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.*;

public class CF1 {
    public static void main(String[] args) {
        FastScanner sc=new FastScanner();
        int T=sc.nextInt();
//        int T=1;
        for (int tt=0; tt<T; tt++){
            int n = sc.nextInt();
            boolean hasIt[]= new boolean [n+1];
            int arr[]= sc.readArray(n);
            sort(arr);
            int i=1;
            int j=0;
            int count=0;
            boolean canBeDone=true;
            while (i<=n){
                if (hasIt[i]) {i++;continue;}
                else if (arr[j]<=n && !hasIt[arr[j]]){
                    hasIt[arr[j]]=true;
                    count++;
                    j++;
                }
                else {
                    int x=0;
                    if (arr[j]%2==0) x=arr[j]/2-1;
                    else x=arr[j]/2;
                    if (i<=x){
                        hasIt[i]=true;
                        i++;
                        j++;
                    }
                    else {
                        canBeDone =false;
                        break;
                    }
                }
            }
            if (canBeDone) System.out.println(n-count);
            else System.out.println(-1);
        }
// arr[i+1]= arr[0]+sum-n*x;
    }

    static long mod =998244353L;
    static long power (long a, long b){
        long res=1;
        while (b>0){
            if ((b&1)== 1){
                res= (res * a % mod)%mod;
            }
            a=(a%mod * a%mod)%mod;
            b=b>>1;
        }
        return res;
    }
    boolean[] sieveOfEratosthenes(int n)
    {

        boolean prime[] = new boolean[n+1];
        for(int i=0;i<=n;i++)
            prime[i] = true;

        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                for(int i = p*p; i <= n; i += p)
                    prime[i] = false;
            }
        }
        return prime;
    }
    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    static void sortLong(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    static long gcd (long n, long m){
        if (m==0) return n;
        else return gcd(m, n%m);
    }

    static class Pair{
        int x,y;
        public Pair(int x, int y){
            this.x = x;
            this.y = y;
        }
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}