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 PaprikaandPermutation {

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

        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);

        int tc, i, j;
        String s;
        char p;

        tc = sc.nextInt();
        while (tc-- > 0) {
            int n = sc.nextInt();
            int arr[] = sc.readArray(n);
            sc.sort(arr);
            TreeSet<Integer> set = new TreeSet<>();
            ArrayList<Integer> ls = new ArrayList<>();

            for(i = 1; i<=n; i++)
                set.add(i);

            for(i = 0; i<n; i++) {
                if(set.contains(arr[i]))
                    set.remove(arr[i]);
                else
                    ls.add(arr[i]);
            }

            Collections.sort(ls);
            boolean flag = true;
            int ans = 0;

            for(int v : ls) {
                i = set.pollFirst();
                if(v==i) continue;
                if(v-i<=0  || v%(v-i) != i) {
                    flag = false;
                    break;
                }
                ans++;
            }
            if(flag)
                out.println(ans);
            else
                out.println(-1);
        }
        out.close();
    }
	


/*--------------------------------------------------------
----------------------------------------------------------*/


    //Pair Class

    public static class Pair implements Comparable<Pair> {
        int x, y;

        Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            return this.x - o.x;
        }
    }

    /*
		FASTREADER
	*/
    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;
        }

        /*DEFINED BY ME*/

        //READING ARRAY
        int[] readArray(int n) {
            int arr[] = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }

        //COLLECTIONS SORT
        void sort(int arr[]) {
            ArrayList<Integer> l = new ArrayList<>();
            for (int i : arr)
                l.add(i);
            Collections.sort(l);
            for (int i = 0; i < arr.length; i++)
                arr[i] = l.get(i);
        }

        //EUCLID'S GCD
        int gcd(int a, int b) {
            if (b != 0)
                return gcd(b, a % b);
            else
                return a;
        }

        void swap(int arr[], int i, int j) {
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }
}