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 t, a[109], n, vis[300];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> t;
  while (t--) {
    cin >> n;
    memset(vis, 0, sizeof vis);
    int good = 1;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      vis[a[i]]++;
      if (vis[a[i]] > 1) good = 0;
    }
    if (!good) {
      cout << -1 << "\n";
      continue;
    }
    vector<int> v;
    for (int i = 1; i <= n; i++) {
      v.push_back(a[i]);
      for (int j = a[i] + 1; j <= 2 * n; j++)
        if (!vis[j]) {
          v.push_back(j);
          vis[j]++;
          break;
        }
      if ((int)v.size() % 2) break;
    }
    if (v.size() != 2 * n) {
      cout << -1 << "\n";
      continue;
    }
    for (auto i : v) cout << i << " ";
    cout << "\n";
  }
}