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<iostream>
#include<iomanip>
#include<queue>
#include<stack>
#include<numeric>
#include<cstring>
#include<vector>
#include<algorithm>
#include<set>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<climits>
#include<cmath>

using namespace std;
#define ll long long
#define pp pair<int,int>
#define ppl pair<ll,ll> 
#define mod 1000000007

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	
	int t;
	cin>>t;

	while(t--)
	{
		int n;
		cin>>n;

		vector<int> v(n);
		set<int> s1,s2;
		
		for(int i=0;i<n;i++)
		{
			cin>>v[i];	
			s1.insert(i+1);
			s2.insert(i+1);
		}

		vector<int> mini,maxi;

		for(int i=0;i<n;i++)
		{
			if(s1.count(v[i]))
			{
				mini.push_back(v[i]);
				s1.erase(v[i]);
			}

			else
			{
				mini.push_back(*(s1.begin()));
				s1.erase(s1.begin());
			}

			auto it=s2.lower_bound(v[i]);

			if(it==s2.end() || (*it)!=v[i])
				it--;
			
			maxi.push_back(*it);
			s2.erase(it);
		}

		for(int i=0;i<n;i++)
			cout<<mini[i]<<" ";

		cout<<'\n';

		for(int i=0;i<n;i++)
			cout<<maxi[i]<<" ";

		cout<<'\n';
	}

	return 0;
}