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() {
  long long int t = 1;
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> t;
  while (t--) {
    long long int start = 0, end = 0, n, m, x = 0, y = 0, index = 0;
    cin >> n;
    long int arr[n];
    unordered_map<long int, bool> mp;
    for (long int i = 1; i <= 2 * n; i++) mp[i] = true;
    for (long int i = 0; i < n; i++) {
      cin >> arr[i];
      mp[arr[i]] = false;
    }
    vector<long int> v;
    for (long int i = 0; i < n; i++) {
      v.push_back(arr[i]);
      start = 0;
      for (long int j = arr[i] + 1; j <= 2 * n; j++) {
        if (mp[j]) {
          start = 1;
          mp[j] = false;
          v.push_back(j);
          break;
        }
      }
      if (start == 0) {
        end = 1;
        cout << -1 << '\n';
        break;
      }
    }
    if (end == 0) {
      for (auto it : v) cout << it << " ";
      cout << '\n';
    }
  }
}