#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> a(n);
    multiset<int> rem;
    for (auto& c : a) {
      int x;
      cin >> x;
      c = x;
      rem.insert(x);
    }
    sort((a).begin(), (a).end());
    int ans = 0;
    bool worked = true;
    for (int i = n; i >= 1; i--) {
      auto exists = rem.find(i);
      if (exists != rem.end()) {
        rem.erase(exists);
      } else {
        auto best = rem.upper_bound(i * 2);
        if (best == rem.end()) {
          worked = false;
          break;
        } else {
          rem.erase(best);
          ans++;
        }
      }
    }
    if (worked)
      cout << ans << '\n';
    else
      cout << -1 << '\n';
  }
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

Paprika loves permutations. She has an array a_1, a_2, ..., a_n. She wants to make the array a permutation of integers 1 to n.

In order to achieve this goal, she can perform operations on the array. In each operation she can choose two integers i (1 ≤ i ≤ n) and x (x > 0), then perform a_i := a_i mod x (that is, replace a_i by the remainder of a_i divided by x). In different operations, the chosen i and x can be different.

Determine the minimum number of operations needed to make the array a permutation of integers 1 to n. If it is impossible, output -1.

A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

Input

Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

The first line of each test case contains an integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, ..., a_n. (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output the minimum number of operations needed to make the array a permutation of integers 1 to n, or -1 if it is impossible.

Example

Input


4
2
1 7
3
1 5 4
4
12345678 87654321 20211218 23571113
9
1 2 3 4 18 19 5 6 7


Output


1
-1
4
2

Note

For the first test, the only possible sequence of operations which minimizes the number of operations is: 

  * Choose i=2, x=5. Perform a_2 := a_2 mod 5 = 2. 



For the second test, it is impossible to obtain a permutation of integers from 1 to n.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    vector<int> a(n);
    multiset<int> rem;
    for (auto& c : a) {
      int x;
      cin >> x;
      c = x;
      rem.insert(x);
    }
    sort((a).begin(), (a).end());
    int ans = 0;
    bool worked = true;
    for (int i = n; i >= 1; i--) {
      auto exists = rem.find(i);
      if (exists != rem.end()) {
        rem.erase(exists);
      } else {
        auto best = rem.upper_bound(i * 2);
        if (best == rem.end()) {
          worked = false;
          break;
        } else {
          rem.erase(best);
          ans++;
        }
      }
    }
    if (worked)
      cout << ans << '\n';
    else
      cout << -1 << '\n';
  }
  return 0;
}

```