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>
int b[100];
bool used[201];
int pair[201];
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    std::fill(used, used + 201, false);
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; ++i) {
      int input;
      scanf("%d", &input);
      b[i] = input;
      used[input] = true;
    }
    bool success = true;
    for (int i = 0; i < n; ++i) {
      bool found = false;
      for (int j = b[i]; j <= 2 * n; ++j) {
        if (!used[j]) {
          used[j] = true;
          pair[b[i]] = j;
          found = true;
          break;
        }
      }
      if (!found) {
        success = false;
        break;
      }
    }
    if (success) {
      for (int i = 0; i < n; ++i) {
        printf("%d %d ", std::min(b[i], pair[b[i]]),
               std::max(b[i], pair[b[i]]));
      }
      printf("\n");
    } else {
      printf("-1\n");
    }
  }
  return 0;
}