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

/* JAIKARA SHERAWAALI DA BOLO SACHE DARBAR KI JAI
HAR HAR MAHADEV JAI BHOLENAATH
Rohit Kumar 
NIT JAMSHEDPUR
*/

import java.util.*;

import java.io.*;

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.hasMoreTokens()){
         
         try{

          st=new StringTokenizer(br.readLine());

         }
         catch(IOException e){

            e.printStackTrace();
         }
           



       }
       return st.nextToken();}

      long nextLong(){ return Long.parseLong(next());}

      int nextInt(){ return Integer.parseInt(next());}


       }
     
   static <t>void print(t o){
    System.out.println(o);
   }
    
   static boolean islapindrome(String s){

       int fhalf[]=new int[26];
       int shalf[]=new int[26];

        int i=0,j=s.length()-1;
        while(i<j){
           fhalf[s.charAt(i)-'a']++;
           shalf[s.charAt(j)-'a']++;
   i++;
   j--;
   

        }

        for(int k=0;k<26;k++){
          if(fhalf[k]!=shalf[k])return false;
        }
    return true;




   }

    static int mod=(int)1e9+7;
  static String text="foo";
  public static void main (String args[]) throws IOException{
  try{
    System.setIn(new FileInputStream("input.txt"));
    System.setOut(new PrintStream(new FileOutputStream("output.txt"))); } 
    catch (Exception e) {
    System.err.println("Error");
     }
     
     
     FastReader sc=new FastReader();
     int tt=sc.nextInt();
      while(tt-->0)
      {
         int n=sc.nextInt();
          List<Integer> arr=new ArrayList<>();
        
         for(int i=0;i<n;i++)
         {
             arr.add(sc.nextInt());
         }
         Collections.sort(arr);
         long ans=0;
         List<Integer> notp=new ArrayList<>();
         boolean flag=false;
         boolean visited[]=new boolean[n+1];
         for(int i=0;i<n;i++)
         {
             if(arr.get(i)>=1&&arr.get(i)<=n&&!visited[arr.get(i)])
             {
                visited[arr.get(i)]=true;
             }
             else
             {
                 notp.add(arr.get(i));
             }
         }
         List<Integer> idx=new ArrayList<>();
         for(int i=1;i<=n;i++)
         {
             if(!visited[i])
             {
                 idx.add(i);
             }
         }
         int k=0;
         Collections.sort(notp);
         for(int i=0;i<notp.size();i++)
         {
             if(notp.get(i)!=(i+1))
             {
                 int num1=notp.get(i);
                 int num=notp.get(i)-idx.get(k);
                //  if(num==0)
                //  {
                //      flag=true;
                //      break;
                //  }
                 if(num1%num==(idx.get(k)))
                 {
                     ans++;
                     k++;
                 }
                 else
                 {
                     flag=true;
                     break;
                 }   
             }
         }
         if(flag)
         {
             System.out.println(-1);
         }
         else{
            System.out.println(ans);
         }
        //  




      } 


       




    }

 
    static void reverse(int[] arr, int from, int till) {
        for (int i = from, j = till; i < j; i++, j--) {
            swap(arr, i, j);
        }
    }

    static void swap(int[] arr, int a, int b) {
        int tmp = arr[a];
        arr[a] = arr[b];
        arr[b] = tmp;
    }

    
    
    
    void sieveOfEratosthenes(int n)
    {
        boolean prime[] = new boolean[n+1];
        for(int i=0;i<=n;i++)
            prime[i] = true;
         
        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                for(int i = p*p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        for(int i = 2; i <= n; i++)
        {
            if(prime[i] == true)
                System.out.print(i + " ");
        }
    }
    static long gcd(long a,long b)
    {
        if(b==0) return a;
        
        return gcd(b,a%b);
    }
    static boolean isprime(int n)
    {
        if(n<=1)
         return false;
        
        if(n<=3)
         return true;
        
        if(n%2==0||n%3==0)
         return false;
        
        for(int i=5;i*i<=n;i=i+6)
        {
            if(n%i==0||n%(i+2)==0)
              return false;
        }
        return true;
    }



   }
 