#include <bits/stdc++.h>
using namespace std;
const long long int mod = 1000000000 + 7;
const long long int MAX = 1e15;
long long int b, t, al, ba, k, bas, m, son;
long long int a, e;
long long int d, q;
long long int n, r;
string s;
long long int x1, x2, p1, p2, w, h, x;
string y;
vector<long long int> v;
vector<long long int> v2;
long long int c;
long long int visited[2000037];
long long int cvp, yer;
long long int dizi[200037];
int main() {
  cin >> t;
  while (t--) {
    memset(dizi, 0, sizeof dizi);
    cin >> n;
    cvp = 0;
    v.clear();
    v2.clear();
    for (int i = 0; i < n; ++i) {
      cin >> a;
      if (a > n or dizi[a] != 0) {
        cvp++;
        v.push_back(a);
      } else {
        dizi[a] = 1;
      }
    }
    for (int i = 1; i <= n; ++i) {
      if (dizi[i] == 0) {
        v2.push_back(i);
      }
    }
    sort(v.begin(), v.end());
    long long int f = 1;
    for (int i = 0; i < v.size(); ++i) {
      if (v[i] <= v2[i] * 2) {
        f = 0;
      }
    }
    if (f)
      cout << cvp << endl;
    else
      cout << -1 << endl;
  }
}

### 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 int mod = 1000000000 + 7;
const long long int MAX = 1e15;
long long int b, t, al, ba, k, bas, m, son;
long long int a, e;
long long int d, q;
long long int n, r;
string s;
long long int x1, x2, p1, p2, w, h, x;
string y;
vector<long long int> v;
vector<long long int> v2;
long long int c;
long long int visited[2000037];
long long int cvp, yer;
long long int dizi[200037];
int main() {
  cin >> t;
  while (t--) {
    memset(dizi, 0, sizeof dizi);
    cin >> n;
    cvp = 0;
    v.clear();
    v2.clear();
    for (int i = 0; i < n; ++i) {
      cin >> a;
      if (a > n or dizi[a] != 0) {
        cvp++;
        v.push_back(a);
      } else {
        dizi[a] = 1;
      }
    }
    for (int i = 1; i <= n; ++i) {
      if (dizi[i] == 0) {
        v2.push_back(i);
      }
    }
    sort(v.begin(), v.end());
    long long int f = 1;
    for (int i = 0; i < v.size(); ++i) {
      if (v[i] <= v2[i] * 2) {
        f = 0;
      }
    }
    if (f)
      cout << cvp << endl;
    else
      cout << -1 << endl;
  }
}

```