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 Main {
	
	
	public static void main(String[] args) throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));		
		
		int num_tests = Integer.parseInt(in.readLine());
		int[] A = new int[200200];
		int[] count = new int[200200];
		int[] start = new int[200200];
		int[] end = new int[200200];
		
		for (int ts=1; ts<=num_tests; ts++) {
			int N = Integer.parseInt(in.readLine());
			
			{
				int idx=1;
				for (final String st : in.readLine().split(" ")) {
					A[idx] = Integer.parseInt(st);
					idx++;
				}
			}
			
			for (int i=1; i<=N; i++) {
				count[i] = 0;
				start[i] = 0;
				end[i] = 0;
			}
			
			int ans = 0;
			
			for (int i=1; i<=N; i++) {
				if (A[i] <= N) {
					if (count[A[i]] > 0) {
						start[1]++;
						end[Math.max(1, (A[i]-1)/2)]++;
						ans++;
					}
					count[A[i]]++;
				} else {
					start[1]++;
					end[Math.max(1, Math.min((A[i]-1)/2, N))]++;
					ans++;
				}
			}
			
			int candidates = 0;
			for (int i=1; i<=N; i++) {
				candidates += start[i];
				
				if (count[i] == 0 && candidates == 0) {
					ans = -1;
				}
				
				candidates -= end[i];
			}
			
			
			out.write(ans + "\n");
			
		}
		
		in.close();
		out.close();
	}

}
