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;
const int Max = 1e5 + 10;
const int MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  int t;
  cin >> t;
  while (t--) {
    int n, x, mx = -1;
    vector<int> v, ans;
    map<int, int> mp, pay;
    bool done = false;
    cin >> n;
    for (int i = 0; i < n; i++) {
      cin >> x;
      v.push_back(x);
      pay[x] = 1;
    }
    for (int i = 0; i < n; i++) {
      ans.push_back(v[i]);
      for (int j = v[i] + 1;; j++) {
        if (!mp[j] and !pay[j]) {
          ans.push_back(j);
          mp[j] = 1;
          break;
        }
      }
    }
    for (int i = 0; i < 2 * n; i++)
      if (ans[i] > 2 * n) {
        done = true;
        break;
      }
    if (done)
      cout << -1 << endl;
    else {
      for (int i = 0; i < 2 * n; i++) cout << ans[i] << " ";
      cout << endl;
    }
  }
}