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 Test
{
    final static FastReader fr = new FastReader();
    final static PrintWriter out = new PrintWriter(System.out) ;
    static int mod = 1000000007;
    static long dp[][] ;

    static void solve()
    {

        int n  = fr.nextInt();

        int flags[] = new int[n+1] ;

        long arr[] = new long[n] ;
        for (int i = 0 ; i < n ; i++) arr[i] = fr.nextLong() ;

        long ans = 0 ;
        long f = 0 ;
        for (int i = 0 ; i < n ; i++)
        {
            if (arr[i] <=n) flags[(int)arr[i]] = 1 ;
            else ans++ ;

            int pos = (int)(arr[i] - 1)/2 ;
            if (pos <= n)
            flags[pos] = 1  ;
            else
            f++ ;
        }

        if (ans <= f) {
            out.println(ans);
            return ;
        }

        for (int  i = 1 ; i <= n ; i++) {
            if (flags[i] == 0) {
                out.println(-1);
                return ;
            }
        }

        out.println(ans);





    }


    public static void main(String[] args)
    {
        int t  = fr.nextInt() ;
        while (t-- > 0)
        {
            solve() ;
        }
        out.close() ;
    }

    static long gcd(long a, long b)
    {
        if (b == 0) return a ;
        return gcd(b,  a%b) ;
    }

    static int lower_bound(List<Integer> arr, int key)
    {
        int pos = Collections.binarySearch(arr, key) ;
        if (pos < 0)
        {
            pos = -(pos + 1) ;
        }
        return pos ;
    }

    static int upper_bound(List<Long> arr, long key)
    {
        int pos = Collections.binarySearch(arr, key);
        pos++ ;
        if (pos < 0)
        {
            pos = -(pos) ;
        }
        return pos ;
    }


    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;
        }
    }


}