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 Main
{
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    static long modPow(long var, long num) {
    long m = 1;
    while (num > 0) {
        m = (m * var) %1000000007;
        --num;
    }
    return m;}
	public static void main (String[] args) throws java.lang.Exception
	{
		FastReader s = new FastReader();
		 BufferedWriter output = new BufferedWriter(
            new OutputStreamWriter(System.out));
		int t=s.nextInt();
		for(int w=0;w<t;w++)
		{
		    int n=s.nextInt();
		   
		    int[] arr= new int[n];
		    
		    for(int i=0;i<n;i++)
		    {
		        arr[i]=s.nextInt();
		        
		    }
		    int flag=0;
		    int ans=0;
		    Arrays.sort(arr);
		    int[] arr2= new int[n];
		    int[] lim= new int[n+1];
		    for(int i=0;i<n;i++)
		    {
		        if(arr[i]<=n)
		        {
		            if(arr2[i]>0)
		            {
		               ans++;
		                arr2[i]--;
		                if(Math.max(arr[i]%((arr[i]+1)/2),arr[i]%((arr[i]+1)/2+1))<n)
		                 lim[Math.max(arr[i]%((arr[i]+1)/2),arr[i]%((arr[i]+1)/2+1))]++;
		                else
		                 lim[n]++;
		            }
		            arr2[i]++;
		            
		        }
		        else
		        {    if(Math.max(arr[i]%((arr[i]+1)/2),arr[i]%((arr[i]+1)/2+1))<n)
		                 lim[Math.max(arr[i]%((arr[i]+1)/2),arr[i]%((arr[i]+1)/2+1))]++;
		                else
		                 lim[n]++;
		            ans++;
		        }
		        
		    }
		     for(int i=n-1;i>0;i--)
		     {
		         lim[i]=lim[i]+lim[i+1];
		     }
		     int k=0;
		      for(int i=n-1;i>-1;i--)
		      {
		          if(arr2[i]==0)
		          {
		              //output.write(String.valueOf(lim[i]-k)+"\n");
		              if(lim[i+1]-k>0)
		              {
		                  lim[i+1]--;
		                  k++;
		              }
		              else
		              {
		                  flag=1;
		                  break;
		              }
		          }
		      }
		      if(flag==1)
		      {
		          output.write("-1\n");
		      }
		     else
		         output.write(String.valueOf(ans)+"\n");
		
		}
		output.flush();
	}
}
