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:
T = int(input())

for t in range(T):
    n = int(input())
    q = [int(ea) for ea in input().split(' ')]
    maxP = [0 for i in range(n)]
    minP = [0 for i in range(n)]
    prev = -1
    numsLeft = set(range(1, n + 1))
    lowerThanMe = {ea: ea-1 for ea in range(1, n+1)}
    higherThanMe = {ea: ea+1 for ea in range(1, n+1)}

    # Establish unmovables
    for i in range(n):
        if q[i] != prev:
            cur = q[i]
            maxP[i] = cur
            minP[i] = cur
            # higherThanMe[lowerThanMe[cur]] = higherThanMe[cur]
            # lowerThanMe[higherThanMe[cur]] = lowerThanMe[cur]
            numsLeft.remove(cur)
        prev = q[i]

    # Fill in minP (lowest to highest left to right)
    numsLeftForMin = sorted(list(numsLeft))
    ni = 0
    for i in range(n):
        if minP[i] == 0:
            minP[i] = numsLeftForMin[ni]
            ni += 1

    # Fill in maxP (just lower than cell to left according to lowerThanMe)
    for i in range(n):
        if maxP[i] == 0:
            cur = maxP[i-1]
            while cur not in numsLeft:
                higherThanMe[lowerThanMe[cur]] = higherThanMe[cur]
                lowerThanMe[higherThanMe[cur]] = lowerThanMe[cur]
                cur = lowerThanMe[cur]
            maxP[i] = cur
            numsLeft.remove(cur)
    print(*minP)
    print(*maxP)