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;
void debug_out() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int dx[] = {1, -1, 0, 0}, dy[] = {0, 0, 1, -1};
const int maxn = 105;
long long n, m, k;
long long a[maxn * 2], b[maxn], c[maxn * 2];
int main(void) {
  ios_base::sync_with_stdio(0), cin.tie(0);
  int tc;
  cin >> tc;
  while (tc--) {
    memset(c, 0, sizeof(c));
    cin >> n;
    for (int i = 1; i <= n; ++i) {
      cin >> b[i];
      ++c[b[i]];
    }
    bool valid = true;
    set<int> s;
    for (int i = 1; i <= n * 2; ++i) {
      if (!c[i]) s.insert(i);
      if (c[i] > 1) valid = false;
    }
    for (int i = 1; i <= n; ++i) {
      auto it = s.lower_bound(b[i]);
      if (it == s.end()) {
        valid = false;
        break;
      }
      a[i * 2 - 1] = b[i];
      a[i * 2] = *it;
      s.erase(it);
    }
    if (!valid)
      cout << -1 << '\n';
    else {
      for (int i = 1; i <= n * 2; ++i) cout << a[i] << ' ';
      cout << '\n';
    }
  }
  return 0;
}