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.*;

public class new1{
	
	
	public static void main(String[] args)  throws IOException{
    	BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
		FastReader s = new FastReader();
		int t = s.nextInt();
    	for(int z = 0; z < t; z++) {
    		int n = s.nextInt();
    		TreeSet<Integer> ts=  new TreeSet<Integer>();
    		HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
    		int[] arr  = new int[n + 1];
    		for(int i = 0; i < n; i++) {
    			int val = s.nextInt();
    			if(val <= n && arr[val] == 0) arr[val] = 1;
    			else {
	    			if(ts.contains(val)) {
	    				map.put(val, map.get(val) + 1);
	    			}
	    			else {
	    				ts.add(val);
	    				map.put(val, 1);
	    			}
    			}
    		}
    		boolean pos= true;
    		int count = 0;
    		for(int i = 1; i <= n; i++) {
    			if(arr[i] == 1) continue;
    			else {
    				if(ts.last() <= 2 * i) {
    					pos = false; break;
    				}
    				int v1 = ts.higher(2 * i);
    				int fr = map.get(v1) - 1;
    				if(fr == 0) {
    					ts.remove(v1);
    					map.remove(v1);
    				}
    				else map.put(v1, fr);
    				count++;
    			}
    		}
    		if(!ts.isEmpty()) pos= false;
    		if(!pos) System.out.println(-1);
    		else System.out.println(count);
    		
    		
    		
    		
    	}
    	//output.flush();

    }
}


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();
    }
 
    public 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;
}}