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.
8
2
2 3
3
3 4 5
1
1
1
2
1
3
1
4
1
12071207
5
5 5 5 9 14

1
2
0
-1
1
1
1
4

/* package codechef; // don't place package name! */
 
import java.util.*;
import java.lang.*;
import java.io.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner(System.in);
		
        int t=in.nextInt();
        while(t-- > 0){
         
         int n=in.nextInt();
         int[] arr=new int[n];
         boolean[] visit=new boolean[n+1];
         ArrayList<Integer> al1=new ArrayList<Integer>();
         ArrayList<Integer> al2=new ArrayList<Integer>();
         
         for(int i=0;i<n;i++){
             arr[i]=in.nextInt();
             if(arr[i]<=n) visit[arr[i]]=true;
             else{
                 al1.add(arr[i]);
             }
         }
         
         for(int i=1;i<=n;i++){
             if(!visit[i]) al2.add(i);
         }
         
         Collections.sort(al1);
         Collections.sort(al2);
         
         boolean flag=false;
         for(int i=0;i<al1.size();i++){
             int k=al1.get(i);
             int m=al2.get(i);
             int l=k%(k-m);
             if(l!=m){
                 flag=true;
                 break;
             }
         }
         
         if(flag) out.println(-1);
         else out.println(al1.size());
         
        }
        out.flush();
	}
	
	public static long GCD(long a, long b)
    {
      if (b == 0)
        return a;
      return GCD(b, a % b);
    }
    
}
