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--) {
    int n;
    cin >> n;
    int a[n + 1];
    int b[2 * n + 1];
    int temp[2 * n + 1];
    for (int i = 1; i <= 2 * n; i++) temp[i] = 0;
    bool con1 = false, con2 = false;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      if (a[i] == 1) con1 = true;
      if (a[i] == 2 * n) con2 = true;
      temp[a[i]] = 1;
    }
    if (con1 == false or con2 == true)
      cout << "-1" << endl;
    else {
      int check = 0;
      for (int i = 1; i <= n; i++) {
        b[2 * i - 1] = a[i];
        int j;
        for (j = a[i] + 1; j <= 2 * n; j++) {
          if (temp[j] == 0) {
            temp[j] = 1;
            b[2 * i] = j;
            break;
          }
        }
        if (j == 2 * n + 1) {
          check = -1;
        }
      }
      if (check != -1) {
        for (int i = 1; i <= 2 * n; i++) cout << b[i] << " ";
        cout << endl;
      } else
        cout << "-1" << endl;
    }
  }
  return 0;
}