#include <bits/stdc++.h>
using namespace std;
void fun() {
  long long a, s, d, i, j, k;
  cin >> a;
  vector<long long> vec;
  set<pair<long long, long long> > se;
  set<pair<long long, long long> >::iterator ii;
  se.insert({1000000000000, 1000000000000});
  for (i = 0; i < a; i++) {
    cin >> s;
    se.insert({s, i});
  }
  long long otv = 0;
  for (i = a; i >= 1; i--) {
    ii = se.lower_bound({i, 0});
    long long a1, a2;
    a1 = (*ii).first;
    a2 = (*ii).second;
    if (a1 == i) {
      se.erase(*ii);
    } else {
      ii = se.lower_bound({i * 2 + 1, 0});
      a1 = (*ii).first;
      a2 = (*ii).second;
      if (a1 == 1000000000000) {
        cout << -1 << endl;
        return;
      }
      se.erase(*ii);
      otv++;
    }
  }
  cout << otv << endl;
}
int main() {
  long long a, i;
  cin >> a;
  for (i = 0; i < a; i++) fun();
}

### 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;
void fun() {
  long long a, s, d, i, j, k;
  cin >> a;
  vector<long long> vec;
  set<pair<long long, long long> > se;
  set<pair<long long, long long> >::iterator ii;
  se.insert({1000000000000, 1000000000000});
  for (i = 0; i < a; i++) {
    cin >> s;
    se.insert({s, i});
  }
  long long otv = 0;
  for (i = a; i >= 1; i--) {
    ii = se.lower_bound({i, 0});
    long long a1, a2;
    a1 = (*ii).first;
    a2 = (*ii).second;
    if (a1 == i) {
      se.erase(*ii);
    } else {
      ii = se.lower_bound({i * 2 + 1, 0});
      a1 = (*ii).first;
      a2 = (*ii).second;
      if (a1 == 1000000000000) {
        cout << -1 << endl;
        return;
      }
      se.erase(*ii);
      otv++;
    }
  }
  cout << otv << endl;
}
int main() {
  long long a, i;
  cin >> a;
  for (i = 0; i < a; i++) fun();
}

```