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



import java.util.*;

//import javax.swing.plaf.basic.BasicInternalFrameTitlePane.SystemMenuBar;

import java.lang.*;
import java.io.*;

public class Main
{
 public static class FastReader {

		BufferedReader b;
		StringTokenizer s;
		public FastReader() {
			b=new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {
			while(s==null ||!s.hasMoreElements()) {
				try {
					s=new StringTokenizer(b.readLine());
				}
				catch(IOException e) {
					e.printStackTrace();
				}
			}
			return s.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		
		String nextLine() {
			String str="";
			try {
				str=b.readLine();
			}
			catch(IOException e) {
				e.printStackTrace();
			}
			return str;
		}
		boolean hasNext() {
		    if (s != null && s.hasMoreTokens()) {
		        return true;
		    }
		    String tmp;
		    try {
		        b.mark(1000);
		        tmp = b.readLine();
		        if (tmp == null) {
		            return false;
		        }
		        b.reset();
		    } catch (IOException e) {
		        return false;
		    }
		    return true;
		}
	
}
 /*static int LEN = 10000000;
 int lp[]=new int[LEN+1];
 List<Inter>
 public void sieve()
 {
	 for (int i=2; i <= N; ++i) {
		    if (lp[i] == 0) {
		        lp[i] = i;
		        pr.push_back(i);
		    }
		    for (int j=0; j < (int)pr.size() && pr[j] <= lp[i] && i*pr[j] <= N; ++j) {
		        lp[i * pr[j]] = pr[j];
		    }
		}
 }*/
 
 public static long gcd(long a,long b) {if(a==0)return b; return gcd(b%a,a);}
 public static int gcd(int a,int b) {if(a==0)return b; return gcd(b%a,a);};
 
 static int power(int x, int y){
     if (y == 0)
         return 1;
     else if (y % 2 == 0)
         return power(x, y / 2) * power(x, y / 2);
     else
         return x * power(x, y / 2) * power(x, y / 2);
 }
 
 static long power(long x , long y)
 {
	 if (y == 0)
         return 1;
     else if (y % 2 == 0)
         return power(x, y / 2) * power(x, y / 2);
     else
         return x * power(x, y / 2) * power(x, y / 2);
 }

	
	public static void main (String[] args) throws java.lang.Exception
	{
		
		
		long mod=1000000007;
		
		FastReader in=new FastReader();
		if(in.hasNext()){
		  
		if(in.hasNext()){
		
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		
		int test=in.nextInt();
		
		outer:while(test-->0)
		{
			int n=in.nextInt();
			int arr[]=new int[n];
			
			for(int i=0;i<n;i++)
				arr[i]=in.nextInt();
			
			Arrays.sort(arr);
			
			Set<Integer>set=new HashSet<>();
			
			int c=1;
			
			int ans=0;
			for(int i=0;i<n;i++)
			{
				
				
				if(arr[i]<=n&&!set.contains(arr[i])) {
					set.add(arr[i]);
					continue;}
				
				while(set.contains(c))
					c++;
				
				if(((arr[i]-1)/2)>0&&((arr[i]-1)/2)>=c) {
					set.add(c);ans++;}
				else {
					
					System.out.println(-1);
					continue outer;
				}
			}
			
			System.out.println(ans);
		}
		
		}
}
}
}


	


	

