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

/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{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; 
        } 
    } 
//    static int mod = 998244353 ;
//    static int N = 200005;
//    static long factorial_num_inv[] = new long[N+1];
//    static long natual_num_inv[] = new long[N+1];
//    static long fact[] = new long[N+1];
//    static void InverseofNumber() 
//{ 
//    natual_num_inv[0] = 1;
//    natual_num_inv[1] = 1; 
//    for (int i = 2; i <= N; i++) 
//        natual_num_inv[i] = natual_num_inv[mod % i] * (mod - mod / i) % mod; 
//} 
//static void InverseofFactorial() 
//{ 
//    factorial_num_inv[0] = factorial_num_inv[1] = 1; 
  
//    for (int i = 2; i <= N; i++) 
//        factorial_num_inv[i] = (natual_num_inv[i] * factorial_num_inv[i - 1]) % mod; 
//} 
//static long nCrModP(long N, long R) 
//{ 
//    long ans = ((fact[(int)N] * factorial_num_inv[(int)R]) % mod * factorial_num_inv[(int)(N - R)]) % mod; 
//    return ans%mod; 
//}
    //static boolean prime[];
    //static void sieveOfEratosthenes(int n)
    //{
    //    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] is not changed, then it is a
    //        // prime
    //        if (prime[p] == true)
    //        {
    //            // Update all multiples of p
    //            for (int i = p * p; i <= n; i += p)
    //                prime[i] = false;
    //        }
    //    }
 
        
    //}
    
    static int visited[];
	public static void main (String[] args) throws java.lang.Exception
	{
    //    InverseofNumber();
    //    InverseofFactorial();
    //   fact[0] = 1; 
    //   for (long i = 1; i <= 2*100000; i++)
    //   { 
    //       fact[(int)i] = (fact[(int)i - 1] * i) % mod; 
    //   }
    
		FastReader scan = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
        int t = scan.nextInt();
        while(t-->0){
            int n = scan.nextInt();
            int a[] = new int[n+1];
            int visited[] = new int[n+1];
            int ans = 0;
            for(int i=0;i<n;i++){
                int x = scan.nextInt();
                if(x<=n && visited[x]!=1){
                    visited[x] = 1;
                    ans++;
                }
                else{
                if(x%2==0){
                    int index = x/2-1;
                    if(index>n)
                    a[n]++;
                    else
                    a[index]++;
                }
                else{
                    int index = x/2;
                    if(index>n)
                    a[n]++;
                    else
                    a[index]++;
                }}
            }
            int count = 0;
            int i=n;
            for(i=n;i>0;i--){
                count = count+a[i];
                if(visited[i]==0){
                    visited[i] = 1;
                    if(count>0){
                        count--;
                    }
                    else{
                        break;
                    }
                }
            }
            if(i==0)
            pw.println(n-ans);
            else
            pw.println(-1);
            pw.flush();
        }
    
    }
      
        //static long bin_exp_mod(long a,long n){
            
        //    long res = 1;
            
        //    if(a==0)
        //    return 0;
        //    while(n!=0){
        //        if(n%2==1){
        //            res = ((res)*(a));
        //        }
        //           n = n/2;
        //            a = ((a)*(a));
        //    }
           
        //    return res;
        //}
    //static long bin_exp_mod(long a,long n){
	//    long mod = 998244353;
	//    long res = 1;
	//    a = a%mod;
	//    if(a==0)
	//    return 0;
	//    while(n!=0){
	//        if(n%2==1){
	//            res = ((res%mod)*(a%mod))%mod;
	//        }
	//           n = n/2;
	//            a = ((a%mod)*(a%mod))%mod;
	//    }
	//    res = res%mod;
	//    return res;
	//}
//   static long gcd(long a,long b){
//       if(a==0)
//       return b;
//       return gcd(b%a,a);
//   }
//   static long lcm(long a,long b){
//       return (a/gcd(a,b))*b;
//   }
}
//class Pair{
//    int x,y;
//    Pair(int x,int y){
//        this.x = x;
//        this.y = y;
//    }
//}
//    public boolean equals(Object obj) {
//        // TODO Auto-generated method stub
//        if(obj instanceof Pair)
//        {
//            Pair temp = (Pair) obj;
//            if(this.x.equals(temp.x) && this.y.equals(temp.y))
//                return true;
//        }
//        return false;
//    }

//    @Override
//    public int hashCode() {
//        // TODO Auto-generated method stub
        
//        return (this.x.hashCode() + this.y.hashCode());        
//    }
//}
//class Compar implements Comparator<Pair>{
//    public int compare(Pair p1,Pair p2){
//        if(p1.y>p2.y)
//        return 1;
//        else
//        return -1;
//    }
//}