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 A {
    //--------------------------INPUT READER---------------------------------//
    static class fs {
        public BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        public fs() { this(System.in); }
        public fs(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }
        String next() {
            while (!st.hasMoreTokens()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }

        int ni() { return Integer.parseInt(next()); }
        long nl() { return Long.parseLong(next()); }
        double nd() { return Double.parseDouble(next()); }
        String ns() { return next(); }

        int[] na(long nn) {
            int n = (int) nn;
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = ni();
            return a;
        }

        long[] nal(long nn) {
            int n = (int) nn;
            long[] l = new long[n];
            for(int i = 0; i < n; i++) l[i] = nl();
            return l;
        }
    }
    //-----------------------------------------------------------------------//

    //---------------------------PRINTER-------------------------------------//
    static class Printer {
        static PrintWriter w;
        public Printer() {this(System.out);}
        public Printer(OutputStream os) {
            w = new PrintWriter(os);
        }
        public void p(int i) {w.println(i);}
        public void p(long l) {w.println(l);}
        public void p(double d) {w.println(d);}
        public void p(String s) { w.println(s);}
        public void pr(int i) {w.print(i);}
        public void pr(long l) {w.print(l);}
        public void pr(double d) {w.print(d);}
        public void pr(String s) { w.print(s);}
        public void pl() {w.println();}
        public void close() {w.close();}
    }
    //-----------------------------------------------------------------------//

    //--------------------------VARIABLES------------------------------------//
    static fs sc = new fs();
    static OutputStream outputStream = System.out;
    static Printer w = new Printer(outputStream);
    static long lma = Long.MAX_VALUE, lmi = Long.MIN_VALUE;
    static long ima = Integer.MAX_VALUE, imi = Integer.MIN_VALUE;
    static long mod = 1000000007;
    //-----------------------------------------------------------------------//

    //--------------------------ADMIN_MODE-----------------------------------//
    private static void ADMIN_MODE() throws IOException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            w = new Printer(new FileOutputStream("output.txt"));
            sc = new fs(new FileInputStream("input.txt"));
        }
    }
    //-----------------------------------------------------------------------//

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

        ADMIN_MODE();

        int t = sc.ni();while(t-->0)
            solve();


        w.close();
    }

    static void solve() throws IOException {
        int n = sc.ni();
        Long[] arr = new Long[n];
        for(int i = 0; i < n; i++) arr[i] = sc.nl();
        Arrays.sort(arr);
        Long[] arr2 = new Long[n];
        for(int i = 0; i < n; i++) arr2[i] = (long)(i+1);
        TreeMap<Long, Integer> ts = new TreeMap<>();

        int ans = 0;
        for(int i = 0; i < n; i++) {
            if(arr[i].equals(arr2[i])) continue;
            if(arr[i] < arr2[i] && ts.size()==0) {
                w.p(-1);
                return;
            } if(arr[i] < arr2[i]) {
                long first = ts.firstKey();
                if(first >= Math.ceil(arr[i]/2.0)) {
                    w.p(-1);
                    return;
                } else {
                    ts.replace(first, ts.get(first)-1);
                    if(ts.get(first) == 0) ts.remove(first);
                    ans++;
                }
            } else if(arr2[i] >= Math.ceil(arr[i]/2.0)) {
                if(ts.containsKey(arr[i])) {
                    ts.replace(arr[i], ts.get(arr[i])+1);
                } else ts.put(arr[i], 1);
            } else {
                ans++;
            }
        }
        if(ts.size() != 0) {
            w.p(-1);
        } else w.p(ans);
    }

}