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 maxn = 2e2 + 10;
bool mark[maxn];
int ans[maxn];
int main() {
  ios::sync_with_stdio(false);
  int t;
  cin >> t;
  while (t--) {
    bool flag = true;
    memset(mark, false, sizeof(mark));
    int n;
    cin >> n;
    for (int i = 0; i < n; i++) {
      cin >> ans[2 * i];
      if (mark[ans[2 * i]] == true) {
        flag = false;
      } else
        mark[ans[2 * i]] = true;
    }
    if (flag == false) {
      cout << -1 << endl;
      continue;
    }
    for (int i = 1; i < 2 * n; i += 2) {
      bool ok = false;
      for (int k = ans[i - 1] + 1; k <= 2 * n; k++)
        if (mark[k] == false) {
          ans[i] = k;
          mark[k] = true;
          ok = true;
          break;
        }
      if (ok == false) {
        flag = false;
        break;
      }
    }
    if (flag == false)
      cout << -1 << endl;
    else {
      for (int i = 0; i < 2 * n; i++) cout << ans[i] << ' ';
      cout << endl;
    }
  }
  return 0;
}