#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5;
int a[N], b[N], vis[N];
signed main() {
  int T;
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    int tot = 0, cnt = 0;
    for (int i = 1; i <= n; i++) b[i] = vis[i] = 0;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      if (a[i] <= n) {
        vis[a[i]]++;
        if (vis[a[i]] > 1) {
          b[(a[i] - 1) / 2]++;
        } else {
          b[a[i]]++;
          cnt++;
        }
      } else if (a[i] > 2 * n) {
        tot++;
        b[n]++;
      } else {
        b[(a[i] - 1) / 2]++;
      }
    }
    int sum = 0, fg = 1;
    for (int i = 1; i <= n; i++) {
      sum += b[i];
      if (sum > i) {
        fg = 0;
        break;
      }
    }
    if (sum != n) fg = 0;
    if (fg) {
      cout << n - cnt << endl;
    } else
      cout << "-1\n";
  }
}

### Prompt

Your challenge is to write 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;
const int N = 1e6 + 5;
int a[N], b[N], vis[N];
signed main() {
  int T;
  cin >> T;
  while (T--) {
    int n;
    cin >> n;
    int tot = 0, cnt = 0;
    for (int i = 1; i <= n; i++) b[i] = vis[i] = 0;
    for (int i = 1; i <= n; i++) {
      cin >> a[i];
      if (a[i] <= n) {
        vis[a[i]]++;
        if (vis[a[i]] > 1) {
          b[(a[i] - 1) / 2]++;
        } else {
          b[a[i]]++;
          cnt++;
        }
      } else if (a[i] > 2 * n) {
        tot++;
        b[n]++;
      } else {
        b[(a[i] - 1) / 2]++;
      }
    }
    int sum = 0, fg = 1;
    for (int i = 1; i <= n; i++) {
      sum += b[i];
      if (sum > i) {
        fg = 0;
        break;
      }
    }
    if (sum != n) fg = 0;
    if (fg) {
      cout << n - cnt << endl;
    } else
      cout << "-1\n";
  }
}

```