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;
typedef pair<int,int>pi;
int main() {
  int t;
  cin>>t;
  while(t--)
  {
      
     int n;
     cin>>n;
     
     int q[n];priority_queue<int,vector<int>,greater<int>>pq;
     for(int i=0;i<n;i++)
     {
         cin>>q[i];
     }
     
     for(int i=1;i<=n;i++)
     {
         pq.push(i);
     }
     bool vis[n+1];memset(vis,false,sizeof(vis));
     int prema=-1;
     int sm[n];
     for(int i=0;i<n;i++)
     {
         if(q[i]>prema)
         {
             sm[i]=q[i];
             vis[q[i]]=true;prema=q[i];
         }
         else
         {
             while(pq.empty()==false && vis[pq.top()])
             {
                 pq.pop();
             }
             sm[i]=pq.top();vis[pq.top()]=true;pq.pop();
         }
     }
     
     memset(vis,false,sizeof(vis));prema=-1;int la[n];memset(la,0,sizeof(la));
     priority_queue<int>pv;
     
     for(int i=0;i<n;i++)
     { if(q[i]>prema)
         {
             la[i]=q[i];
             vis[q[i]]=true;
             for(int j=q[i]-1;j>max(prema,0);j--)
             {
                 if(vis[j]==false)
                 {
                     pv.push(j);
                 }
             }
             
             prema=q[i];
         }
         else
         {
             la[i]=pv.top();
             vis[pv.top()]=true;
             pv.pop();
         }
    
     }
     
    
     for(int i=0;i<n;i++)
     {
         cout<<sm[i]<<" ";
     }
     cout<<endl;
   for(int i=0;i<n;i++)
   {
       cout<<la[i]<<" ";
   }
   cout<<endl;

  }
}