#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
int a[N], b[N], len;
bool vis[N];
int xx(int x) {
  if (x & 1)
    return x / 2;
  else
    return x / 2 - 1;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    len = 0;
    memset(vis, 0, sizeof vis);
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      if (a[i] >= 1 && a[i] <= n) {
        if (!vis[a[i]])
          vis[a[i]] = 1;
        else
          b[++len] = a[i];
      } else {
        b[++len] = a[i];
      }
    }
    sort(b + 1, b + len + 1);
    int j = len;
    bool flag = 0;
    for (int i = n; i > 0; i--) {
      if (vis[i]) continue;
      if (xx(b[j]) < i) {
        flag = 1;
        break;
      } else {
        j--;
      }
    }
    if (flag)
      cout << -1 << endl;
    else
      cout << len << endl;
  }
  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 int N = 1e5 + 10;
int a[N], b[N], len;
bool vis[N];
int xx(int x) {
  if (x & 1)
    return x / 2;
  else
    return x / 2 - 1;
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    len = 0;
    memset(vis, 0, sizeof vis);
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      if (a[i] >= 1 && a[i] <= n) {
        if (!vis[a[i]])
          vis[a[i]] = 1;
        else
          b[++len] = a[i];
      } else {
        b[++len] = a[i];
      }
    }
    sort(b + 1, b + len + 1);
    int j = len;
    bool flag = 0;
    for (int i = n; i > 0; i--) {
      if (vis[i]) continue;
      if (xx(b[j]) < i) {
        flag = 1;
        break;
      } else {
        j--;
      }
    }
    if (flag)
      cout << -1 << endl;
    else
      cout << len << endl;
  }
  return 0;
}

```