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
import math
from itertools import permutations
from bisect import bisect_left
import heapq
from collections import deque
def II():
	return int(sys.stdin.readline())
 
def LI():
	return list(map(int, sys.stdin.readline().split()))
 
def MI():
	return map(int, sys.stdin.readline().split())
 
def SI():
	return sys.stdin.readline().strip()
 
def FACT(n, mod):
    s = 1
    facts = [1]
    for i in range(1,n+1):
        s*=i
        s%=mod
        facts.append(s)
    return facts[n]
 
def C(n, k, mod):
    return (FACT(n,mod) * pow((FACT(k,mod)*FACT(n-k,mod))%mod,mod-2, mod))%mod
 
def lcm(a,b):
    return abs(a*b) // math.gcd(a, b)

for _ in range(II()):
    n = II()
    a = LI()
    b = [0 for i in range(n)]
    d = {}
    b[0] = a[0]
    d[b[0]] = 1
    for i in range(1,n):
        if a[i]!=a[i-1]:
            b[i] = a[i]
            d[b[i]] = 1
    temp = []
    for i in range(1,n+1):
        if not d.get(i):
            temp.append(i)
    temp2 = temp[:]
    temp2.reverse()
    c = b[:]
    temp = [i for i in range(1,b[0])]
    m = b[0]
    for i in range(n):
        if b[i] == 0:
            b[i] = temp2.pop()
            c[i] = temp.pop()
            d[c[i]] = 1
        elif b[i] > m:
            for j in range(m+1, b[i]):
                if not d.get(j):
                    temp.append(j)
            m = b[i]
    print(*b)
    print(*c)