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.util.*;
import java.util.regex.Pattern;

import javax.lang.model.element.Element;
import javax.sql.rowset.spi.SyncResolver;
import javax.swing.text.TableView;
import javax.swing.text.StyledEditorKit.BoldAction;

import java.io.*;
import java.nio.file.attribute.GroupPrincipal;
import java.nio.file.attribute.PosixFilePermission;
import java.sql.PseudoColumnUsage;

public class Solution {

    static FastReader fr = new FastReader();
    static final Random random = new Random();
    static long mod = 1000000007L;

        public static void main(String args[]) throws IOException {
        
        // int t= fr.nextInt();
        StringBuilder str = new StringBuilder();
        int t= fr.nextInt();

        while(t-->0)
        {   
            int n = fr.nextInt();
           int[] arr = new int[n];
           HashSet<Integer> pNum = new HashSet<Integer>();
           PriorityQueue<Integer> extra = new PriorityQueue<Integer>();

           for(int i=0;i<n;i++)
           {
                    
                arr[i] = fr.nextInt();
                if(arr[i] <=n && !pNum.contains(arr[i]))
                {   
                    pNum.add(arr[i]);
                    
                }
                else
                extra.add(arr[i]);
           }
           int min = extra.size();
        //    System.out.println(extra);
        boolean notPoss = false;
           for(int i=1;i<=n;i++)
           {
               if(!pNum.contains(i))
               {
                    int num = extra.poll();
                    if(num-i<=i)
                    {
                        str.append(-1+"\n");
                        notPoss = true;
                        break;
                    }

               }
           }
           if(notPoss)
           continue;
           
           str.append(min+"\n");
        
        
        }
        System.out.println(str.toString());

    }

    static void printArray(int[] a) {
        System.out.println();
        for (int i = 0; i < a.length; i++) {

            System.out.println(a[i] );
            // System.out.println();
        }
        System.out.println();
    }

    static int max(int a, int b) {
        if (a < b)
            return b;
        return a;
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static <E> void print(E res) {
        System.out.println(res);
    }

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

    static int lcm(int a, int b) {
        return (a / gcd(a, b)) * b;
    }

    static int abs(int a) {
        if (a < 0)
            return -1 * a;
        return a;
    }

    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;
        }

        int[] readintarray(int n) {
            int res[] = new int[n];
            for (int i = 0; i < n; i++)
                res[i] = nextInt();
            return res;
        }

        long[] readlongarray(int n) {
            long res[] = new long[n];
            for (int i = 0; i < n; i++)
                res[i] = nextLong();
            return res;
        }
    }

}
