#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 55;
long long a[MAXN], mark[MAXN];
vector<long long> ans;
int main() {
  long long T, T1;
  cin >> T;
  for (T1 = 1; T1 <= T; T1++) {
    long long n, i, j, sz, st, vall, f2 = 0, lg = 0;
    cin >> n;
    for (i = 1; i <= n; i++) cin >> a[i];
    sort(a + 1, a + n + 1);
    for (i = 1; i <= n; i++) {
      if (a[i] > n || (a[i] <= n && mark[a[i]])) {
        ans.push_back(a[i]);
        continue;
      }
      mark[a[i]] = 1;
    }
    sz = ans.size();
    st = 0;
    for (i = 1; i <= n; i++) {
      if (mark[i] == 0) {
        vall = ans[st];
        if (((i * 2) + 1) > vall) {
          f2 = 1;
          break;
        }
        st++;
        lg++;
      }
    }
    if (f2)
      cout << -1 << endl;
    else
      cout << lg << endl;
    for (i = 1; i <= n; i++) mark[i] = 0;
    ans.clear();
  }
}

### 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;
const int MAXN = 2e5 + 55;
long long a[MAXN], mark[MAXN];
vector<long long> ans;
int main() {
  long long T, T1;
  cin >> T;
  for (T1 = 1; T1 <= T; T1++) {
    long long n, i, j, sz, st, vall, f2 = 0, lg = 0;
    cin >> n;
    for (i = 1; i <= n; i++) cin >> a[i];
    sort(a + 1, a + n + 1);
    for (i = 1; i <= n; i++) {
      if (a[i] > n || (a[i] <= n && mark[a[i]])) {
        ans.push_back(a[i]);
        continue;
      }
      mark[a[i]] = 1;
    }
    sz = ans.size();
    st = 0;
    for (i = 1; i <= n; i++) {
      if (mark[i] == 0) {
        vall = ans[st];
        if (((i * 2) + 1) > vall) {
          f2 = 1;
          break;
        }
        st++;
        lg++;
      }
    }
    if (f2)
      cout << -1 << endl;
    else
      cout << lg << endl;
    for (i = 1; i <= n; i++) mark[i] = 0;
    ans.clear();
  }
}

```