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.io.*;
import java.util.*;
import java.util.Map.Entry;

public class Div21608B {

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		
		int t = Integer.parseInt(br.readLine());		
	
	    while(t --> 0){
	        
	        int n = Integer.parseInt(br.readLine());	
	        
	        ArrayList<Integer> ar = new ArrayList<Integer>();
	        StringTokenizer st = new StringTokenizer(br.readLine());
	        
	        boolean[] cont = new boolean[n+1];
	        
	        for(int i = 0; i < n; i++){
	            
	            int v = Integer.parseInt(st.nextToken());
	            
	            if(v > n || cont[v])
	                ar.add(v);
	            else if(v <= n)
	                cont[v] = true;
	            
	        }
	        
	        Collections.sort(ar);
	        
	        int score = 0;
	        int ind = 0;
	        
	        boolean g = true;
	        
	        for(int i = 1; i <= n; i++){
	             
	            if(cont[i])
	                continue;
	             
	            if(ar.get(ind) >= 2*i+1){
	                
	                score++;
	                ind++;
	                
	            }else
	                g = false;
            
	        }
	        
	        if(g)
	            pw.println(score);
	        else
	            pw.println(-1);
	            
	    }
	    
	    pw.close();

	}

}