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_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t, n, last;
  cin >> t;
  bool can;
  for (int u = 0; u < t; ++u) {
    cin >> n;
    vector<int> a(2 * n + 1, 0);
    vector<int> c(2 * n + 1, 0);
    last = 1;
    vector<pair<int, int>> b(n);
    for (int i = 0; i < n; ++i) {
      cin >> b[i].first;
      ++c[b[i].first];
      b[i].second = i + 1;
    }
    can = true;
    for (int i = 0; i < n && can; ++i) {
      last = 1;
      while (can && (c[last] > 0 || b[i].first > last)) {
        ++last;
        if (last > 2 * n) can = false;
      }
      a[b[i].second * 2 - 1] = b[i].first;
      a[b[i].second * 2] = last;
      c[last] = 1;
    }
    if (can) {
      for (int i = 1; i <= 2 * n; ++i) {
        cout << a[i] << " ";
      }
    } else {
      cout << -1;
    }
    cout << '\n';
  }
  return 0;
}