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 N = 2e5 + 5;
int a[N];
int b[N];
int c[N];

void solve() {
  int n; cin >> n;
  set<int> used;
  for (int i = 1;i <= n;i++) {
    scanf("%d",a+i);
    if (a[i] != a[i - 1]) {
      c[i] = b[i] = a[i];
      used.insert(a[i]);
    }
    else c[i] = b[i] = 0;
  }
  set<int> unused;
  for (int i = 1;i <= n;i++) {
    if (used.count(i) == 0) unused.insert(i);
  }
  auto bb = unused.begin();
  auto cc = unused.end();
  for (int i = 1;i <= n;i++) {
    if (!b[i]) b[i] = *(bb++);
  }
  for (int i = 1;i <= n;i++) {
    if (!c[i]) {
      cc = unused.lower_bound(a[i]);
      assert(cc != unused.begin());
      c[i] = *(--cc);
      unused.erase(cc);
    }
  }
  for (int i = 1;i <= n;i++) {
    printf("%d ",b[i]);
  }
  cout << endl;
  for (int i = 1;i <= n;i++) {
    printf("%d ",c[i]);
  }
  cout << endl;

}

int main() {
  int t; cin>>t;
  while(t--) {
    solve();
  }
}