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>
//#include"testlib.h"
using namespace std;
//#define int long long
template<typename T> void read(T &x) {
	x=0;int f=1;
	char c=getchar();
	for(;!isdigit(c);c=getchar())if(c=='-') f=-1;
	for(;isdigit(c);c=getchar())x=x*10+c-'0';
	x=x*f;
}
priority_queue<int>q;
int T,n,d[200020],cnt;
bool b[200020];
signed main(){
	cin>>T;
	while(T){
		T--;	
		cin>>n;
		cnt=1;
		for(int i=1;i<=n;i++) cin>>d[i],b[i]=0;
		//b[n+1]=1;
		for(int i=1;i<=n;i++){
			if(!b[d[i]]){cout<<d[i]<<' ';b[d[i]]=1;continue;}
			while(b[cnt]) cnt++;
			cout<<cnt<<' ';
			b[cnt]=1;
		}
		cout<<endl;
		for(int i=1;i<=n;i++){
			if(b[d[i]]){cout<<d[i]<<' ';b[d[i]]=0;	cnt=d[i]-1;
			while(b[cnt] and cnt>0){q.push(cnt);b[cnt]=0;cnt--;}continue;}	
		
			cout<<q.top()<<' ';
			q.pop();
		}
		cout<<endl;
		while(!q.empty()) q.pop();
	}
	return 0;
}