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() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int a[n], b[2 * n];
    unordered_map<int, int> m;
    int flag = 0;
    for (long long int i = 0; i < n; i++) {
      cin >> a[i];
      m[a[i]]++;
    }
    if (!m[1] or m[2 * n])
      cout << -1 << endl;
    else {
      flag = 0;
      int j = 0;
      for (long long int i = 0; i < n; i++) {
        b[j] = a[i];
        j += 2;
      }
      j = 1;
      int in = b[j - 1];
      for (long long int i = 0; i < n; i++) {
        in = b[j - 1] + 1;
        while (m[in]) {
          in++;
          if (in == 2 * n + 1) {
            flag = 1;
            break;
          }
        }
        m[in]++;
        b[j] = in;
        j += 2;
      }
      if (flag)
        cout << -1 << endl;
      else
        for (long long int i = 0; i < 2 * n; i++) cout << b[i] << " ";
      cout << endl;
    }
  }
  return 0;
}