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 javax.swing.*;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.io.PrintWriter;
    import java.util.*;
    public class Main extends PrintWriter {
        static BufferedReader s = new BufferedReader(new InputStreamReader(System.in));Main () { super(System.out); }public static void main(String[] args) throws IOException{ Main  d1=new Main   ();d1.main();d1.flush(); }

        void main() throws IOException {
            StringBuilder sb = new StringBuilder();
            int t = 1;
            t = i(s()[0]);
            while (t-- > 0) {
               int n = i(s()[0]);
               int[] a=new int[n];arri(a, n);
               Arrays.sort(a);
               int flag = 0;
               int cnt = 0;
               for(int i = 0; i < n; i++){
                   if(a[i] < i + 1){
                       flag = 1; break;
                   }else if(a[i] > i + 1){
                       if((a[i] + 1) / 2 <= i + 1){
                           flag = 1; break;
                       }cnt++;
                   }
               }if(flag == 1) sb.append("-1\n");
               else sb.append(cnt + "\n");
            }
            System.out.println(sb);
        }  static long gcd(long a, long b) {
                if (b == 0)
                    return a;
                return gcd(b, a % b);
            }
        static String[] s() throws IOException { return s.readLine().trim().split("\\s+"); }
        static int i(String ss) {return Integer.parseInt(ss); }
        static long l(String ss) {return Long.parseLong(ss); }
        public void arr(long[] a,int n) throws IOException {String[] s2=s();for(int i=0;i<n;i++){ a[i]=l(s2[i]); }}
        public void arri(int[] a,int n) throws IOException {String[] s2=s();for(int i=0;i<n;i++){ a[i]=(i(s2[i])); }}

    }class Pair{
           int start, end;
           public Pair(long a, long b){
               this.start = (int)a ; this.end = (int)b;
        }
    }


