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 long long ll;
#define  loop(n)     for(ll i=0;i<(n);i++)
#define  all(v)      v.begin(),v.end()
#define  pb          push_back
#define  ff          first
#define  ss          second
#define  sz(x)       (int)x.size()
 
const ll M=1e9+7;
const ll N1=1e5+10;
 
int code(){
    ll n;
    cin>>n;
    ll ar[n];
    loop(n) cin>>ar[i];
    set<ll> s1;
    set<ll,greater<ll>> s2;
    loop(n) s1.insert(i+1),s2.insert(i+1);
    vector<ll>  ans1(n),ans2(n);
    for(ll i=0;i<n;i++){
        if(s1.count(ar[i])){
            ans1[i]=ar[i];
            s1.erase(ar[i]);
        }
        else{
            ll tmp=*s1.begin();
            ans1[i]=tmp;
            s1.erase(tmp);
        }
        if(s2.count(ar[i])){
            ans2[i]=ar[i];
            s2.erase(ar[i]);
        }
        else{
            ll tmp=*s2.upper_bound(ar[i]);
            ans2[i]=tmp;
            s2.erase(tmp);
        }
    }
    for(auto x:ans1) cout<<x<<' ';
    cout<<"\n";
    for(auto x:ans2) cout<<x<<' ';
    cout<<"\n";
    return 0;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    // freopen("input.txt","r",stdin);
    // freopen("output.txt","w",stdout);
    ll tc=1;
    cin>>tc;
    while(tc--)  code();
    return 0;
}