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

public class C_Paprika_and_Permutation
 {
     static int M = 1_000_000_007;
     static final PrintWriter out =new PrintWriter(System.out);
     static final FastReader fs = new FastReader();
     static boolean prime[];
     public static void main (String[] args) throws java.lang.Exception
     {
           
           int t= fs.nextInt();
         aaa:  for(int i=0;i<t;i++)
           {
               int n= fs.nextInt();
               int a[]=fs.arrayIn(n);
               int gg[]=new int[n+1];
               ArrayList<Integer> al = new ArrayList<>();
               for(int j=0;j<n;j++){
                   if(a[j]<=n&&gg[a[j]]==0){
                       gg[a[j]]=1;
                   }else{
                       al.add(a[j]);
                   }
               }
               Collections.sort(al);
               int ans=0;
               int in=0;
               for(int j=1;j<=n;j++){
                   if(gg[j]==0){
                       int req=j;
                       int op=al.get(in);
                       if((op-1)/2>=req){
                           in++;
                           gg[j]=1;
                           ans++;
                       }else{
                           out.println(-1);
                           continue aaa;
                       }
                   }
               }
               out.println(ans);
           }
           out.flush();
  }
  public static long power(long x, long y)
  {
      long temp;
      if (y == 0)
          return 1;
      temp = power(x, y / 2);

      if (y % 2 == 0)
          return modMult(temp,temp);
      else {
          if (y > 0)
              return modMult(x,modMult(temp,temp));
          else
              return (modMult(temp,temp)) / x;
      }
  }
  static void sieveOfEratosthenes(int n)
    {
         prime = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
            prime[i] = true;
            prime[0]=false;
            if(1<=n)
            prime[1]=false;
        for (int p = 2; p * p <= n; p++)
        {
            
            if (prime[p] == true)
            {
               
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
         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;
         }
 int [] arrayIn(int n) throws IOException
     {
         int  arr[] = new int[n];
         for(int i=0; i<n; i++)
         {
             arr[i] = nextInt();
         }
         return arr;
     }
     }
     
     public static class Pairs implements Comparable<Pairs>
     {
         int value,index;
         Pairs(int value, int index)
         {
             this.value = value;
             this.index = index;
         }
         public int compareTo(Pairs p)
         {
             return Integer.compare(this.value, p.value);
         }
     }
     static final Random random = new Random();
  
     static void ruffleSort(int arr[])
     {
         int n = arr.length;
         for(int i=0; i<n; i++)
         {
             int j = random.nextInt(n),temp = arr[j];
             arr[j] = arr[i];
             arr[i] = temp;
         }
         Arrays.sort(arr);
     }
     static long nCk(int n, int k) {
         return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
     }
  
     static long fact (long n) {
  
         long fact =1;
         for(int i=1; i<=n; i++) {
             fact = modMult(fact,i);
         }
         return fact%M;
     }
  
     static long modMult(long a,long b) {
         return a*b%M;
     }
  
     static long fastexp(long x, int y){
         if(y==1) return x;
  
         long ans = fastexp(x,y/2);
         if(y%2 == 0) return modMult(ans,ans);
         else return modMult(ans,modMult(ans,x));
     }
 }