(BIT_large,i,1)
            curr_max = i
        else:
            smallest = findSmallest(BIT_small,i)
            largest = findLargest(BIT_large,i)
            #print(smallest,largest,curr_max,i)
            minimal.append(str(smallest))
            maximal.append(str(largest))
            updateQuery(BIT_small,smallest,1)
            updateQuery(BIT_large,largest,1)

    ans.append(' '.join(minimal))
    ans.append(' '.join(maximal))

def main():
    t = int(input())
    ans = []
    for i in range(t):
        n = int(input())
        arr = list(map(int,input().split()))
        solve(arr,n,ans)

    print('\n'.join(ans))
    

main()