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.io.*;
import java.util.*;
public final class PROBOBAL {
    
    
	public static void main(String[] args)throws IOException {
	    
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine()),n=0,j=0,l=0,c=0,c1=0;
		double d=0;
		
		for(int i=1;i<=t;i++)
		{
		    boolean b=true;
		    c=0;
		    n=Integer.parseInt(br.readLine());
			String arg[]=br.readLine().split(" ");
		    int a[]=new int[n];
		    Set<Integer> h = new HashSet<Integer>();
		    for(j=0;j<n;j++)
		    {
		        a[j]=Integer.parseInt(arg[j]);
		        if(a[j]>n)
		        c++;
		        else
		        h.add(a[j]);
		    }  
		    
		    Arrays.sort(a);
		    List<Integer> ht=new ArrayList<>();
		    if(a[0]>n)
		    ht.add(a[0]);
		    for(j=1;j<n;j++)
		    {
		        if(a[j]==a[j-1]||a[j]>n)
		        ht.add(a[j]);
		        
		    }
		   
		    c1=n-c;
		    c=0;
		    b=true;
		    for(j=1;j<=n&&b;j++)
		    {
		        if(!h.contains(j))
		        {
		            l=ht.get(0);
		            if(l>2*j)
		            c++;
		            else
		            b=false;
		            ht.remove(0);
		        }
		    }
		    if(b)
		    System.out.println(c);
		    else
		    System.out.println(-1);
		}
		
	}
}