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.awt.*;
import java.awt.desktop.SystemEventListener;
import java.io.*;
import java.text.DecimalFormat;
import java.util.*;
import java.util.concurrent.locks.ReadWriteLock;


public class Main {

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = Reader.nextInt();
        while ( t > 0){
            int n = Reader.nextInt();
            int [] array = new int[n];
            int [] copy  = new int[n];
            int i = 0;
            while ( i < n){
                array[i] = Reader.nextInt();

                i++;
            }
            Arrays.sort(array);
            PriorityQueue<Integer> pq = new PriorityQueue<>();
            i = 0;
            while ( i < n){
                if ( array[i] <= n){
                    if ( copy[array[i]-1] == 1){
                        pq.add(array[i]);
                    }
                    else{
                        copy[array[i]-1] = 1;
                    }
                }else{
                    pq.add(array[i]);
                }
                i++;
            }
            i = 0;
            boolean ans = true;
            int count = 0;
            while ( i < n){
                if (copy[i] == 0){
                    int v = pq.poll();
                    if ( sub(i+1,v) !=1){
                        ans =false;
                        break;
                    }
                    else{
                        count++;
                    }
                }
                i++;
            }
            if ( ans){
                System.out.println(count);
            }
            else{
                System.out.println(-1);
            }




            t--;
        }
        output.flush();


    }
    public static int sub(int a, int b){
       int half = b/2;
       if ( b%2 == 0){
           if ( a < half){
               return 1;
           }
           else{
               return -1;
           }
       }
       else{
           if ( a<= half){
               return 1;
           }
           else{
               return -1;
           }
       }
    }


    private static int bs(int low,int high,int[] array,int find){
        if ( low <= high ){
            int  mid = low + (high-low)/2;
            if ( array[mid] > find){
                high = mid -1;
                return bs(low,high,array,find);
            }
            else if ( array[mid] < find){
                low = mid+1;
                return bs(low,high,array,find);
            }
            return mid;
        }
        return -1;
    }

    private static int max(int a, int b) {
        return  Math.max(a,b);
    }

    private static int min(int a,int b){
        return  Math.min(a,b);
    }

    public static long modularExponentiation(long a,long b,long mod){
        if ( b == 1){
            return a;
        }
        else{
            long ans = modularExponentiation(a,b/2,mod)%mod;
            if ( b%2 == 1){
                return (a*((ans*ans)%mod))%mod;
            }

            return ((ans*ans)%mod);
        }
    }

    public static long sum(long n){
        return  (n*(n+1))/2;
    }
    public static long abs(long a){
        return a < 0 ? (-1*a) : a;
    }
    public static long gcd(long a,long b){
        if ( a == 0){
            return b;
        }
        else{
            return gcd(b%a,a);
        }
    }


}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;


    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {

            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }

    static long nextLong() throws IOException{
        return Long.parseLong(next());
    }
}

class NComparator implements Comparator<Node>{
    @Override
    public int compare(Node o1, Node o2) {
        if ( o2.position > o1.position){
            return 1;
        }
        else if ( o2.position < o1.position){
            return -1;
        }
        else{
            if ( o2.time < o1.time){
                return 1;
            }
            else if ( o2.time > o2.time){
                return -1;
            }
            else{
                return 0;
            }
        }
    }
}
class DComparator implements Comparator<Integer>{
    @Override
    public int compare(Integer o1, Integer o2) {
        if ( o2 > o1){
            return 1;
        }
        else if ( o2 < o1){
            return -1;
        }
        else{
            return 0;
        }
    }
}


class Node{
    int position;
    long time;

    Node(int p,long t){
        position = p;
        time = t;
    }

}