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 tcase int _; cin >> _; while(_--)
#define int long long
#define endl '\n'
const int INF = 1e18;
const int MAX = 1e6+100;

int n;
int v[MAX];

void lmin() {
    int up=0;
    priority_queue<int, vector<int>, greater<int>> av;
    for(int i=1; i<=n; i++) {
        if(v[i] != v[i-1]) {
            if(up < v[i]) {
                for(int j=up+1; j<v[i]; j++) av.push(j);
            }
            up = max(up, v[i]);
            cout << v[i] << " ";
        } else {
            cout << av.top() << " ";
            av.pop();
        }
    }
    cout << endl;
}

void lmax() {
    int up=0;
    priority_queue<int> av;
    for(int i=1; i<=n; i++) {
        if(v[i] != v[i-1]) {
            if(up < v[i]) {
                for(int j=up+1; j<v[i]; j++) av.push(j);
            }
            up = max(up, v[i]);
            cout << v[i] << " ";
        } else {
            cout << av.top() << " ";
            av.pop();
        }
    }
    cout << endl;
}

void solve() {
    cin >> n;
    v[0] = 0;
    for(int i=1; i<=n; i++) cin >> v[i];
    lmin();
    lmax();
}

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    tcase solve();

    return 0;
}