#include <bits/stdc++.h>
using namespace std;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    int a[n], b[n];
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      b[i] = a[i];
    }
    sort(b, b + n);
    vector<int> c;
    vector<int> fx(n + 1, 0);
    for (int i = 0; i < n; i++) {
      if (b[i] >= 1 && b[i] <= n && fx[b[i]] == 0) {
        fx[b[i]] = 1;
      } else {
        c.push_back(b[i]);
      }
    }
    int f = 0;
    int cx = 0;
    int p = 0;
    for (int i = 1; i <= n; i++) {
      if (fx[i] == 0) {
        if (c[p] - i <= i) {
          f = 1;
          break;
        } else
          cx += 1;
        p += 1;
      }
    }
    if (f) {
      printf("-1");
    } else {
      printf("%d", cx);
    }
    printf("\n");
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    int a[n], b[n];
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      b[i] = a[i];
    }
    sort(b, b + n);
    vector<int> c;
    vector<int> fx(n + 1, 0);
    for (int i = 0; i < n; i++) {
      if (b[i] >= 1 && b[i] <= n && fx[b[i]] == 0) {
        fx[b[i]] = 1;
      } else {
        c.push_back(b[i]);
      }
    }
    int f = 0;
    int cx = 0;
    int p = 0;
    for (int i = 1; i <= n; i++) {
      if (fx[i] == 0) {
        if (c[p] - i <= i) {
          f = 1;
          break;
        } else
          cx += 1;
        p += 1;
      }
    }
    if (f) {
      printf("-1");
    } else {
      printf("%d", cx);
    }
    printf("\n");
  }
  return 0;
}

```