#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long x = 0, ff = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') ff = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = (x << 1) + (x << 3) + (c ^ '0');
    c = getchar();
  }
  return x * ff;
}
long long n, tot, x, b[100005], a[100005], cnt, ans;
signed main() {
  long long t = read();
  while (t--) {
    ans = 0;
    cnt = 0;
    n = read();
    for (long long i = 1; i <= n; i++) b[i] = 0;
    for (long long i = 1; i <= n; i++) {
      x = read();
      if (x <= n && !b[x]) {
        b[x] = 1;
        continue;
      }
      a[++cnt] = (x - 1) / 2;
    }
    sort(a + 1, a + cnt + 1);
    tot = 1;
    for (long long i = 1; i <= n; i++) {
      if (b[i]) continue;
      if (a[tot] < i) {
        ans = -1;
        break;
      }
      tot++;
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Develop a solution in CPP 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;
inline long long read() {
  long long x = 0, ff = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') ff = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = (x << 1) + (x << 3) + (c ^ '0');
    c = getchar();
  }
  return x * ff;
}
long long n, tot, x, b[100005], a[100005], cnt, ans;
signed main() {
  long long t = read();
  while (t--) {
    ans = 0;
    cnt = 0;
    n = read();
    for (long long i = 1; i <= n; i++) b[i] = 0;
    for (long long i = 1; i <= n; i++) {
      x = read();
      if (x <= n && !b[x]) {
        b[x] = 1;
        continue;
      }
      a[++cnt] = (x - 1) / 2;
    }
    sort(a + 1, a + cnt + 1);
    tot = 1;
    for (long long i = 1; i <= n; i++) {
      if (b[i]) continue;
      if (a[tot] < i) {
        ans = -1;
        break;
      }
      tot++;
      ans++;
    }
    cout << ans << endl;
  }
  return 0;
}

```