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.Scanner;
import java.util.Arrays;
import java.util.Comparator;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
 

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;
        }
    }   
    static long gcd(long a,long b){
        long max = Math.max(a,b);
        b = Math.min(a,b);
        a = max;
        if(b == 0 ){
            return a;
        }
        return gcd(b,a%b);
    }
    
	public static void main(String[] args) {
		FastReader at  = new FastReader();
		int t = at.nextInt();
		while(t-->0){
		    int n = at.nextInt();
		    int [] arr = new int[n+1];
		    boolean vis[] = new  boolean[n+1];
		    int count = 0;
		   for(int i = 1;i<n+1;i++){
		       arr[i]=  at.nextInt();
		       if(arr[i] <= n && !vis[arr[i]]){
		           vis[arr[i]] = true;
		           count++;
		       }
		   }
		   if(count == n){System.out.println(0);continue;}
		   Arrays.sort(arr);
		   boolean ok = true;
		   int temp = 0;
		   for(int i = 1;i<n+1;i++){
		       if(arr[i] <= n && vis[arr[i]]){continue;}
		       else{
		           long pos = (arr[i]/2)+1;
		           long gpr = arr[i]%pos;
		           if(i > gpr){ok = false; break;}
		           else{
		               vis[i] = true;
		               temp++;
		           }
		       }
		   }
		   if(ok && temp+count == n){
		   System.out.println(temp);
		   }
		   else{
		       System.out.println(-1);
		   }
		   
		}
	}
}