description: 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.
solution: import java.io.*;
  import java.util.*;
  
  public class Codeforces
  {
      public static void main(String args[])throws Exception
      {
          BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
          StringBuilder sb=new StringBuilder();
          int t=Integer.parseInt(bu.readLine());
          while(t-->0)
          {
              int n=Integer.parseInt(bu.readLine());
              int a[]=new int[n],i;
              String s[]=bu.readLine().split(" ");
              HashMap<Integer,Integer> hm=new HashMap<>();
              for(i=0;i<n;i++)
              {
                  a[i]=Integer.parseInt(s[i]);
                  hm.put(a[i],hm.getOrDefault(a[i],0)+1);
              }
  
              for(i=0;i<n;i++)
              if(hm.get(i+1)!=null)   //only 1 reduction per number will happen
              {
                  a[i]=i+1;
                  hm.put(a[i],hm.get(a[i])-1);
              }
              else a[i]=-1;
  
              PriorityQueue<Integer> pq=new PriorityQueue<>();
              for(int x:hm.keySet())
              {
                  int v=hm.get(x);
                  while(v-->0) pq.add(x);
              }
  
              int ans=0;
              for(i=0;i<n;i++)
              if(a[i]==-1)
              {
                  a[i]=pq.poll();
                  int mod=a[i]-(i+1);
                  if(mod<=0 || a[i]%mod!=(i+1)) {ans=-1; break;}
                  ans++;
              }
              sb.append(ans+"\n");
          }
          System.out.print(sb);
      }
  }