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:
if __name__ == '__main__':
	for _ in range (int(input())):
		n = int(input())
		l = list(map(int, input().split()))
		b = l.copy()
		d = {l[0]:0}
		ans = [l[0]]
		a = []
		for i in range (1,n):
			d.setdefault(l[i],i)
			if b[i]==b[i-1]:
				l[i]='X'
			else:
				ans.append(l[i])
		for i in range (1,n+1):
			d.setdefault(i,-1)
			if d[i] == -1:
				a.append(i)
		ans1 = l.copy()
		i = 0
		k = 0
		while i < len(ans) :
			j = d[ans[i]]+1
			if j < n:
				while ans1[j] == 'X':
					ans1[j]=a[k]
					k+=1
					j+=1
					if j == n:
						break
			i+=1
		k = 1
		ans2 = l.copy()
		i = 0
		s = []
		while i < len(ans) :
			j = d[ans[i]]+1
			if j < n:
				while ans2[j] == 'X':
					while k < ans[i]:
						if d[k] == -1:
							s.append(k)
							d[k] = -2
						k+=1
					ans2[j] = s.pop()
					j+=1
					if j == n:
						break
			i+=1
		print(*ans1)
		print(*ans2)