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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.ArrayList;
import java.util.Collections;
public class yibianguo{
    public static void main(String[]args) {
        FastScanner c = new FastScanner();
        int a = c.nextInt();
        for(int aa=0;aa<a;aa++){
            int b = c.nextInt();
            HashSet<Integer> h  = new HashSet<Integer>();
            int []z =new int[b]; 
            int []x=new int[b+1];
            int g =0;
            boolean i = true;
            ArrayList<Integer> d = new ArrayList<Integer>();
            for(int q= 0;q<b;q++){
                z[q]= c.nextInt();
                if(z[q]<=b&&h.add(z[q])){
                    x[z[q]]++;
                    h.add(z[q]);
                }
                else{
                    d.add((z[q]-1)/2);
                    g++;
                }
            }
            int p =0;
            Collections.sort(d);
            for(int q= 1;q<b+1;q++){
                if(x[q]==0){
                    if(d.get(p++)>=q){}
                    else{
                        i = false;
                        break;
                    }
                }
            }
            if(i){
                System.out.println(g);
            }
            else{
                System.out.println(-1);
            }
        }
    System.out.close();
}
static class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner() {
        try	{
            br = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer(br.readLine());
        } catch (Exception e){e.printStackTrace();}
    }

    public String next() {
        if (st.hasMoreTokens())	return st.nextToken();
        try {st = new StringTokenizer(br.readLine());}
        catch (Exception e) {e.printStackTrace();}
        return st.nextToken();
    }

    public int nextInt() {return Integer.parseInt(next());}

    public long nextLong() {return Long.parseLong(next());}

    public double nextDouble() {return Double.parseDouble(next());}

    public String nextLine() {
        String line = "";
        if(st.hasMoreTokens()) line = st.nextToken();
        else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
        while(st.hasMoreTokens()) line += " "+st.nextToken();
        return line;
    }
}
}
