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;

inline void printArr(const int* a, int n) {
    cout << a[0];
    for(int i = 1; i < n; i++) {
        cout << " " << a[i];
    }
    cout << '\n';
}

void solve1(const int* q, int n) {
    bool vis[n];
    memset(vis, false, sizeof vis);

    int a[n]; a[0] = q[0];
    vis[q[0]-1] = true;

    int pre = q[0], p = 0;
    for(int i = 1; i < n; i++) {
        if(q[i] == pre) {
            while(p < n && vis[p]) p++;
            a[i] = p+1;
            vis[p] = true;
        }
        else {
            a[i] = q[i];
            vis[q[i]-1] = true;
            pre = q[i];
        }
    }

    printArr(a, n);
}

void solve2(const int* q, int n) {
    list<int> li;
    for(int i = n; i > 0; i--)
        li.emplace_back(i);

    typedef list<int>::iterator Iter;
    Iter its[n]; int k = n-1;
    for(auto iter = li.begin(); iter != li.end(); iter++) {
        its[k--] = iter;
    }

    int a[n]; a[0] = q[0];
    auto it = li.erase(its[q[0]-1]);
    int pre = q[0];
    for(int i = 1; i < n; i++) {
        if(q[i] == pre) {
            a[i] = *it;
            it = li.erase(it);
        }
        else {
            a[i] = q[i];
            pre = q[i];
            it = li.erase(its[q[i]-1]);
        }
    }

    printArr(a, n);
}

int main() {
    int t; cin >> t;
    while(t--) {
        int n; cin >> n;
        int q[n];
        for(int& x: q) cin >> x;

        solve1(q, n);
        solve2(q, n);
    }

    return 0;
}