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.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.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[] nextIntArray(int n)
        {
            int arr[]=new int[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }
        Integer[] nextIntegerArray(int n)
        {
            Integer arr[]=new Integer[n];
            for(Integer i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }
        long[] nextLongArray(int n)
        {
            long arr[]=new long[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Long.parseLong(next());
            }
            return arr;
        }
    } 
	
	/*
	If we keep on subtracting the larger number from a smaller number gcd doesn't change. Hence, when smaller==larger (or) smaller divides larger we have our gcd=smaller.
	*/
	static long gcd(long larger,long smaller){
		if(larger%smaller==0){
			return smaller;
		}
		return gcd(smaller,larger%smaller);
	}
	
	/*static long modularInverse(long a,long mod){
	    long ans=1;
	    long y=mod-2;
	    while(y>0){
	        if((y&1)==1){
	            ans=((ans%mod)*(a%mod))%mod;
	        }
	        y>>=1;
	        a=((a%mod)*(a%mod))%mod;
	    }
	    return ans%mod;
	}
	
	static long nCr(int n,int r){//Uses fermat's little theorem for calculating modular inverse of r! and (n-r)!
	    if(r>n){
	        return 0;
	    }
	    if(r==0 || r==n){
	        return 1;
	    }
	    if(n-r<r){
	        r=n-r;
	    }
	    long mod=1000000000+7;
	    long ans=1;
	    long product=1;
	    long in1=1;
	    long in2=1;
	    for(int i=1;i<=n;i++){
	        product=((product%mod)*(i%mod))%mod;
	        if(i==r){
	            in1=modularInverse(product,mod);
	        }
	        if(i==n-r){
	            in2=modularInverse(product,mod);
	        }
	    }
	    return ((((product%mod)*(in1%mod))%mod)*(in2%mod));
	}*/
	
	
	/*static void swap(char [] s,int i,int j){
		char t=s[i];
		s[i]=s[j];
		s[j]=t;
	}
	
	static void permute(char[] s,int l,int r,int n){
		
		if(l<r){
			for(int i=l;i<=r;i++){
				swap(s,l,i);
				permute(s,l+1,r,n);
				swap(s,l,i);
			}
		}
		else{
			System.out.println(new String(s));
		}
		
	}*/
	
	static long power(long a,long b){
	    int mod=1000000007;
	    long ans=1;
	    while(b>0){
	        if(b%2==1){
	            ans=(ans*a)%mod;
	        }
	        b/=2;
	        a=(a*a)%mod;
	    }
	    return ans;
	}
	
	static int min(int a,int b){
	    return (int)Math.min(a,b);
	}
	
	static int max(int a,int b){
	    return (int)Math.max(a,b);
	}
	
	static int abs(int a,int b) {
		return (int)Math.abs(a-b);
	}
	
    public static void main(String args[]) throws UnsupportedEncodingException, IOException {
        FastReader sc=new FastReader();
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
		//Below is the code to be used when dealing file handling for input and output.
		/*BufferedReader br = new BufferedReader(
                               new FileReader("input.txt"));
		PrintWriter pw=new PrintWriter(new
                BufferedWriter(new FileWriter("output.txt")));
		pw.flush();
		pw.close();*/
		int te=sc.nextInt();
		for(int qu=0;qu<te;qu++){
			int n=sc.nextInt(),count=0;
			int[] arr=sc.nextIntArray(n);
			int[] set=new int[n+1];
			ArrayList<Integer> list=new ArrayList<>();
			for(int i=0;i<n;i++) {
				if(arr[i]<=n && set[arr[i]]==0) {
					set[arr[i]]=1;
				}
				else {
					list.add(arr[i]);
				}
			}
			Collections.sort(list);
			int j=0;
			for(int i=1;i<=n;i++) {
				if(set[i]==1) continue;
				if(list.get(j)<=2*i) {
					count=-1;
					break;
				}
				count++;
				j++;
				set[i]=1;
			}
			out.write(count+"\n");
			out.flush();
		}
		out.close();
    }
}
