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 FIO ios_base::sync_with_stdio (false) ;cin.tie(NULL);
#define tc  int t;cin>>t;for(int i=0;i<t;i++)
#define ll long long int
#define forn(i,n) for(int i=0;i<n;i++)
#define forn1(i,a,b) for(int i=a;i<=b;i++)
#define pb push_back
#define um(a,b) unordered_map<a,b>
#define vv(a) vector<a>
#define pp(a,b) pair<a,b>
ll power(ll a,ll b,ll mod){  ll ans=1;  while(b>0){
  if(b&1){ ans=(ans*a)%mod;} a=(a*a)%mod;  b=b/2; } return ans;}

int main(){
FIO
tc{
    ll n;
    cin>>n;
    vector<ll> arr(n+1),ans(n+1),ans2(n+1);
    map<ll,bool> vis,vis2;
    for(ll i=1;i<=n;i++){
        cin>>arr[i];
    }
    ll start=1;
    ans[1]=arr[1];
    vis[ans[1]]=true;

    set<ll,greater<ll>> myset;
    for(ll i=2;i<=n;i++){
        if(arr[i]==arr[i-1]){

           while(vis.find(start)!=vis.end()){
            start++;
           }
           ans[i]=start;
           vis[start]=true;
        }else{
           ans[i]=arr[i];
           vis[ans[i]]=true;
        }
    }
    for(ll i=1;i<arr[1];i++){
        myset.insert(i);
    }
    start=arr[1];
    ans2[1]=arr[1];
    for(ll i=2;i<=n;i++){
        if(arr[i]==arr[i-1]){
           ans2[i]=*(myset.begin());
           myset.erase(myset.begin());
        }else{
           ans2[i]=arr[i];
           for(ll j=start+1;j<arr[i];j++){
            myset.insert(j);
           }
           start=arr[i];

        }
    }
    for(ll i=1;i<=n;i++)
        cout<<ans[i]<<" ";
    cout<<endl;
    for(ll i=1;i<=n;i++)
        cout<<ans2[i]<<" ";
    cout<<endl;
     }
}