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>
#define ll long long;
using namespace std;
vector <long long> miniperm(vector<long long> v, long long n){
    set<long long> s;
    for(long long i=1; i<=n; i++){
        s.insert(i);
    }
    vector<long long> res;
    for(long long i=0; i<v.size(); i++){
        if(i==0 || v[i] != v[i-1]){
            res.push_back(v[i]);
            s.erase(v[i]);
        }
        else{
            auto pos = s.begin();
            res.push_back(*pos);
            s.erase(*pos);
        }
    }
    return res;
}

vector<long long> maxiperm(vector<long long> v, long long n){
    set<long long> s;
    for(long long i=-1; i>=-n; i--){
        s.insert(i);
    }
    
    vector<long long> res;
    for(long long i=0; i<v.size(); i++){
        if(i==0 || v[i] != v[i-1]){
            res.push_back(v[i]);
            s.erase(-v[i]);
        }
        else{
            res.push_back(-(*s.lower_bound(-v[i])));
            s.erase(s.lower_bound(-v[i]));
        }
    }
    return res;
}

int main(){
    long long t;
    cin>>t;
    while(t--){
        long long n;
        cin>>n;
        vector<long long> v;
        for(long long i=0; i<n; i++){
            long long le;
            cin>>le;
            v.push_back(le);
        }
        vector<long long> mini = miniperm(v, n);
        vector<long long> maxi = maxiperm(v, n);
        for(auto it: mini){
            cout<<it<<" ";
        }
        cout<<endl;
        for(auto it: maxi){
            cout<<it<<" ";
        }
        cout<<endl;
        
    }
}