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

//package com.codeforces.Practise;

import java.io.*;
import java.util.*;

public class permutation01 {

    // you can solve one problem by many approaches.
    // Everything is easy. you feel its hard because of you don't know, and you not understand it very well.
    ////     How to Improve Your problem-solving skill ??( By practise ). ***simple
    /// ==>> Solve problems slightly above of your level (to know some logic and how to approach cp problems)
    //       Otherwise You will stay as it is okk.
    /////////////////////////////////////////////////////////////////////////
    ///      How to Solve Problem in CP ? ( if you feel problem is hard then your approach is wrong )
    // ==>> Step01 :- Understanding problem statement clearly. Then Only Move Forward (Because Everything is mentioned in problem statement).
    //      Step02 :- Think a lot about Solution. if you are confident that your solution might be correct Then only Move Forward
    //      Step03 :- First think of brute force then move to optimal approach
    //      Step04 :- Finally Code ( there is no any sense to code. if you not follow about steps okk)
    ///////////////////////////////////////////////////////////////////////////
    public static void solve(int arr[],int n, BufferedWriter bw) throws IOException{
        TreeSet<Integer> set=new TreeSet<>();
        for (int i = 1; i <= n ; i++) {
            set.add(i);
        }
        for (int i = 0; i < n; i++) {
            if(set.contains(arr[i])){
                set.remove(arr[i]);
                arr[i]=-1;
            }
        }
        int ans=0;
        boolean flag=false;
        for (int i = 0; i < n; i++) {
            if(arr[i]!=-1){
                int val=(arr[i]-1)/2;
                if(set.floor(val) != null){
                   ans++;
                   set.remove(val);
                }
                else {
                    flag=true;
                    break;
                }
            }
        }
        if(flag){
            bw.write("-1");
        }
        else {
            bw.write(ans+"");
        }
        bw.newLine();
    }
    public static void main(String[] args)throws IOException {
        Reader scan=new  Reader();
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t=scan.nextInt();
        while (t-->0) {
            int n=scan.nextInt();
            int[] arr=fillArray(n,scan);
            solve(arr,n,bw);
        }
        bw.flush();
    }
    private static int[] fillArray(int n, Reader scan)
    {
        int[] arr=new int[n];
        for (int i = 0; i < n; i++) {
            arr[i]=scan.nextInt();
        }
        return arr;
    }

    //FAST READER
    static class Reader {
        public int BS = 1<<16;
        public char NC = (char)0;
        byte[] buf = new byte[BS];
        int bId = 0, size = 0;
        char c = NC;
        double num = 1;
        BufferedInputStream in;

        public Reader() {
            in = new BufferedInputStream(System.in, BS);
        }

        public Reader(String s) throws FileNotFoundException {
            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
        }

        public char nextChar(){
            while(bId==size) {
                try {
                    size = in.read(buf);
                }catch(Exception e) {
                    return NC;
                }
                if(size==-1)return NC;
                bId=0;
            }
            return (char)buf[bId++];
        }

        public int nextInt() {
            return (int)nextLong();
        }

        public long nextLong() {
            num=1;
            boolean neg = false;
            if(c==NC)c=nextChar();
            for(;(c<'0' || c>'9'); c = nextChar()) {
                if(c=='-')neg=true;
            }
            long res = 0;
            for(; c>='0' && c <='9'; c=nextChar()) {
                res = (res<<3)+(res<<1)+c-'0';
                num*=10;
            }
            return neg?-res:res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c!='.' ? cur:cur+(cur < 0 ? -1*nextLong()/num : nextLong()/num);
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=nextChar();
            while(c>32) {
                res.append(c);
                c=nextChar();
            }
            return res.toString();
        }
    }
}
