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.
  /* package codechef; // don't place package name! */
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;
 
 
 
 
 
public class hello{
 
   static class Pair implements Comparable<Pair>{
 
    long val;
    long ind;
    public Pair(long val,long ind)
    {
        this.val=val;
        this.ind=ind;
    }
 
    public int compareTo(Pair o)
    {
        return Long.compare(this.val, o.val);
}
}
     static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            try {
               br=new BufferedReader(new FileReader("input.txt"));
               PrintStream out= new PrintStream(new FileOutputStream("output.txt"));
               System.setOut(out);
            }
  
            // Catch block to handle the exceptions
            catch (Exception e) {
                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 int computeXOR(int n)
    {
        // If n is a multiple of 4
        if (n % 4 == 0)
            return n;
      
        // If n%4 gives remainder 1
        if (n % 4 == 1)
            return 1;
      
        // If n%4 gives remainder 2
        if (n % 4 == 2)
            return n + 1;
      
        // If n%4 gives remainder 3
        return 0;
    }
    static long helper(List<Long> l,long k)
    {
        int length = l.size()-1;
        long val = 0;

        while(length>=0)
        {
            val+=2*(l.get(length));
            length-=k;
        }

        return val;
    }

   static long findGCD(long a, long b){
    if(b == 0)
      return a;
    return findGCD(b, a%b);
}
    public static void main (String[] args) throws java.lang.Exception
    {
 
       try{
        FastReader sc=new FastReader();
        BufferedWriter out = new BufferedWriter(
            new OutputStreamWriter(System.out));
        int t = sc.nextInt();
        while(t-->0)
        {
            int n = sc.nextInt();

            long arr[] = new long[n];

            HashMap<Long,Integer> map = new HashMap<>();

            for(int i=0;i<n;i++)
            {
                arr[i] = sc.nextLong();
                if(map.containsKey(arr[i]))
                {
                    int c = map.get(arr[i]);
                    map.put(arr[i],c+1);
                }
                else
                {
                    map.put(arr[i],1);
                }
            }

            PriorityQueue<Long> pq = new PriorityQueue<>();

            for(int i=0;i<n;i++)
            {
                long k = i+1;
                if(map.containsKey(k))
                {
                    int c = map.get(k);
                    if(c==1)
                        map.remove(k);
                    else
                    {
                        map.put(k,c-1);
                    }
                }
                else
                {
                    pq.add(k);
                }
            }

            PriorityQueue<Long> pq2 = new PriorityQueue<>();

            for(long key:map.keySet())
            {
                int c = map.get(key);
                while(c-->0)
                {
                    pq2.add(key);
                }
            }

            int count = 0;
            boolean isTrue = true;

            
           
           while(pq2.size()!=0&&pq.size()!=0)
           {
                long val1 = pq2.remove();
                long val2 = pq.remove();

                long h = val1-val2;

                if(val2%h==val2)
                {
                    count++;
                }
                else
                {
                    isTrue=false;
                    break;
                }
           }

            if(isTrue)
            {
                System.out.println(count);
            }
            else
            {
                System.out.println(-1);
            }
        }
    }catch(Exception e){
            return;
        }
    }
}