#include <bits/stdc++.h>
using namespace std;
int n, A[2100005];
int Tmp[2100005], Vis[2100005];
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    int Ans = 0, Now = 1, Sum = 0;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      scanf("%d", &A[i]);
      Vis[i] = 0;
    }
    sort(A + 1, A + n + 1);
    for (int i = 1; i <= n; i++) {
      if (A[i] <= n) {
        if (!Vis[A[i]])
          Vis[A[i]] = 1;
        else
          Tmp[++Ans] = A[i];
        continue;
      }
      Tmp[++Ans] = A[i];
    }
    for (int i = 1; i <= n; i++) {
      if (Vis[i]) continue;
      if ((Tmp[Now] - 1) / 2 >= i) {
        Sum++, Now++;
        continue;
      }
      break;
    }
    if (Now == Ans + 1)
      printf("%d\n", Sum);
    else
      puts("-1");
  }
}

### Prompt

Your task is to create 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;
int n, A[2100005];
int Tmp[2100005], Vis[2100005];
int main() {
  int T;
  scanf("%d", &T);
  while (T--) {
    int Ans = 0, Now = 1, Sum = 0;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      scanf("%d", &A[i]);
      Vis[i] = 0;
    }
    sort(A + 1, A + n + 1);
    for (int i = 1; i <= n; i++) {
      if (A[i] <= n) {
        if (!Vis[A[i]])
          Vis[A[i]] = 1;
        else
          Tmp[++Ans] = A[i];
        continue;
      }
      Tmp[++Ans] = A[i];
    }
    for (int i = 1; i <= n; i++) {
      if (Vis[i]) continue;
      if ((Tmp[Now] - 1) / 2 >= i) {
        Sum++, Now++;
        continue;
      }
      break;
    }
    if (Now == Ans + 1)
      printf("%d\n", Sum);
    else
      puts("-1");
  }
}

```