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 PYTHON):

Solution:
import heapq
def ansmn(n,q):
    mn=[]
    cur=-1
    start=1
    done=[0 for i in range(n)]
    for i in range(n):
        if q[i]!=cur:
            cur=q[i]
            mn.append(q[i])
            done[q[i]-1]=1
            if q[i]==start:
                start+=1
        else:
            while done[start-1]==1:
                start+=1
            done[start-1]=1
            mn.append(start)
            start+=1
    return mn
def ansmx(n,q):
    done=[0 for i in range(n)]
    cur=-1
    mx=[-1 for i in range(n)]
    hp=[]
    for i in range(n):
        if q[i]!=cur:
            mx[i]=q[i]
            if cur==-1:
                cur=1
            for j in range(cur,q[i]):
                if done[j-1]==0:
                    heapq.heappush(hp,-j)
            cur=q[i]
            done[q[i]-1]=1
        else:
            tt=heapq.heappop(hp)
            mx[i]=-tt
    return mx
            
            

        
for _ in range(input()):
    n=input()
    q=map(int,raw_input().split())
    mn=ansmn(n,q)
    mx=ansmx(n,q)
    for i in mn:
        print i,
    print
    for i in mx:
        print i,
    print