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;
 
#define ll long long
#define vi vector<int>
#define ii pair<int,int>
#define vii vector<ii>
#define si set<int>
#define msi map<string,int>
#define pb push_back
#define fi first
#define se second

#define sp " "

#pragma GCC optimize("Ofast")  
#pragma GCC target("avx,avx2,fma") 

const int inf = 0x3f3f3f3f;
const int MX = 5e5+5;
const int mxl = 105;
const int mod = 1e9+7;

int main(){
	int tc; cin>>tc;
	for(int ntc=1;ntc<=tc;ntc++){
		int n; cin>>n;
		int arr[n+1],ans[n+1],mx[n+1];
		arr[0]=0; memset(ans,0,sizeof(ans)); memset(mx,0,sizeof(mx));
		for(int i=1;i<=n;i++)
			cin>>arr[i];
		set<int>s1,s2;
		int mncnt=1;
		for(int i=1;i<=n;i++){
			if(arr[i]!=arr[i-1]){
				ans[i]=arr[i];
				s1.insert(ans[i]);
			}
		}
		for(int i=1;i<=n;i++){
			if(ans[i]==0){
				while(s1.count(mncnt))
					mncnt++;
				ans[i]=mncnt;
				s1.insert(ans[i]);
			}
		}
		int mxcnt=n;
		set<int>rem;
		for(int i=1;i<=n;i++)
			rem.insert(i);
		for(int i=1;i<=n;i++){
			if(arr[i]!=arr[i-1]){
				mx[i]=arr[i];
				rem.erase(arr[i]);
			}
		}
		for(int i=1;i<=n;i++){
			if(mx[i]!=0)mxcnt=mx[i];
			else if(mx[i]==0){
				auto idx=--rem.lower_bound(mxcnt);
				mx[i]=*idx;
				rem.erase(idx);
			}
		}
		for(int i=1;i<=n;i++)
			cout<<ans[i]<<sp;
		cout<<"\n";
		for(int i=1;i<=n;i++)
			cout<<mx[i]<<sp;
		cout<<"\n";
	}
}