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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    map<int, int> m;
    bool f = true;
    vector<int> v;
    while (n--) {
      int a;
      cin >> a;
      v.push_back(a);
      m[a] += 1;
      if (m[a] > 1) f = false;
    }
    if (!f || !m[1]) {
      cout << -1 << endl;
      continue;
    }
    vector<int> o;
    set<int> s;
    for (int a : v) {
      o.push_back(a);
      s.insert(a);
      for (int i = a + 1; i < 201; i++)
        if (!m[i] && s.find(i) == s.end()) {
          o.push_back(i);
          s.insert(i);
          m[i] += 1;
          break;
        }
    }
    bool r = true;
    int p;
    for (int a : s) {
      if (f) p = a, f = false;
      if (a - p > 1) {
        r = false;
        break;
      }
      p = a;
    }
    f = false;
    if (r)
      for (int a : o) {
        if (f) cout << ' ';
        cout << a;
        f = true;
      }
    else
      cout << -1;
    cout << endl;
  }
  return 0;
}