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 sys
input = sys.stdin.readline

def update(v,w):
    while v<=LEN:
        BIT[v]+=w
        v+=(v&(-v))

def getvalue(v):
    ANS=0
    while v!=0:
        ANS+=BIT[v]
        v-=(v&(-v))
    return ANS

def bisect_on_BIT(x):

    if x<=0:
        return 0
    
    ANS=0
    h=1<<(LEN.bit_length()-1)
    while h>0:
        if ANS+h<=LEN and BIT[ANS+h]<x:
            x-=BIT[ANS+h]
            ANS+=h
        h//=2

    return ANS+1

t=int(input())
for tests in range(t):
    n=int(input())
    Q=list(map(int,input().split()))
    Q.append(1<<30)

    ANSMIN=[-1]*n
    ANSMAX=[-1]*n
    USE=[0]*(n+2)

    LEN=n+2
    BIT=[0]*(LEN+1)

    for i in range(n):
        if Q[i]!=Q[i-1]:
            ANSMIN[i]=Q[i]
            ANSMAX[i]=Q[i]
            USE[Q[i]]=1

    ind=0
    USE[0]=1

    for i in range(n+1):
        if USE[i]==0:
            update(i,1)
        
    for i in range(n):
        while USE[ind]==1:
            ind+=1
            
        if ANSMIN[i]==-1:
            ANSMIN[i]=ind
            ind+=1
    print(*ANSMIN)

    MAX=-1

    for i in range(n):
        MAX=max(MAX,ANSMAX[i])
        
        if ANSMAX[i]==-1:
            x=getvalue(MAX)

            y=bisect_on_BIT(x)
            ANSMAX[i]=y
            update(y,-1)

    print(*ANSMAX)