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;
signed main() {
  long long int t = 1;
  cin >> t;
  while (t--) {
    long long int n;
    cin >> n;
    vector<long long int> b(n);
    for (auto &x : b) cin >> x;
    vector<bool> use(2 * n + 1, 0);
    vector<long long int> a(2 * n + 1, 0);
    for (auto x : b) use[x] = 1;
    bool ok = 1;
    for (long long int i = 1; i <= n; i++) {
      a[2 * i - 1] = b[i - 1];
      use[b[i - 1]] = 1;
      bool f = 0;
      for (long long int j = b[i - 1] + 1; j <= 2 * n; j++) {
        if (use[j] == 0) {
          a[2 * i] = j;
          use[j] = 1;
          f = 1;
          break;
        }
      }
      if (!f) {
        ok = 0;
        break;
      }
    }
    if (!ok)
      cout << -1 << endl;
    else {
      for (long long int i = 1; i <= 2 * n; i++) cout << a[i] << " ";
      cout << endl;
    }
  }
}