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>

using namespace std;

// Theorem: I

typedef long long ll;

int main(){
 ios::sync_with_stdio(0);cin.tie(0);
 int  t; cin >> t;
 while(t > 0){
 	t--;
 	int n; cin >> n;
 	vector<int> arr(n);for(int i = 0; i < n; i++)cin >> arr[i];
 	// for minimal choose smallest smaller than max
 	// for maximal choose largest smaller than max
 	set<int> st;for(int i = 1; i <= n; i++)st.insert(i);
 	st.erase(arr[0]);
 	cout << arr[0] << " ";
 	for(int i = 1; i < n; i++){
 		if(arr[i] == arr[i - 1]){
 			cout << *st.begin() << " ";
 			st.erase(*st.begin());
 		}else{
 			cout << arr[i] << " " ;
 			st.erase(arr[i]);
 		}
 	}
 	cout << endl;
		for(int i = 1; i <= n; i++)st.insert(-1 * i);
		st.erase(-1 * arr[0]);
		cout << arr[0] << " ";
		for(int i = 1; i < n; i++){
			if(arr[i] != arr[i - 1]){
				cout << arr[i] << " ";
				st.erase(-1 * arr[i]);
			}else{
				cout << -1 * *st.lower_bound(-1 * arr[i]) << " ";
				st.erase(*st.lower_bound(-1 * arr[i]));
			}
		}
		cout << endl;
	}

}