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 java.io.*;

////***************************************************************************
 /* public class E_Gardener_and_Tree implements Runnable{

       public static void main(String[] args) throws Exception {
        new Thread(null, new E_Gardener_and_Tree(), "E_Gardener_and_Tree", 1<<28).start();
       }
    public void run(){
         WRITE YOUR CODE HERE!!!!
         JUST WRITE EVERYTHING HERE WHICH YOU WRITE IN MAIN!!!
       }

  }
*/
/////**************************************************************************


public class C_Paprika_and_Permutation{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
        //PrintWriter out=new PrintWriter(System.out);
        //end of program
        //out.println(answer);
        //out.close();
        StringBuilder res = new StringBuilder();
        int t=s.nextInt();
        int p=0;
        while(p<t){
        int n=s.nextInt();
        ArrayList<Long> nice = new ArrayList<Long>();
        for(int i=0;i<n;i++){
            long a=s.nextLong();
            nice.add(a);
        }
        Collections.sort(nice);
        long val=1;
        long count=0;
        for(int i=0;i<n;i++){
            long num=nice.get(i);
            if(num==val){
                val++;
            }
            else{
                long b=2;
                long hh=(num+1)/b;
                if(val<hh){
                    count++;
                    val++;
                }
            }
        }
        if(val==n+1){
            res.append(count+" \n");
        }
        else{
            res.append("-1 \n");
        }
        p++;
    }
    System.out.println(res);
    }
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}


    static long modpower(long x, long y, long p)
     {
      long res = 1; // Initialize result
   
      x = x % p; // Update x if it is more than or
      // equal to p
   
      if (x == 0)
        return 0; // In case x is divisible by p;
   
      while (y > 0)
      {
   
        // If y is odd, multiply x with result
        if ((y & 1) != 0)
          res = (res * x) % p;
   
        // y must be even now
        y = y >> 1; // y = y/2
        x = (x * x) % p;
      }
      return res;
    }

  
   // SIMPLE POWER FUNCTION=>


      static long power(long x, long y)
        {
            long res = 1;     // Initialize result
        
            while (y > 0)
            {
            
                // If y is odd, multiply x with result
                if ((y & 1) != 0)
                    res = res * x;
        
                // y must be even now
                y = y >> 1; // y = y/2
                x = x * x;  // Change x to x^2
            }
            return res;
        }





}