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;

const int mod = 1e9 + 7;

const int N = 2e7 + 5;

int a[N];

typedef long long ll;


int main() {
    int t;
    cin >> t;
    while(t--) {
        int n;
        cin >> n;
        vector<int> q(n);
        vector<int> mnp(n);
        vector<int> mxp(n);
        int curmn = 1;
        vector<int> slcmn(n + 1);
        priority_queue<int> pq;
        int prev = -1;
        for (int i = 0; i < n; ++i) {
            cin >> q[i];
            slcmn[q[i]] = 1;
            if (q[i] == prev) {
                while(curmn <= n && slcmn[curmn])
                    ++curmn;
                mnp[i] = curmn;
                slcmn[curmn] = 1;
                mxp[i] = pq.top();
                pq.pop();
            } else {
                for (int j = q[i] - 1; j > max(0, prev); --j)
                    pq.push(j);
                mnp[i] = q[i];
                mxp[i] = q[i];
            }
            prev = q[i];
        }

        for(auto pi: mnp) {
            cout << pi << " ";
        }
        cout << "\n";
        for(auto pi: mxp) {
            cout << pi << " ";
        }
        cout << "\n";
    }
    return 0;
}