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 pb push_back
const int infty = 1e9;

int main(){

    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    set<int> st;
    int t, n, a;
    vector<int> q, ans;

    cin >> t;
    while(t--){
        
        q.clear();
        cin >> n;
        q.pb(0);
        for(int i = 0; i < n; i++){
            cin >> a;
            q.pb(a);
        }


        ans.clear();
        for(int i = 1; i <= n; i++) st.insert(i);
        for(int i = 1; i <= n; i++){
            if(q[i] > q[i-1]){
                ans.pb(q[i]);
                st.erase(st.find(q[i]));
            }
            else{
                ans.pb(*st.begin());
                st.erase(st.find(ans[i-1]));
            }
        }
        for(auto it: ans) cout << it << " ";
        cout << "\n";

        ans.clear();
        for(int i = 1; i <= n; i++) st.insert(i);
        for(int i = 1; i <= n; i++){
            if(q[i] > q[i-1]){
                ans.pb(q[i]);
                st.erase(st.find(q[i]));
            }
            else{
                ans.pb(*prev(st.lower_bound(q[i]))); 
                st.erase(prev(st.lower_bound(q[i])));
            }
        }
        for(auto it: ans) cout << it << " ";
        cout << "\n";

    }

    return 0;

}