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 CPP):

Solution:
#include<bits/stdc++.h>
#define ll long long
#define pb push_back 
using namespace std;

//int main() {
//  int t; cin >> t;
//  while(t--) {
//    long long n, k;
//    cin >> n >> k;
//    
//    long long cf = (n + k - 1) / k;
//    k *= cf;
//    
//    cout << (k + n - 1) / n << endl;
//  }
//  return 0;
//}
int N=200006;
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		int n;
		cin>>n;
		int a[N];
		set<int> s1, s2;
		int v1[N], v2[N];
		for(int i=1; i<=n; i++)
		{
			cin>>a[i];
			if(a[i] > a[i-1])
			{
				v1[i]=v2[i]=a[i];
				for(int j=a[i-1]+1; j<=a[i]-1; j++) s1.insert(j), s2.insert(j);
			}
			else
			{
				v1[i]=*(--s1.end());
				s1.erase(v1[i]);
				v2[i]=*s2.begin();
				s2.erase(v2[i]);
			}
		}
		for(int i=1; i<=n; i++) cout<<v2[i]<<" ";
		cout<<endl;
		for(int i=1; i<=n; i++) cout<<v1[i]<<" ";
		cout<<endl;
	}
}