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<stdio.h>
#include<math.h>
#include<string>
#include<string.h>
#include<algorithm>
#include<queue>
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define Cans cout<<ans<<endl;
#define Cneg {cout<<-1<<endl;return;}
#define Cno {cout<<"NO"<<endl;return;}
#define Cyes {cout<<"YES"<<endl;return;}
#define mem(a,n) memset(a,n,sizeof(a))
#define IOS ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define bug(x) cout<<"---"<<x<<endl;
using namespace std;
priority_queue <int,vector<int>,less<int> > QM;
const int eps=1319,mod= 1e9+7;
inline ll Qpow(ll a,ll b){ll s=1;while(b){if(b&1){s=(s*a)%mod;}a=a*a%mod;b>>=1;}return s;}
inline ll Qinv(ll a){return Qpow(a,mod-2);}
const int INF= 0x3f3f3f3f;
const int maxn= 2e5+5;
 
ll a[maxn];
set<int> st;
vector<int> num1,num2;
void solve(){
	int n; cin >> n;
	for(int i = 1;i <= n;i++) cin >> a[i];
	
	for(int i=1; i<=n; i++) st.insert(i);
	for(int i = 1;i <= n;i++)
		if(a[i]!=a[i-1]) num1.push_back(a[i]), st.erase(a[i]);
		else num1.push_back(*st.begin()),st.erase(st.begin());
	for(int i = 0;i < n;i++) cout<<num1[i]<<" ";cout << endl;
	
	for(int i=1; i<=n; i++) st.insert(i);
	for(int i=1; i<=n; i++)
		if(a[i]!=a[i-1]) num2.push_back(a[i]), st.erase(a[i]);
		else {
			auto it = prev(st.lower_bound(a[i]));
            num2.push_back(*it);
            st.erase(it);
		}
	for(int i = 0;i < n;i++) cout<<num2[i]<<" ";cout << endl;
	
	num1.clear();
	num2.clear();
}
int main(int argc,char *argv[]){
	IOS;
	int _;
	cin >> _;
	while(_--) 
	solve();
	return 0;
}