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 C {
    void go() {
        int n = Reader.nextInt();
        int[] arr = new int[n];

        for(int i = 0; i < n; i++) {
            arr[i] = Reader.nextInt();
        }

        Arrays.sort(arr);

        int ans = 0;
        for(int i = 1; i <= n; i++) {
            int x = arr[i - 1];
            if(x != i && x < 2 * i) {
                ans = -1;
                break;
            }

            if(x != i) ans++;
        }

        Writer.println(ans);
    }
    void solve() {
        for(int T = Reader.nextInt(); T > 0; T--) go();
    }
    void run() throws Exception {
        Reader.init(System.in);
        Writer.init(System.out);
        solve();
        Writer.close();
    }

    public static void main(String[] args) throws Exception {
        new C().run();
    }

    public static class Reader {
        public static StringTokenizer st;
        public static BufferedReader br;

        public static void init(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = new StringTokenizer("");
        }

        public static String next() {
            while(!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return st.nextToken();
        }

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

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

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

    public static class Writer {
        public static PrintWriter pw;

        public static void init(OutputStream os) {
            pw = new PrintWriter(new BufferedOutputStream(os));
        }

        public static void print(String s) {
            pw.print(s);
        }

        public static void print(char c) {
            pw.print(c);
        }

        public static void print(int x) {
            pw.print(x);
        }

        public static void print(long x) {
            pw.print(x);
        }

        public static void println(String s) {
            pw.println(s);
        }

        public static void println(char c) {
            pw.println(c);
        }

        public static void println(int x) {
            pw.println(x);
        }

        public static void println(long x) {
            pw.println(x);
        }

        public static void close() {
            pw.close();
        }
    }
}