#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long T;
  cin >> T;
  for (long long tc = 1; tc <= T; ++tc) {
    long long n;
    cin >> n;
    vector<long long> need(n + 1, true), spare;
    for (long long i = 0; i < n; ++i) {
      long long a;
      cin >> a;
      if (a <= n && need[a])
        need[a] = false;
      else
        spare.push_back((a + 2 - 1) / 2 - 1);
    }
    sort(spare.begin(), spare.end());
    long long ans = (long long)spare.size();
    for (long long i = n; i >= 1; --i) {
      if (need[i]) {
        if (spare.back() >= i)
          spare.pop_back();
        else
          ans = -1;
      }
    }
    cout << ans << "\n";
  }
}

### Prompt

Generate a CPP solution to 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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long T;
  cin >> T;
  for (long long tc = 1; tc <= T; ++tc) {
    long long n;
    cin >> n;
    vector<long long> need(n + 1, true), spare;
    for (long long i = 0; i < n; ++i) {
      long long a;
      cin >> a;
      if (a <= n && need[a])
        need[a] = false;
      else
        spare.push_back((a + 2 - 1) / 2 - 1);
    }
    sort(spare.begin(), spare.end());
    long long ans = (long long)spare.size();
    for (long long i = n; i >= 1; --i) {
      if (need[i]) {
        if (spare.back() >= i)
          spare.pop_back();
        else
          ans = -1;
      }
    }
    cout << ans << "\n";
  }
}

```