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() {
  int t;
  cin >> t;
  while (t-- > 0) {
    int n;
    cin >> n;
    int ar[n];
    unordered_map<int, int> umap;
    for (int i = 0; i < n; i++) {
      cin >> ar[i];
      umap[ar[i]] = 1;
    }
    int ans[2 * n];
    int k = 0;
    int flag1 = 0;
    for (int i = 0; i < n; i++) {
      int flag = 0;
      for (int j = ar[i] + 1; j <= (2 * n); j++) {
        if (umap.find(j) == umap.end()) {
          ans[k] = ar[i];
          ans[k + 1] = j;
          umap[j] = 1;
          flag = 1;
          k += 2;
          break;
        }
      }
      if (flag == 0) {
        flag1 = 1;
        break;
      }
    }
    if (flag1 == 1) {
      cout << "-1\n";
    } else {
      for (int i = 0; i < 2 * n; i++) {
        if (i == (2 * n) - 1) {
          cout << ans[i] << "\n";
        } else {
          cout << ans[i] << " ";
        }
      }
    }
    umap.clear();
  }
}