Problem: You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, a_{2n} such that b_i = min(a_{2i-1}, a_{2i}), or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case consists of one integer n — the number of elements in the sequence b (1 ≤ n ≤ 100).

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 2n).

It is guaranteed that the sum of n by all test cases doesn't exceed 100.

Output

For each test case, if there is no appropriate permutation, print one number -1.

Otherwise, print 2n integers a_1, …, a_{2n} — required lexicographically minimal permutation of numbers from 1 to 2n.

Example

Input


5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8


Output


1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, flag = 1;
    cin >> n;
    int a[201] = {0}, b[n], ans[2 * n];
    for (int i = 0; i < n; i++) {
      cin >> b[i];
      a[b[i]] = 1;
    }
    if (a[1] == 0 || a[2 * n] == 1) {
      cout << "-1\n";
      continue;
    }
    for (int i = 0, j = 0; i < n; i++, j++) {
      ans[j] = b[i];
      j++;
      b[i]++;
      while (a[b[i]] != 0) {
        b[i]++;
      }
      if (b[i] > 2 * n) {
        cout << "-1";
        flag = 0;
        break;
      }
      ans[j] = b[i];
      a[b[i]] = 1;
    }
    if (flag)
      for (int i = 0; i < 2 * n; i++) cout << ans[i] << " ";
    cout << endl;
    ;
  }
}