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 t, n, i, j;
int b[105];
int a[210];
bool dd[210];
long tong;
int sl;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> t;
  while (t--) {
    cin >> n;
    memset(dd, false, sizeof(dd));
    tong = 0;
    for (i = 1; i <= n; i++) {
      cin >> b[i];
      a[2 * i - 1] = b[i];
      tong += b[i];
      dd[b[i]] = true;
    }
    sl = 0;
    for (i = 2; i <= 2 * n; i += 2) {
      for (j = a[i - 1] + 1; j <= 300; j++) {
        if (dd[j] == false) {
          tong += j;
          a[i] = j;
          dd[j] = true;
          break;
        }
      }
    }
    sl = 2 * n;
    if (sl * (sl + 1) != tong * 2)
      cout << -1;
    else
      for (i = 1; i <= 2 * n; i++) cout << a[i] << ' ';
    cout << '\n';
  }
  return 0;
}