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<unordered_map>
using namespace std;
#define ll long long
int main()
{
        ll t;
        cin>>t;
        ll td=t;
        while(t--)
        {
             ll n;
             cin>>n;
             ll arr[n];
             for(ll i=0;i<n;i++)
             cin>>arr[i];
             ll visited[n];
             for(ll i=0;i<n;i++)
             visited[i]=arr[i];
             ll v[n+1];
             for(ll i=0;i<=n;i++)
             v[i]=0;
             ll x=arr[0];
             v[x]=1;
             ll i=1,j=1;
             while(i<n)
             {
                     if(x==arr[i])
                     {
                             if(v[j]==0)
                             {
                             arr[i]=j;
                             v[j]=1;
                             j++;
                             i++;
                             }
                             else
                             j++;
                     }
                        else
                        {
                                x=arr[i];
                                v[arr[i]]=1;
                                i++;
                        }
             }
             for(ll i=0;i<n;i++)
             cout<<arr[i]<<" ";
             cout<<endl;
             set<ll> s;
             for(ll i=0;i<n;i++)
             s.insert(i+1);
             for(ll i=0;i<n;i++)
             {
                     if(s.find(visited[i])!=s.end())
                     s.erase(visited[i]);
             }
             x=visited[0];
             cout<<x<<" ";
             i=1;
             while(i<n)
             {
                     if(x!=visited[i])
                     {
                             x=visited[i];
                             cout<<visited[i]<<" ";
                             i++;
                     }
                     else
                     {
                             cout<<*(--s.lower_bound(visited[i]))<<" ";
                             s.erase(*(--s.lower_bound(visited[i])));
                             i++;
                     }
             }
             cout<<endl;
        }
        return 0;
}